Pemetaan Kondisi Sarana Kesehatan Antar Provinsi di Indonesia Melalui Pendekatan Multidimensional Scaling
Bungaria Nathasia Oktavia Siahaan
28 November 2025
1. PENDAHULUAN
1.1 Latar Bekalang
Sarana kesehatan merupakan salah satu komponen penting dalam penyelenggaraan pelayanan kesehatan dan peningkatan derajat kesehatan masyarakat. Salah satu indikator penting dalam menilai kemajuan pembangunan sektor kesehatan adalah ketersediaan sarana dan fasilitas pelayanan kesehatan, seperti rumah sakit, puskesmas, poliklinik, puskesmas pembantu, apotek, dan fasilitas pendukung lainnya. Jumlah dan pemerataan sarana kesehatan antar provinsi menjadi aspek penting yang menentukan aksesibilitas masyarakat terhadap layanan kesehatan yang bermutu.
Indonesia merupakan negara yang memiliki wilayah geografis yang luas dan memiliki jumlah provinsi yang beragam. Hal ini memberikan tantangan yang cukup besar dalam pemerataan sarana kesehatan. Kondisi ini berpotensi menimbulkan berbagai masalah, mulai dari rendahnya akses terhadap pelayanan medis dasar, keterlambatan penanganan penyakit, hingga meningkatnya angka kesakitan dan kematian yang dapat dicegah.Oleh sebab itu, ketimpangan sarana kesehatan antarprovinsi di Indonesia menjadi isu penting untuk diteliti. Dengan adanya analisis yang mampu memetakan hubungan antarprovinsi secara visual akan memberikan gambaran mengenai kedekatan karakteristik antarwilayah.
1.2 Data
Data yang digunakan dalam penelitian ini merupakan data sarana kesehatan yang memuat informasi mengenai jumlah fasilitas kesehatan yang tersebar di seluruh provinsi di Indonesia. Data tersebut memuat variabel rumah sakit, rumah sakit bersalin, poliklinik, puskesmas, puskesmas pembantu, dan apotek yang merepresentasikan ketersediaan fasilitas di tiap-tiap wilayah. Beberapa provinsi tercatat memiliki jumlah fasilitas kesehatan yang sangat banyak, terutama provinsi dengan penduduk dan wilayah luas. Namun disisi lain terdapat provinsi yang memiliki jumlah fasilitas relatif lebih sedikit. Variasi ini penting dan dapat dianalisis untuk mengetahui pola kesamaan atau perbedaan kondisi sarana kesehatan antar provinsi di Indonesia.
1.3 Cuplikan Data
Berikut data yang digunakan pada kasus ini:
| Provinsi | Rumah Sakit | Rumah Sakit Bersalin | Poliklinik | Puskesmas | Puskesmas Pembantu | Apotek |
|---|---|---|---|---|---|---|
| ACEH | 64 | 255 | 258 | 395 | 971 | 346 |
| SUMATERA UTARA | 199 | 441 | 800 | 661 | 1887 | 740 |
| SUMATERA BARAT | 54 | 139 | 127 | 294 | 721 | 257 |
| RIAU | 55 | 207 | 329 | 272 | 1033 | 351 |
| JAMBI | 36 | 151 | 103 | 231 | 654 | 211 |
| SUMATERA SELATAN | 65 | 248 | 195 | 403 | 935 | 244 |
| BENGKULU | 20 | 5 | 49 | 190 | 456 | 141 |
| LAMPUNG | 53 | 238 | 307 | 350 | 936 | 356 |
| KEP. BANGKA BELITUNG | 21 | 25 | 25 | 63 | 148 | 73 |
| KEPULAUAN RIAU | 23 | 35 | 76 | 88 | 243 | 90 |
| DKI JAKARTA | 119 | 156 | 230 | 257 | 3 | 242 |
| JAWA BARAT | 292 | 1245 | 1670 | 1170 | 1800 | 1758 |
| JAWA TENGAH | 274 | 871 | 1232 | 921 | 1832 | 2068 |
| DI YOGYAKARTA | 61 | 102 | 158 | 126 | 300 | 226 |
| JAWA TIMUR | 317 | 1183 | 1101 | 1036 | 2338 | 1842 |
| BANTEN | 87 | 280 | 467 | 267 | 346 | 402 |
| BALI | 49 | 61 | 71 | 124 | 495 | 214 |
| NTB | 31 | 20 | 72 | 173 | 550 | 237 |
| NTT | 48 | 42 | 108 | 414 | 1030 | 172 |
| KALIMANTAN BARAT | 39 | 95 | 98 | 264 | 836 | 123 |
| KALIMANTAN TENGAH | 19 | 63 | 95 | 221 | 1101 | 85 |
| KALIMANTAN SELATAN | 34 | 126 | 131 | 253 | 464 | 162 |
| KALIMANTAN TIMUR | 39 | 56 | 125 | 199 | 727 | 196 |
| KALIMANTAN UTARA | 11 | 4 | 15 | 59 | 179 | 49 |
| SULAWESI UTARA | 46 | 77 | 68 | 217 | 540 | 170 |
| SEULAWESI TENGAH | 29 | 58 | 60 | 224 | 698 | 181 |
| SULAWESI SELATAN | 75 | 121 | 180 | 493 | 1394 | 490 |
| SULAWESI TENGGARA | 31 | 56 | 40 | 283 | 557 | 189 |
| GORONTALO | 14 | 2 | 42 | 96 | 250 | 97 |
| SULAWESI BARAT | 10 | 8 | 16 | 100 | 340 | 47 |
| MALUKU | 27 | 20 | 31 | 235 | 481 | 66 |
| MALUKU UTARA | 20 | 11 | 28 | 142 | 277 | 76 |
| PAPUA BARAT | 16 | 10 | 29 | 177 | 495 | 79 |
| PAPUA | 41 | 26 | 115 | 422 | 1146 | 125 |
1.4 Latar Belakang Metode
Multidimensional Scaling (MDS) merupakan teknik yang digunakan untuk mencari hubungan antara data secara spasial yang membentuk sebuah grafik untuk menggambarkan posisi sebuah objek dengan objek yang lain berdasarkan kemiripan objek-objek tersebut (Pradita dkk., 2019). MDS akan menyederhanakan struktur data yang kompleks ke ruang dimensi rendah berdasarkan tingkat kemiripan atau ketidaksamaannya. Kelebihan MDS adalah fleksibilitasnya dalam menangani berbagai jenis data baik metrik maupun nonmetrik. Hal ini menjadikan MDS menjadi metode relevan di berbagai bidang.
1.5 Tujuan
Tujuan dari penelitian ini adalah sebagai berikut:
- Mengukur tingkat kemiripan dan perbedaan antar provinsi di Indonesia dalam hal ketersediaan sarana kesehatan menggunakan matriks jarak ketidaksamaan MDS.
- Memetakan provinsi-provinsi di Indonesia ke ruang dua dimensi berdasarkan kondisi fasilitas kesehatan.
- Mengidentifikasi kelompok provinsi yang memiliki karakteristik sarana kesehatan yang mirip melalui kedekatannya pada hasil pemetaan MDS.
- Memberikan gambaran visual mengenai pola penyebaran sarana kesehatan antar provinsi,untuk mengetahui provinsi mana yang berada pada posisi lebih maju, rata-rata, atau tertinggal dalam penyediaan sarana kesehatan.
1.6 Tinjauan Pustaka
1.6.1 Definisi MDS
Multidimensional Scaling (MDS) merupakan teknik analisis multivariat yang berfungsi untuk menentukan posisi suatu objek dengan mengacu pada kesamaan atau ketidaksamaannya (Mahida, 2020). Analisis ini dapat digunakan untuk mengetahui keberlanjutan tiap dimensi dan keseimbangan antar dimensi (Mahida, 2020).
1.6.2 Jenis MDS
Menurut Kuswandari dkk. 2021, MDS dibagi menjadi dua, yaitu sebagai berikut:
MDS Metrik
Data jarak yang digunakan dalam MDS metrik adalah interval atau rasio. MDS metrik digunakan untuk menentukan himpunan titik dalam ruang n dengan masing-masing titik mewakili suatu objek.
MDS Non-Metrik
Data jarak yang digunakan dalam MDS non-metrik adalah nominal atau ordinal. Pada MDS non-metrik perhitungan dilakukan dengan memperhatikan peringkat jarak.
1.6.3 Validitas Model
Analisis kelayakan atau validitas model pada MDS mengacu pada besaran nilai STRESS dan koefisien determinasi (\(R^2\)).
STRESS
STRESS adalah ukuran yang menunjukkan ketidakcocokan, dimana jika nilai stress semakin tinggi maka model MDS semakin tidak cocok (Aswin dan Wahidun, 2016). Kriteria nilai stress adalah sebagai berikut:Stress (%) Kriteria MDS ≥ 20% Jelek 10% - 20% Cukup 5% - 10% Baik 2.5% - 5% Sangat Baik < 2.5% Sempurna Koefisien Determiasi (\(R^2\))
\(R^2\) adalah koefisien korelasi kuadrat yang menunjukkan proporsi varians dari data jarak asli yang dijelaskan oleh model spasial MDS. Nilai \(R^2\) berkisar antara 0 hingga 1, yang mana semakin tinggi nilai \(R^2\), maka semakin baik pula model spasial MDS. Namun, secara umum tingkat minimum yang dapat diterima dari \(R^2\) adalah 0.6.
2. SOURCE CODE
2.1 Library
readxl
Library ini digunakan untuk membaca data dari excel ke dalam R.
dplyr
Library ini digunakan untuk mengatur dataset agar kolom koordinat MDS dapat digabung dengan label daerah, data bersih sebelum dihitung MDS, dan memfilter variabel yang akan digunakan.
ggplot2
Library ini digunakan untuk memvisualisasikan MDS dalam bentuk scatter plot. Dengan library ini visualisasi dari grafik akan lebih rapi dan koordinat yang ditampilkan MDS akan membentuk titik yang mewakili objek.
MASS
Library ini digunakan untuk multidimensional scaling. Library ini menyediakan fungsi isoMDS() yang digunakan untuk Non-Metrik MDS dan fungsi sammon() yang digunakan untuk sammon mapping.
2.2 Code
#data
data <- read_excel("C:/Users/ACER/Downloads/DATA_SARANA_KESEHATAN.xlsx")
data_num <- data %>% select_if(is.numeric)
#rownames
labels <- rownames(data_num)
if (is.null(labels)) labels <- paste0("Obs_", 1:nrow(data_num))
rownames(data_num) <- labels## Warning: Setting row names on a tibble is deprecated.head(data_num)## # A tibble: 6 × 6
## `Rumah Sakit` `Rumah Sakit Bersalin` Poliklinik Puskesmas `Puskesmas Pembantu`
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 64 225 258 395 971
## 2 199 441 800 661 1887
## 3 54 139 127 294 721
## 4 55 207 329 272 1033
## 5 36 151 103 231 654
## 6 65 248 195 403 935
## # ℹ 1 more variable: Apotek <dbl>#matrik jarak D
D <- dist(data_num, method = "euclidean")
D_mat <- as.matrix(D)
D_mat## 1 2 3 4 5 6 7
## 1 0.00000 1193.1861 324.4673 156.3458 419.3984 127.5265 665.80177
## 2 1193.18607 0.0000 1514.1638 1152.9488 1606.7072 1280.6694 1847.84767
## 3 324.46726 1514.1638 0.0000 389.9910 107.7868 272.8956 345.96676
## 4 156.34577 1152.9488 389.9910 0.0000 468.5029 240.7301 710.05774
## 5 419.39838 1606.7072 107.7868 468.5029 0.0000 358.2569 265.09055
## 6 127.52647 1280.6694 272.8956 240.7301 358.2569 0.0000 606.47259
## 7 665.80177 1847.8477 345.9668 710.0577 265.0906 606.4726 0.00000
## 8 77.72387 1205.8822 318.3771 130.2574 405.1962 167.7558 651.28105
## 9 978.88712 2152.2033 663.3513 1015.3256 570.5164 919.1164 341.45864
## 10 872.16627 2042.9276 559.6311 905.9216 467.2954 814.3089 244.97347
## 11 987.65075 2091.2200 729.5485 1043.7931 669.6872 950.0258 534.09924
## 12 2523.43773 1647.7072 2800.9547 2511.2220 2882.0317 2617.2262 3101.71727
## 13 2322.36367 1487.0635 2590.8338 2304.7683 2676.1760 2430.4502 2890.50636
## 14 749.75996 1901.3466 456.9519 783.9209 377.6467 709.2101 242.13220
## 15 2491.98876 1487.7900 2790.2077 2475.2790 2878.1993 2584.8147 3119.87788
## 16 676.29875 1671.3812 546.7623 707.1011 533.2720 682.5489 583.94178
## 17 616.06087 1789.1478 301.7781 646.5547 214.5507 568.2799 125.16789
## 18 562.24194 1736.1368 248.9920 598.0635 181.6673 519.0790 138.62179
## 19 300.60439 1333.7721 356.2471 358.2304 434.0922 254.2125 621.48773
## 20 358.10613 1510.3043 187.3046 396.2550 212.4312 277.9514 401.32530
## 21 412.47424 1383.0148 432.8256 393.4069 473.1617 363.7334 652.38256
## 22 581.29081 1760.5363 278.1007 637.2197 200.9925 520.5824 161.35365
## 23 409.05623 1576.2075 141.0674 433.2009 126.8700 360.0333 292.03596
## 24 969.05521 2144.6881 651.8213 1003.8078 558.0600 907.0551 321.85711
## 25 553.84926 1740.1649 231.6204 603.2719 147.2209 491.7601 121.84827
## 26 446.44485 1624.9185 151.2614 488.5356 115.8965 384.4477 253.63557
## 27 475.69948 914.3025 741.8848 477.9958 838.1140 543.8299 1061.64778
## 28 534.56805 1723.2046 215.9352 599.8658 160.0500 471.5443 154.78049
## 29 877.56937 2052.7915 560.5702 913.5951 469.9394 819.5175 230.87226
## 30 826.53252 2006.5007 508.2470 861.3037 413.9408 759.8085 177.73576
## 31 662.58811 1846.8281 348.8094 715.4404 270.9170 588.5134 94.19660
## 32 848.04304 2028.6158 529.4733 891.2368 440.1772 784.4692 197.60314
## 33 668.10104 1850.0086 352.3322 709.0719 267.1666 598.7504 77.29812
## 34 375.19861 1284.8506 476.9853 406.3225 549.3041 339.5630 731.72263
## 8 9 10 11 12 13 14
## 1 77.72387 978.88712 872.16627 987.6507 2523.4377 2322.3637 749.7600
## 2 1205.88225 2152.20329 2042.92756 2091.2200 1647.7072 1487.0635 1901.3466
## 3 318.37713 663.35134 559.63113 729.5485 2800.9547 2590.8338 456.9519
## 4 130.25744 1015.32556 905.92163 1043.7931 2511.2220 2304.7683 783.9209
## 5 405.19625 570.51643 467.29541 669.6872 2882.0317 2676.1760 377.6467
## 6 167.75577 919.11642 814.30891 950.0258 2617.2262 2430.4502 709.2101
## 7 651.28105 341.45864 244.97347 534.0992 3101.7173 2890.5064 242.1322
## 8 0.00000 953.58219 845.64709 953.4899 2512.6558 2316.2375 715.7744
## 9 953.58219 0.00000 112.44554 394.9835 3325.9050 3128.6769 275.1363
## 10 845.64709 112.44554 0.00000 396.0278 3233.3410 3038.0137 189.3304
## 11 953.48991 394.98354 396.02778 0.0000 3106.5228 2942.7312 342.1842
## 12 2512.65577 3325.90499 3233.34100 3106.5228 0.0000 700.8345 3054.9818
## 13 2316.23747 3128.67688 3038.01366 2942.7312 700.8345 0.0000 2856.9597
## 14 715.77441 275.13633 189.33040 342.1842 3054.9818 2856.9597 0.0000
## 15 2497.50936 3385.04741 3288.19069 3235.9913 801.6770 660.8260 3117.1054
## 16 620.98712 673.65125 597.49142 464.6698 2681.1788 2526.0528 425.2223
## 17 593.93771 384.97662 285.57486 547.4879 3032.9496 2813.3148 218.0986
## 18 545.63633 450.48196 351.26628 597.9080 2998.7164 2772.0821 282.5774
## 19 353.31289 958.55777 856.77710 1056.9763 2761.5975 2548.8747 790.5878
## 20 368.79669 725.80851 622.93980 857.6969 2877.6814 2673.9572 566.6410
## 21 440.49064 969.36319 868.92980 1126.2429 2853.1402 2639.5659 823.2624
## 22 560.09821 406.79602 304.42897 486.6857 2976.6167 2788.4243 221.7093
## 23 398.15324 616.56387 510.79448 746.3786 2898.0630 2681.7144 438.4598
## 24 945.39040 46.84015 106.97663 434.0760 3337.7702 3139.0701 288.1180
## 25 540.54787 438.14039 337.05638 577.0329 3001.4491 2793.6714 279.2257
## 26 443.99324 585.20338 484.37898 731.0533 2943.8898 2725.2728 427.3137
## 27 527.70352 1395.51496 1292.18497 1434.4832 2400.3237 2138.6718 1184.1714
## 28 530.01509 480.02396 384.99740 603.5271 2988.6989 2776.2291 330.1621
## 29 854.18675 113.73654 49.87986 421.9479 3253.8614 3050.7460 213.7896
## 30 807.85333 198.49433 126.09520 505.7905 3247.9886 3045.9263 256.7450
## 31 654.77172 374.99200 284.77184 571.4062 3119.9393 2920.8581 307.0033
## 32 828.49502 151.97697 84.59905 432.9977 3240.1143 3040.8325 223.9353
## 33 657.09664 365.65968 272.81679 589.3717 3130.8780 2924.4350 298.9398
## 34 429.64753 1065.87523 964.42522 1176.2534 2760.5970 2551.6365 906.3984
## 15 16 17 18 19 20 21
## 1 2491.989 676.2988 616.06087 562.24194 300.6044 358.1061 412.4742
## 2 1487.790 1671.3812 1789.14784 1736.13680 1333.7721 1510.3043 1383.0148
## 3 2790.208 546.7623 301.77806 248.99197 356.2471 187.3046 432.8256
## 4 2475.279 707.1011 646.55472 598.06354 358.2304 396.2550 393.4069
## 5 2878.199 533.2720 214.55069 181.66728 434.0922 212.4312 473.1617
## 6 2584.815 682.5489 568.27986 519.07899 254.2125 277.9514 363.7334
## 7 3119.878 583.9418 125.16789 138.62179 621.4877 401.3253 652.3826
## 8 2497.509 620.9871 593.93771 545.63633 353.3129 368.7967 440.4906
## 9 3385.047 673.6512 384.97662 450.48196 958.5578 725.8085 969.3632
## 10 3288.191 597.4914 285.57486 351.26628 856.7771 622.9398 868.9298
## 11 3235.991 464.6698 547.48790 597.90802 1056.9763 857.6969 1126.2429
## 12 801.677 2681.1788 3032.94955 2998.71639 2761.5975 2877.6814 2853.1402
## 13 660.826 2526.0528 2813.31477 2772.08207 2548.8747 2673.9572 2639.5659
## 14 3117.105 425.2223 218.09860 282.57742 790.5878 566.6410 823.2624
## 15 0.000 2811.2791 3044.73069 3001.82345 2692.0139 2841.4760 2763.4549
## 16 2811.279 0.0000 533.11819 551.75901 854.0556 700.4570 928.8310
## 17 3044.731 533.1182 0.00000 89.22444 611.4082 382.2918 628.3041
## 18 3001.823 551.7590 89.22444 0.00000 542.9319 330.8141 575.7873
## 19 2692.014 854.0556 611.40821 542.93186 0.0000 255.9824 226.5171
## 20 2841.476 700.4570 382.29177 330.81415 255.9824 0.0000 273.7718
## 21 2763.455 928.8310 628.30407 575.78729 226.5171 273.7718 0.0000
## 22 3014.233 459.5008 168.39240 184.78907 595.1118 376.9629 646.6931
## 23 2881.874 601.3859 250.62721 194.56361 373.0630 153.8993 392.4666
## 24 3390.241 694.2752 373.00804 435.75911 936.3851 703.6363 942.1088
## 25 3010.468 544.1057 113.50771 100.07497 530.7937 305.4619 568.8726
## 26 2922.348 626.8102 229.84342 170.97661 386.4272 164.0762 415.9135
## 27 2246.895 1124.6857 1018.18220 950.02421 502.0110 712.1727 581.0189
## 28 2991.492 570.7775 176.23847 129.51062 496.2741 295.8158 560.1910
## 29 3300.973 628.2675 282.92225 342.11402 849.8594 620.2467 864.0168
## 30 3277.533 661.2594 244.63238 298.74738 775.4902 542.0535 777.5301
## 31 3134.612 627.2488 195.41238 198.85422 592.9013 374.6638 625.2727
## 32 3283.114 629.4704 268.48091 321.79030 811.3902 584.7145 832.1610
## 33 3139.811 635.9363 162.75134 173.72104 599.4431 371.8884 613.4998
## 34 2670.762 965.0337 723.70643 657.07382 126.8188 355.1366 215.1255
## 22 23 24 25 26 27 28
## 1 581.2908 409.05623 969.05521 553.84926 446.44485 475.6995 534.56805
## 2 1760.5363 1576.20747 2144.68809 1740.16493 1624.91846 914.3025 1723.20457
## 3 278.1007 141.06736 651.82129 231.62038 151.26136 741.8848 215.93518
## 4 637.2197 433.20088 1003.80775 603.27191 488.53557 477.9958 599.86582
## 5 200.9925 126.87001 558.06003 147.22092 115.89651 838.1140 160.04999
## 6 520.5824 360.03333 907.05513 491.76010 384.44766 543.8299 471.54427
## 7 161.3536 292.03596 321.85711 121.84827 253.63557 1061.6478 154.78049
## 8 560.0982 398.15324 945.39040 540.54787 443.99324 527.7035 530.01509
## 9 406.7960 616.56387 46.84015 438.14039 585.20338 1395.5150 480.02396
## 10 304.4290 510.79448 106.97663 337.05638 484.37898 1292.1850 384.99740
## 11 486.6857 746.37859 434.07603 577.03293 731.05335 1434.4832 603.52713
## 12 2976.6167 2898.06297 3337.77021 3001.44915 2943.88977 2400.3237 2988.69888
## 13 2788.4243 2681.71438 3139.07009 2793.67142 2725.27283 2138.6718 2776.22910
## 14 221.7093 438.45980 288.11803 279.22572 427.31370 1184.1714 330.16208
## 15 3014.2334 2881.87352 3390.24070 3010.46757 2922.34752 2246.8952 2991.49210
## 16 459.5008 601.38590 694.27516 544.10569 626.81018 1124.6857 570.77754
## 17 168.3924 250.62721 373.00804 113.50771 229.84342 1018.1822 176.23847
## 18 184.7891 194.56361 435.75911 100.07497 170.97661 950.0242 129.51062
## 19 595.1118 373.06300 936.38507 530.79375 386.42722 502.0110 496.27412
## 20 376.9629 153.89932 703.63627 305.46195 164.07620 712.1727 295.81582
## 21 646.6931 392.46656 942.10880 568.87257 415.91345 581.0189 560.19104
## 22 0.0000 279.64621 400.62326 116.83321 256.21866 1016.9518 153.19269
## 23 279.6462 0.00000 597.57928 199.26866 77.58866 791.3956 208.07210
## 24 400.6233 597.57928 0.00000 423.42532 565.04425 1379.8812 465.17631
## 25 116.8332 199.26866 423.42532 0.00000 160.77313 960.8397 80.34924
## 26 256.2187 77.58866 565.04425 160.77313 0.00000 820.2091 154.38264
## 27 1016.9518 791.39560 1379.88115 960.83974 820.20912 0.0000 927.91756
## 28 153.1927 208.07210 465.17631 80.34924 154.38264 927.9176 0.00000
## 29 313.6351 508.30011 97.24197 333.75890 477.31436 1287.5248 375.35450
## 30 282.3739 443.61808 166.20469 278.53007 407.79039 1226.9898 322.58797
## 31 176.3916 298.30857 351.05128 140.00000 250.44760 1055.7533 156.85025
## 32 280.5637 481.60565 132.36691 300.43635 445.31337 1257.1853 336.66007
## 33 194.4479 282.59158 339.02360 137.17143 239.28226 1056.2107 172.16852
## 34 710.8861 480.97297 1041.16185 645.07441 497.22932 462.7915 613.97313
## 29 30 31 32 33 34
## 1 877.56937 826.53252 662.58811 848.04304 668.10104 375.1986
## 2 2052.79151 2006.50069 1846.82809 2028.61578 1850.00865 1284.8506
## 3 560.57025 508.24699 348.80940 529.47332 352.33223 476.9853
## 4 913.59510 861.30366 715.44042 891.23678 709.07193 406.3225
## 5 469.93936 413.94082 270.91696 440.17724 267.16661 549.3041
## 6 819.51754 759.80853 588.51338 784.46925 598.75037 339.5630
## 7 230.87226 177.73576 94.19660 197.60314 77.29812 731.7226
## 8 854.18675 807.85333 654.77172 828.49502 657.09664 429.6475
## 9 113.73654 198.49433 374.99200 151.97697 365.65968 1065.8752
## 10 49.87986 126.09520 284.77184 84.59905 272.81679 964.4252
## 11 421.94786 505.79047 571.40616 432.99769 589.37170 1176.2534
## 12 3253.86140 3247.98861 3119.93926 3240.11435 3130.87799 2760.5970
## 13 3050.74597 3045.92630 2920.85809 3040.83245 2924.43499 2551.6365
## 14 213.78962 256.74501 307.00326 223.93526 298.93979 906.3984
## 15 3300.97258 3277.53322 3134.61242 3283.11361 3139.81098 2670.7621
## 16 628.26746 661.25940 627.24875 629.47041 635.93632 965.0337
## 17 282.92225 244.63238 195.41238 268.48091 162.75134 723.7064
## 18 342.11402 298.74738 198.85422 321.79030 173.72104 657.0738
## 19 849.85940 775.49017 592.90134 811.39017 599.44307 126.8188
## 20 620.24673 542.05350 374.66385 584.71446 371.88842 355.1366
## 21 864.01678 777.53006 625.27274 832.16104 613.49980 215.1255
## 22 313.63514 282.37387 176.39161 280.56372 194.44794 710.8861
## 23 508.30011 443.61808 298.30857 481.60565 282.59158 480.9730
## 24 97.24197 166.20469 351.05128 132.36691 339.02360 1041.1619
## 25 333.75890 278.53007 140.00000 300.43635 137.17143 645.0744
## 26 477.31436 407.79039 250.44760 445.31337 239.28226 497.2293
## 27 1287.52476 1226.98981 1055.75329 1257.18535 1056.21068 462.7915
## 28 375.35450 322.58797 156.85025 336.66007 172.16852 613.9731
## 29 0.00000 106.50822 272.50138 59.99167 259.12738 957.3453
## 30 106.50822 0.00000 197.80040 82.62566 176.59841 877.7756
## 31 272.50138 197.80040 0.00000 224.73095 62.88084 698.5435
## 32 59.99167 82.62566 224.73095 0.00000 220.85289 918.8019
## 33 259.12738 176.59841 62.88084 220.85289 0.00000 703.0071
## 34 957.34529 877.77560 698.54348 918.80194 703.00711 0.0000#kuadrat jarak
D2 <- D_mat^2
n <- nrow(D2)
#nilai eigen dan vektor eigen
J <- diag(n) - (1/n) * matrix(1, n, n)
B <- -0.5 * J %*% D2 %*% J
B## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 48039.032 261526.9 -13535.380 51089.944 -31122.880 42664.0026
## [2,] 261526.885 1898707.7 -181907.527 324000.797 -308595.027 156072.8555
## [3,] -13535.380 -181907.5 30169.208 -21669.468 42080.708 4624.5908
## [4,] 51089.944 324000.8 -21669.468 78584.856 -37649.968 37092.9144
## [5,] -31122.880 -308595.0 42080.708 -37649.968 65610.208 -4592.9092
## [6,] 42664.003 156072.9 4624.591 37092.914 -4592.909 53551.9732
## [7,] -79245.292 -639535.4 73619.297 -94417.380 116049.797 -38747.3209
## [8,] 38415.973 239694.8 -18180.439 48225.885 -31869.939 30121.9438
## [9,] -149874.027 -1061419.2 100283.561 -170934.115 175277.061 -90395.0562
## [10,] -128144.233 -909249.4 86664.356 -142881.321 151795.856 -76600.2621
## [11,] -159581.674 -933120.8 53089.914 -201333.762 112690.414 -120372.7033
## [12,] 310075.650 3061809.5 -437663.762 356099.561 -650323.262 71764.6202
## [13,] 276567.591 2792909.4 -391890.821 332548.503 -598919.321 22466.5614
## [14,] -112041.880 -713197.0 55690.708 -122964.968 106505.208 -79704.9092
## [15,] 399609.885 3323188.7 -396950.527 456383.797 -628616.027 166736.8555
## [16,] -84398.792 -327131.9 -14118.203 -90431.880 10887.297 -85888.8209
## [17,] -75052.380 -560477.5 60243.208 -79030.468 100482.708 -44001.4092
## [18,] -61852.850 -485546.0 56271.738 -67361.939 88489.238 -35759.8798
## [19,] 55092.032 136133.9 27882.620 51381.944 14841.120 70718.0026
## [20,] 6858.826 -144196.3 44502.414 7742.738 57200.914 35106.7967
## [21,] 56222.473 110259.3 38686.061 79178.385 38134.561 77895.4438
## [22,] -67868.821 -523329.0 53475.767 -86670.909 89667.267 -31665.8503
## [23,] -21997.409 -255214.6 42781.179 -16892.497 62403.679 -389.4386
## [24,] -144513.968 -1049489.1 103649.620 -163522.056 178090.120 -83597.9974
## [25,] -57835.233 -493213.4 59780.356 -71156.321 93487.856 -22618.2621
## [26,] -26269.850 -321459.0 53011.738 -30673.939 75456.238 2243.1202
## [27,] 134767.444 755272.3 -36218.968 148945.356 -94519.468 102793.4144
## [28,] -50502.821 -467004.0 60129.767 -72267.909 88356.267 -16041.8503
## [29,] -127679.409 -924257.6 91330.179 -144670.497 155748.679 -75663.4386
## [30,] -108745.174 -854855.3 94740.414 -122816.262 155944.914 -53065.2033
## [31,] -69652.174 -630193.3 80090.414 -90795.262 121946.914 -20558.2033
## [32,] -118325.497 -891043.6 92157.091 -140615.586 153170.591 -63676.5268
## [33,] -71752.115 -634504.3 80423.473 -84691.203 124523.973 -25067.1445
## [34,] 79062.120 249363.0 26756.708 82173.032 7367.208 94554.0908
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] -79245.292 38415.973 -149874.03 -128144.23 -159581.67 310075.650
## [2,] -639535.439 239694.826 -1061419.17 -909249.38 -933120.82 3061809.503
## [3,] 73619.297 -18180.439 100283.56 86664.36 53089.91 -437663.762
## [4,] -94417.380 48225.885 -170934.12 -142881.32 -201333.76 356099.561
## [5,] 116049.797 -31869.939 175277.06 151795.86 112690.41 -650323.262
## [6,] -38747.321 30121.944 -90395.06 -76600.26 -120372.70 71764.620
## [7,] 236762.385 -76285.350 365300.65 316548.44 279876.00 -1222018.674
## [8,] -76285.350 34833.914 -132026.09 -111969.29 -133028.73 330622.591
## [9,] 365300.650 -132026.086 610432.91 527067.71 531336.27 -1755680.409
## [10,] 316548.444 -111969.292 527067.71 456346.50 453880.06 -1529148.615
## [11,] 279876.003 -133028.733 531336.27 453880.06 608251.62 -1051191.056
## [12,] -1222018.674 330622.591 -1755680.41 -1529148.62 -1051191.06 6939850.267
## [13,] -1109897.733 284173.532 -1639858.47 -1437355.67 -1076473.12 6173575.208
## [14,] 234075.797 -93740.939 412375.06 355258.86 390589.41 -1051523.262
## [15,] -1267843.439 379234.826 -1943462.17 -1697331.38 -1451099.82 6629176.503
## [16,] 68158.885 -55123.850 198585.15 169946.94 316438.50 -4163.174
## [17,] 201241.297 -68270.439 321806.56 278090.36 244947.91 -1038772.762
## [18,] 180958.826 -59256.909 275935.09 238664.88 197564.44 -954039.233
## [19,] 1511.708 31255.973 -77946.03 -62606.23 -178219.67 -267031.350
## [20,] 84809.503 -3629.233 88776.77 81105.56 -16736.88 -623640.556
## [21,] 22850.150 37671.414 -47345.59 -32075.79 -212815.23 -483008.909
## [22,] 182424.856 -62376.880 299536.12 258895.91 262755.47 -883137.203
## [23,] 113385.267 -24199.468 152787.53 135364.33 63231.88 -691812.792
## [24,] 367585.708 -128464.027 605119.97 523451.77 510915.33 -1799429.350
## [25,] 182477.444 -57159.292 280752.71 242889.50 209162.06 -962903.615
## [26,] 135582.826 -31780.909 183352.09 160228.88 86273.44 -813951.233
## [27,] -221273.880 102074.385 -444621.62 -382804.82 -500852.26 813041.061
## [28,] 174761.856 -54681.880 258364.12 222420.91 190362.47 -927876.203
## [29,] 325095.267 -114035.468 532113.53 460294.33 448470.88 -1590516.792
## [30,] 311399.503 -100083.233 494329.77 429036.56 385027.12 -1595976.556
## [31,] 239784.503 -71106.233 360746.77 313465.56 266713.12 -1271245.556
## [32,] 316101.179 -108541.556 510911.44 441838.24 427625.80 -1562001.880
## [33,] 242801.561 -71063.174 365770.83 318366.62 257854.18 -1303865.497
## [34,] -23898.203 50548.061 -137398.94 -111455.14 -262230.59 -215093.262
## [,13] [,14] [,15] [,16] [,17] [,18]
## [1,] 276567.59 -112041.88 399609.88 -84398.792 -75052.38 -61852.85
## [2,] 2792909.44 -713197.03 3323188.74 -327131.939 -560477.53 -485546.00
## [3,] -391890.82 55690.71 -396950.53 -14118.203 60243.21 56271.74
## [4,] 332548.50 -122964.97 456383.80 -90431.880 -79030.47 -67361.94
## [5,] -598919.32 106505.21 -628616.03 10887.297 100482.71 88489.24
## [6,] 22466.56 -79704.91 166736.86 -85888.821 -44001.41 -35759.88
## [7,] -1109897.73 234075.80 -1267843.44 68158.885 201241.30 180958.83
## [8,] 284173.53 -93740.94 379234.83 -55123.850 -68270.44 -59256.91
## [9,] -1639858.47 412375.06 -1943462.17 198585.150 321806.56 275935.09
## [10,] -1437355.67 355258.86 -1697331.38 169946.944 278090.36 238664.88
## [11,] -1076473.12 390589.41 -1451099.82 316438.503 244947.91 197564.44
## [12,] 6173575.21 -1051523.26 6629176.50 -4163.174 -1038772.76 -954039.23
## [13,] 5898469.15 -986866.32 6211483.44 -120965.233 -917441.82 -820799.29
## [14,] -986866.32 290017.21 -1232570.03 174873.297 211918.71 177269.24
## [15,] 6211483.44 -1232570.03 6961188.74 -350778.939 -1063904.53 -952692.00
## [16,] -120965.23 174873.30 -350778.94 240543.385 68857.80 40238.33
## [17,] -917441.82 211918.71 -1063904.53 68857.797 181387.21 158898.74
## [18,] -820799.29 177269.24 -952692.00 40238.326 158898.74 144371.27
## [19,] -222892.41 -91251.88 -66621.12 -168179.792 -19962.38 1052.15
## [20,] -578829.62 31426.91 -509439.32 -78088.997 64579.41 64425.94
## [21,] -417148.97 -76601.44 -220476.67 -193821.350 10581.06 23690.59
## [22,] -861359.26 197492.27 -985145.97 91762.356 153576.77 132173.30
## [23,] -608914.85 86531.68 -634356.56 -22914.233 96933.18 90904.71
## [24,] -1676645.41 404503.12 -1965271.12 180263.208 322126.62 278243.15
## [25,] -881545.67 177544.86 -979343.38 43765.944 155771.36 138697.88
## [26,] -714954.29 103077.24 -740096.00 -26806.674 113646.74 106936.27
## [27,] 886169.00 -332229.47 1180218.30 -288294.380 -203760.97 -155194.44
## [28,] -836130.26 158864.27 -925558.97 25737.356 143522.77 132158.30
## [29,] -1470925.85 355520.68 -1734250.56 156276.767 284036.18 247029.71
## [30,] -1480785.62 320862.91 -1681704.32 110453.003 269584.41 236373.94
## [31,] -1190631.62 223722.91 -1306463.32 49391.003 197440.41 178253.94
## [32,] -1456852.94 337178.59 -1691579.64 139398.679 271896.09 237654.62
## [33,] -1199517.56 227733.97 -1321204.26 45472.061 204857.47 184504.00
## [34,] -180760.32 -140340.79 39538.97 -219943.703 -45752.29 -18257.76
## [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 55092.032 6858.826 56222.47 -67868.82 -21997.4092 -144513.97
## [2,] 136133.885 -144196.321 110259.33 -523328.97 -255214.5562 -1049489.12
## [3,] 27882.620 44502.414 38686.06 53475.77 42781.1791 103649.62
## [4,] 51381.944 7742.738 79178.38 -86670.91 -16892.4974 -163522.06
## [5,] 14841.120 57200.914 38134.56 89667.27 62403.6791 178090.12
## [6,] 70718.003 35106.797 77895.44 -31665.85 -389.4386 -83598.00
## [7,] 1511.708 84809.503 22850.15 182424.86 113385.2673 367585.71
## [8,] 31255.973 -3629.233 37671.41 -62376.88 -24199.4680 -128464.03
## [9,] -77946.027 88776.767 -47345.59 299536.12 152787.5320 605119.97
## [10,] -62606.233 81105.561 -32075.79 258895.91 135364.3261 523451.77
## [11,] -178219.674 -16736.880 -212815.23 262755.47 63231.8849 510915.33
## [12,] -267031.350 -623640.556 -483008.91 -883137.20 -691812.7915 -1799429.35
## [13,] -222892.409 -578829.615 -417148.97 -861359.26 -608914.8503 -1676645.41
## [14,] -91251.880 31426.914 -76601.44 197492.27 86531.6791 404503.12
## [15,] -66621.115 -509439.321 -220476.67 -985145.97 -634356.5562 -1965271.12
## [16,] -168179.792 -78088.997 -193821.35 91762.36 -22914.2327 180263.21
## [17,] -19962.380 64579.414 10581.06 153576.77 96933.1791 322126.62
## [18,] 1052.150 64425.944 23690.59 132173.30 90904.7085 278243.15
## [19,] 152508.032 90449.826 167869.47 -23763.82 44312.5908 -61153.97
## [20,] 90449.826 93918.620 126754.27 52969.97 72763.3849 100407.83
## [21,] 167869.473 126754.267 234540.91 -14774.38 77902.0320 -25513.53
## [22,] -23763.821 52969.973 -14774.38 154122.33 75606.7379 297812.18
## [23,] 44312.591 72763.385 77902.03 75606.74 75293.1497 160096.59
## [24,] -61153.968 100407.826 -25513.53 297812.18 160096.5908 602001.03
## [25,] 6902.767 71825.561 26982.21 141755.91 89312.3261 282875.77
## [26,] 50958.150 82865.944 80145.59 93604.30 84003.7085 190730.15
## [27,] 174139.444 17257.238 172371.88 -216141.41 -51613.9974 -427142.56
## [28,] 21469.179 71564.973 28722.62 133686.33 84358.7379 261165.18
## [29,] -51511.409 87971.385 -22626.97 261242.74 141827.1497 529637.59
## [30,] -15625.174 108861.620 23807.27 246006.97 148061.3849 496001.83
## [31,] 26327.826 102612.620 47627.27 187343.97 118992.3849 365221.83
## [32,] -35679.497 93257.297 -11732.06 254946.65 138918.0614 509483.50
## [33,] 23995.885 105216.679 56487.33 185564.03 125125.4438 370939.88
## [34,] 193642.120 109327.914 219560.56 -50188.73 47408.6791 -115578.88
## [,25] [,26] [,27] [,28] [,29] [,30]
## [1,] -57835.233 -26269.85 134767.44 -50502.821 -127679.41 -108745.17
## [2,] -493213.380 -321459.00 755272.30 -467003.968 -924257.56 -854855.32
## [3,] 59780.356 53011.74 -36218.97 60129.767 91330.18 94740.41
## [4,] -71156.321 -30673.94 148945.36 -72267.909 -144670.50 -122816.26
## [5,] 93487.856 75456.24 -94519.47 88356.267 155748.68 155944.91
## [6,] -22618.262 2243.12 102793.41 -16041.850 -75663.44 -53065.20
## [7,] 182477.444 135582.83 -221273.88 174761.856 325095.27 311399.50
## [8,] -57159.292 -31780.91 102074.38 -54681.880 -114035.47 -100083.23
## [9,] 280752.708 183352.09 -444621.62 258364.120 532113.53 494329.77
## [10,] 242889.503 160228.88 -382804.82 222420.914 460294.33 429036.56
## [11,] 209162.061 86273.44 -500852.26 190362.473 448470.88 385027.12
## [12,] -962903.615 -813951.23 813041.06 -927876.203 -1590516.79 -1595976.56
## [13,] -881545.674 -714954.29 886169.00 -836130.262 -1470925.85 -1480785.62
## [14,] 177544.856 103077.24 -332229.47 158864.267 355520.68 320862.91
## [15,] -979343.380 -740096.00 1180218.30 -925558.968 -1734250.56 -1681704.32
## [16,] 43765.944 -26806.67 -288294.38 25737.356 156276.77 110453.00
## [17,] 155771.356 113646.74 -203760.97 143522.767 284036.18 269584.41
## [18,] 138697.885 106936.27 -155194.44 132158.297 247029.71 236373.94
## [19,] 6902.767 50958.15 174139.44 21469.179 -51511.41 -15625.17
## [20,] 71825.561 82865.94 17257.24 71564.973 87971.38 108861.62
## [21,] 26982.208 80145.59 172371.88 28722.620 -22626.97 23807.27
## [22,] 141755.914 93604.30 -216141.41 133686.326 261242.74 246006.97
## [23,] 89312.326 84003.71 -51614.00 84358.738 141827.15 148061.38
## [24,] 282875.767 190730.15 -427142.56 261165.179 529637.59 496001.83
## [25,] 143039.503 107962.88 -166193.82 136650.914 249187.33 241543.56
## [26,] 107962.885 98734.27 -63111.44 105809.297 168817.71 175033.94
## [27,] -166193.821 -63111.44 447785.86 -138263.409 -371602.00 -320045.76
## [28,] 136650.914 105809.30 -138263.41 136718.326 231278.74 225140.97
## [29,] 249187.326 168817.71 -371602.00 231278.738 466730.15 436506.38
## [30,] 241543.561 175033.94 -320045.76 225140.973 436506.38 417626.62
## [31,] 187559.561 143844.94 -207574.76 181897.973 322076.38 315090.62
## [32,] 243632.238 167458.62 -349121.09 228932.650 448809.06 422643.30
## [33,] 189519.620 148147.00 -206489.70 180946.032 327199.44 320627.68
## [34,] -11111.144 51178.24 242234.53 5307.267 -99460.32 -51002.09
## [,31] [,32] [,33] [,34]
## [1,] -69652.174 -118325.50 -71752.115 79062.120
## [2,] -630193.321 -891043.64 -634504.262 249362.973
## [3,] 80090.414 92157.09 80423.473 26756.708
## [4,] -90795.262 -140615.59 -84691.203 82173.032
## [5,] 121946.914 153170.59 124523.973 7367.208
## [6,] -20558.203 -63676.53 -25067.144 94554.091
## [7,] 239784.503 316101.18 242801.561 -23898.203
## [8,] -71106.233 -108541.56 -71063.174 50548.061
## [9,] 360746.767 510911.44 365770.826 -137398.939
## [10,] 313465.561 441838.24 318366.620 -111455.144
## [11,] 266713.120 427625.80 257854.179 -262230.586
## [12,] -1271245.556 -1562001.88 -1303865.497 -215093.262
## [13,] -1190631.615 -1456852.94 -1199517.556 -180760.321
## [14,] 223722.914 337178.59 227733.973 -140340.792
## [15,] -1306463.321 -1691579.64 -1321204.262 39538.973
## [16,] 49391.003 139398.68 45472.061 -219943.703
## [17,] 197440.414 271896.09 204857.473 -45752.292
## [18,] 178253.944 237654.62 184504.003 -18257.762
## [19,] 26327.826 -35679.50 23995.885 193642.120
## [20,] 102612.620 93257.30 105216.679 109327.914
## [21,] 47627.267 -11732.06 56487.326 219560.561
## [22,] 187343.973 254946.65 185564.032 -50188.733
## [23,] 118992.385 138918.06 125125.444 47408.679
## [24,] 365221.826 509483.50 370939.885 -115578.880
## [25,] 187559.561 243632.24 189519.620 -11111.144
## [26,] 143844.944 167458.62 148147.003 51178.238
## [27,] -207574.762 -349121.09 -206489.703 242234.532
## [28,] 181897.973 228932.65 180946.032 5307.267
## [29,] 322076.385 448809.06 327199.444 -99460.321
## [30,] 315090.620 422643.30 320627.679 -51002.086
## [31,] 251679.620 317831.30 251270.679 7287.914
## [32,] 317831.297 434486.97 320263.356 -79425.409
## [33,] 251270.679 320263.36 254815.738 5727.973
## [34,] 7287.914 -79425.41 5727.973 250859.208eigen_decomp <- eigen(B)
values <- eigen_decomp$values
vectors <- eigen_decomp$vectors
values## [1] 2.593329e+07 2.496920e+06 3.433420e+05 1.164946e+05 9.142386e+04
## [6] 1.050316e+04 1.526936e-09 1.253976e-09 9.334625e-10 7.057659e-10
## [11] 6.746188e-10 5.278365e-10 1.609695e-10 1.244778e-10 1.037466e-10
## [16] 1.935234e-11 -8.800055e-11 -1.062780e-10 -1.363508e-10 -1.646751e-10
## [21] -1.728773e-10 -1.908670e-10 -2.237440e-10 -2.445036e-10 -2.550743e-10
## [26] -3.077544e-10 -3.753473e-10 -4.919893e-10 -5.207728e-10 -6.251737e-10
## [31] -6.504843e-10 -6.592162e-10 -8.339437e-10 -9.270070e-10vectors## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.029001990 -0.097207596 0.0628064825 -0.099668539 -0.014121155
## [2,] -0.249606787 -0.299167050 0.3159157898 0.438548329 0.003080997
## [3,] 0.030777060 -0.036672471 -0.0345681474 -0.124940875 -0.013415713
## [4,] -0.033858105 -0.113259566 0.0669477209 0.265975053 0.274184254
## [5,] 0.048325010 -0.018036064 -0.0226623623 -0.123033665 0.154678396
## [6,] -0.010843738 -0.115721509 0.1372673681 -0.299645194 0.037356298
## [7,] 0.094596489 0.027402873 -0.0669991493 0.020399129 -0.112358444
## [8,] -0.028185268 -0.063760406 0.0884834530 0.022673476 0.096615382
## [9,] 0.144396905 0.164782342 -0.0423838010 0.016427551 0.117428349
## [10,] 0.125673902 0.134019682 0.0007361369 0.084317101 0.108720957
## [11,] 0.104629195 0.350442915 0.1099222998 -0.177661202 -0.263190260
## [12,] -0.502938666 0.332943203 0.5413808772 -0.038292621 -0.121821280
## [13,] -0.465838349 0.239869480 -0.5568329311 0.346508825 -0.268264994
## [14,] 0.090799496 0.170815335 -0.0364794892 0.099116953 0.123160344
## [15,] -0.515330501 -0.051199764 -0.2484710380 -0.496490449 0.432573539
## [16,] 0.021642007 0.290784490 0.2028379543 0.157837134 0.050879062
## [17,] 0.080195520 0.042695115 -0.1375620717 0.089815354 0.161215434
## [18,] 0.071629432 0.013051856 -0.1642557498 0.115439690 -0.025065032
## [19,] 0.006358853 -0.236653739 0.0463769693 -0.088014593 -0.330339296
## [20,] 0.039513559 -0.143393479 0.0622979799 -0.045693185 0.074806838
## [21,] 0.018991001 -0.293204584 0.0628131485 0.153928347 0.262402016
## [22,] 0.073101646 0.066908844 0.0712739170 -0.142121154 -0.037823044
## [23,] 0.047951572 -0.069153327 -0.0395036413 0.151233035 0.075494155
## [24,] 0.146080654 0.136881070 -0.0357171617 0.047814143 0.109082678
## [25,] 0.073826773 0.009345708 -0.0423208223 -0.082227910 -0.002300992
## [26,] 0.056668507 -0.073203783 -0.0756718309 -0.014542579 0.019122847
## [27,] -0.084781365 -0.308789104 -0.2120917221 -0.020584352 -0.292137218
## [28,] 0.069966740 -0.005377223 -0.0764519699 -0.181886065 -0.202607796
## [29,] 0.128714184 0.118825179 -0.0542386824 0.077193464 0.028390344
## [30,] 0.125551677 0.055458786 -0.0191530138 0.033805205 0.095905765
## [31,] 0.097671301 -0.006440417 0.0308560025 -0.118154431 -0.156075988
## [32,] 0.125759620 0.097808161 -0.0203938271 -0.030397500 -0.046167316
## [33,] 0.099010718 -0.011958633 -0.0168734057 -0.005343188 -0.027384566
## [34,] -0.001447051 -0.308836321 0.1027147174 -0.032335289 -0.312024561
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.098604987 0.000000000 0.000000000 0.000000000 0.73601735
## [2,] 0.518409826 0.032089999 -0.101580690 -0.016389586 0.11463138
## [3,] 0.010726977 0.126418970 -0.608002977 0.194975915 -0.21552126
## [4,] -0.128298252 0.043656142 0.250032511 0.033632405 0.02488252
## [5,] -0.101715951 0.128112997 -0.049905165 -0.011008966 -0.11105806
## [6,] -0.028400650 0.482205683 0.002483104 0.014036185 0.05497054
## [7,] -0.087030782 -0.280694289 0.145323850 -0.377487490 -0.01730996
## [8,] -0.213752264 0.165656473 0.076043773 -0.230566067 -0.15357064
## [9,] 0.017799531 0.051755846 -0.364308294 -0.478996317 0.12461465
## [10,] -0.009597772 -0.444925834 -0.196600832 0.070180727 0.07962442
## [11,] 0.581142167 0.114719974 -0.020365593 -0.151666311 -0.05240049
## [12,] -0.330616076 -0.095759969 -0.269090027 0.001401874 0.06515581
## [13,] -0.104402327 0.246309819 -0.043638025 0.098851928 -0.04486862
## [14,] 0.186662477 -0.004315357 -0.085862063 0.304992919 0.10385017
## [15,] 0.245607589 -0.218653601 0.022293491 -0.126149254 -0.07695147
## [16,] 0.017471719 0.122339540 0.074680891 -0.231929232 -0.16578514
## [17,] 0.150289156 0.082912969 -0.109017616 0.016363368 0.22325761
## [18,] -0.037498086 0.065513792 -0.126353472 -0.151025507 0.13547275
## [19,] 0.013835671 -0.087105442 0.052595274 0.059693039 -0.09589414
## [20,] 0.003969032 0.132367726 -0.094121468 0.003414284 -0.10340484
## [21,] -0.107117045 0.109678202 -0.283930415 -0.056142287 -0.13363097
## [22,] -0.112324296 0.110292830 0.058055928 0.196953914 0.01227428
## [23,] 0.011400296 -0.035440359 -0.100667975 -0.114132593 -0.24820300
## [24,] -0.044132915 -0.232222582 -0.081163308 0.280932271 -0.09559208
## [25,] 0.082614094 0.082615845 -0.067659018 0.162971798 0.07334836
## [26,] -0.068696788 0.036546001 -0.142639103 0.061489268 0.14485815
## [27,] -0.009834239 -0.057486471 -0.219934392 -0.202479876 0.08992258
## [28,] -0.087291597 0.028641524 -0.047108884 -0.141696574 0.11614750
## [29,] -0.069976415 -0.116020263 -0.069503725 -0.132192419 -0.05000722
## [30,] -0.072095464 0.189930445 -0.041234055 -0.181421814 0.05376099
## [31,] -0.005909755 -0.062049294 -0.046652890 0.097194511 -0.15782235
## [32,] -0.026701674 0.237877942 0.070538279 0.107142508 0.01403375
## [33,] -0.076681649 -0.147660359 -0.195830897 0.104476878 0.08231215
## [34,] -0.019249549 -0.140612682 -0.028654943 -0.023531537 -0.14737458
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000000 0.0000000000 0.0000000000 0.000000000 0.00000000
## [2,] -0.085166388 0.0233951652 0.0803469226 0.020032720 -0.06579868
## [3,] -0.091470770 -0.0626912265 -0.0404716628 -0.087131904 0.04586359
## [4,] 0.295386267 -0.1887403847 0.1090399217 0.078636509 0.05493143
## [5,] -0.320424404 0.0954683782 0.0514307970 -0.055664749 -0.06141728
## [6,] -0.067965448 -0.5671409888 -0.1533100278 -0.060550323 0.04894095
## [7,] -0.062986932 -0.1488503919 -0.1209736197 0.025340016 0.08919321
## [8,] 0.305959463 -0.1656264424 -0.3113180829 -0.030357529 -0.06765720
## [9,] -0.031206391 -0.0665361077 0.0909082807 0.011370215 -0.05440884
## [10,] -0.005344126 -0.4128415710 -0.0679842615 -0.003343218 -0.16629876
## [11,] 0.237604587 -0.1215052465 0.0513473866 0.061892530 0.15102818
## [12,] 0.022894912 0.1157725514 -0.0326291606 0.055905893 -0.01566915
## [13,] 0.104761575 -0.1540854325 -0.0152649274 0.054763464 -0.04650044
## [14,] 0.238260828 -0.0194544416 0.0032241761 -0.203849819 -0.06939201
## [15,] 0.120183411 0.1016137192 0.0200563819 0.024518065 0.00620927
## [16,] -0.002008415 0.0242880932 0.0104294921 -0.035543428 0.11933112
## [17,] -0.044399784 0.0510795322 -0.3444202878 0.233438228 -0.21784960
## [18,] -0.075151305 0.0534254839 -0.0695074780 0.268009863 0.14237836
## [19,] 0.079086573 -0.0248787527 -0.0995001547 0.012374799 0.16812420
## [20,] 0.232722574 0.1146401775 -0.0002803059 0.580332297 0.24954546
## [21,] 0.036767803 -0.0402536635 0.1919757885 0.059256708 -0.01211154
## [22,] 0.107186574 0.0011083087 0.2186491951 0.252875872 -0.13240395
## [23,] 0.083262525 0.0939655651 -0.0085911459 -0.347604081 -0.08172804
## [24,] 0.046100576 -0.1865722399 0.3397394241 0.252830083 0.14136022
## [25,] 0.174338442 0.1604333198 -0.2943474960 0.057244609 -0.29628578
## [26,] 0.278896818 0.2159091099 -0.0930967387 -0.203607120 0.44405989
## [27,] -0.099833756 -0.0718521997 0.1507955913 0.053976544 0.06032584
## [28,] 0.261104214 0.0011023622 0.4761483932 -0.074195234 -0.21454770
## [29,] 0.003448137 0.2139633901 -0.2190272385 0.242454349 0.05602015
## [30,] 0.292826804 0.2104928161 0.1651346180 -0.080613824 -0.31501183
## [31,] -0.054265660 0.0113609572 -0.1447697706 0.167817814 -0.34337400
## [32,] -0.246678246 0.3191348235 0.0865882886 -0.091061862 0.10772359
## [33,] 0.261620923 0.0008748017 -0.1887409410 -0.229647982 0.26099304
## [34,] 0.240482066 0.0860858764 -0.0858544578 0.029694327 -0.24427812
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000
## [2,] -0.04403487 0.082724599 -0.0333704417 -0.060271923 0.061426566
## [3,] 0.02623884 0.255880432 0.0505548479 -0.041988439 0.066878073
## [4,] -0.02834791 0.110230383 -0.1312790638 0.038451790 -0.092337903
## [5,] 0.05574049 0.101224821 -0.0129759670 -0.040130859 -0.276055192
## [6,] -0.04257826 0.094707542 -0.1411110354 -0.039643271 -0.044254067
## [7,] -0.09057878 0.058734118 -0.1040147590 0.066102923 0.133580439
## [8,] 0.02649476 0.047451422 0.0587118305 0.178330523 0.194361208
## [9,] 0.09520011 -0.139591444 -0.0747261987 0.180142030 -0.028514656
## [10,] 0.06840047 0.007692870 -0.1558086355 -0.080796110 -0.189065817
## [11,] -0.11451248 -0.061653799 -0.0083043214 0.114267610 0.064726882
## [12,] -0.03606755 -0.020243087 -0.1027278317 0.050970625 0.057308211
## [13,] -0.03963518 -0.033443921 0.0093688932 0.007872011 -0.073332657
## [14,] 0.26489368 0.198115815 -0.2751208853 0.016729867 -0.155104390
## [15,] -0.01147930 0.082851889 0.0149295283 -0.069341009 -0.013553623
## [16,] 0.04638147 0.113892636 0.3594238589 -0.208606729 -0.283738804
## [17,] -0.50829929 0.088358024 0.2293140014 0.057003809 -0.168195684
## [18,] 0.19573977 0.232585871 -0.1485726393 -0.557010319 0.339336461
## [19,] 0.14717296 0.143192785 0.1683115407 -0.082140422 0.078476813
## [20,] 0.17162319 -0.239052299 -0.2771556580 -0.080586834 -0.312408145
## [21,] -0.11614997 -0.035354089 0.2633047339 0.085218168 0.153733912
## [22,] -0.24577892 0.040423837 -0.1418360393 0.092819272 -0.018796967
## [23,] -0.20916577 -0.101735154 -0.4749325060 -0.017659234 0.086592956
## [24,] -0.06104498 -0.020465219 0.2052041226 0.185593385 0.260014699
## [25,] 0.39432720 -0.064016274 0.1151726107 0.258852031 0.288773830
## [26,] -0.35966126 -0.009672119 -0.1080677638 0.008325749 0.175541829
## [27,] 0.10049297 -0.196077453 -0.0371812336 0.298150149 -0.186808622
## [28,] -0.13227639 0.358759607 0.0473239558 -0.176054574 -0.018242930
## [29,] -0.02724297 0.463218376 -0.1054599007 0.225122335 -0.083038919
## [30,] 0.14355725 -0.194862159 0.1091144321 -0.160861546 0.008079303
## [31,] -0.27290084 -0.332368524 -0.1134269795 -0.353882397 0.091843685
## [32,] -0.03022161 0.036728041 -0.1543288088 0.197418300 -0.094457675
## [33,] -0.01486881 -0.226980569 0.2718155395 -0.201827092 -0.317516343
## [34,] -0.04456938 0.257332884 -0.0006988779 0.068013769 -0.272806467
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.00000000 0.0000000000 0.000000000 0.000000000 0.000000000
## [2,] 0.16929816 0.0365795229 0.075791473 0.107300343 -0.022391071
## [3,] 0.12576922 0.0113549102 0.018302162 -0.437817892 -0.076679305
## [4,] 0.18016863 0.0612590259 -0.368174306 -0.389102868 0.112047768
## [5,] 0.07653175 -0.0776431725 -0.135466750 0.407444862 -0.027351354
## [6,] 0.02435475 -0.0912399645 -0.158405758 0.187233643 -0.051665170
## [7,] 0.12710171 -0.3364721465 0.171152105 -0.025854483 -0.156537166
## [8,] -0.02417595 0.3477239483 0.363174354 0.135997048 -0.078441483
## [9,] -0.21475582 0.0074058897 -0.255908155 -0.245800317 0.052099900
## [10,] 0.15020917 0.0941838671 0.012756469 0.241238847 -0.054468153
## [11,] 0.16487760 -0.1129604495 -0.021886300 0.071549246 -0.023755560
## [12,] 0.01557947 0.0004866872 -0.090555114 0.080637422 -0.014535331
## [13,] 0.03766797 -0.1382521831 -0.039086214 0.081393592 -0.019943970
## [14,] -0.31381425 0.0923796879 0.290507888 -0.010249354 -0.208935933
## [15,] 0.05885774 0.0868090468 -0.012818443 0.015434045 -0.058469847
## [16,] -0.22401596 0.2628665804 0.039130255 0.052475838 0.119786404
## [17,] -0.07895679 0.1589586983 -0.131518118 0.051495214 0.003769359
## [18,] 0.02324184 0.0553817397 0.003322629 0.141960236 -0.017164978
## [19,] 0.12308635 0.3619254321 -0.330732691 0.017492321 -0.091435567
## [20,] -0.10434270 -0.0956544933 0.053601596 0.080454534 0.106834015
## [21,] 0.01256548 -0.2866161295 0.246189086 0.135592385 0.024554989
## [22,] 0.29077722 0.1508013809 0.274389926 -0.080559925 -0.013285711
## [23,] 0.09148142 0.1448409168 -0.208506761 0.222301535 0.290450446
## [24,] -0.11433363 0.1066413644 -0.251315531 0.299452022 -0.125941077
## [25,] 0.04797871 -0.0955572695 -0.130368050 0.151506779 0.395791590
## [26,] -0.25075168 0.0078313239 -0.067871412 0.124941845 -0.155020741
## [27,] 0.01768661 0.4170947759 0.125057950 0.054444681 -0.031152457
## [28,] -0.04236678 0.0168721027 0.091382869 0.098703501 0.398739333
## [29,] 0.28044771 0.0109660631 0.010978897 0.007402113 0.008672042
## [30,] 0.30843592 0.0164216932 -0.166859909 0.064671270 -0.564691249
## [31,] -0.10882333 0.1358545542 0.038852611 -0.143951171 -0.013726752
## [32,] 0.18772471 0.0974117845 0.006435964 0.089872921 -0.095562251
## [33,] 0.38426483 -0.1142725854 0.095251616 0.042135534 0.196760945
## [34,] -0.27466245 -0.2996310666 -0.188438476 0.074706396 -0.223597700
## [,26] [,27] [,28] [,29] [,30]
## [1,] 0.0000000000 0.00000000 0.000000000 0.0000000000 0.000000000
## [2,] -0.0933168728 0.09698469 -0.207102211 0.1431773058 0.087034815
## [3,] -0.0004775527 0.27726690 -0.231477708 -0.0348039568 -0.032631486
## [4,] -0.1488145786 -0.10463820 -0.087373732 -0.2888477831 -0.086388137
## [5,] 0.0234569739 -0.04042486 -0.133530767 0.0525550295 0.261635701
## [6,] -0.0168774354 -0.13795850 -0.074467647 -0.0337650709 -0.044556665
## [7,] 0.0338809313 0.10523848 -0.334572798 0.1139323170 -0.400128163
## [8,] -0.2257849142 0.29344582 0.111647846 0.0210442552 0.162521657
## [9,] 0.0270737452 -0.03407468 0.193222473 0.2395042769 0.032326811
## [10,] -0.0445372386 -0.01856765 -0.102659433 0.0550207295 -0.135534846
## [11,] -0.0434804363 -0.08475536 0.141378788 -0.1899756317 0.058193083
## [12,] -0.0377805605 -0.02744337 0.063207422 -0.0555513879 -0.091924374
## [13,] -0.0218316434 -0.05244342 -0.023447416 0.1338779297 -0.015775767
## [14,] -0.0156363318 -0.20669133 0.112653986 0.0592096527 -0.147867455
## [15,] -0.0248269735 -0.04000226 0.003502137 -0.0502509437 -0.137097039
## [16,] 0.2052357606 -0.12295116 -0.316023369 -0.1402555897 -0.235821887
## [17,] 0.0467251402 0.19030940 0.118341111 0.0346305457 -0.192663991
## [18,] 0.1202228771 0.05355515 0.226774840 -0.3487863374 -0.055509559
## [19,] 0.0603234926 -0.20300488 0.186516824 0.4937964156 -0.242308928
## [20,] -0.0832614491 0.19799389 -0.104187775 0.2397031196 -0.080166879
## [21,] -0.0137972304 -0.43491568 0.250871640 -0.0003351395 -0.277478361
## [22,] 0.5897226905 -0.02711922 0.008781913 0.0614608043 -0.036484534
## [23,] 0.2213175727 0.09132579 0.117326786 -0.0142472082 -0.085496429
## [24,] -0.1134289791 0.17977540 -0.038769443 -0.0974323855 0.054429473
## [25,] 0.0971246308 -0.07220104 -0.308645005 -0.0947283686 -0.180608435
## [26,] 0.0477431812 -0.15632828 -0.368107556 0.0385857517 0.078424479
## [27,] 0.0409884452 -0.14143280 -0.146955340 -0.3833414139 -0.006123818
## [28,] -0.2867935965 0.09366380 -0.111967167 0.1595260331 -0.016123894
## [29,] -0.1534011291 -0.38886988 -0.036178680 0.0367835837 0.325917761
## [30,] 0.0190349271 0.02011845 -0.153449661 0.0336761022 0.021400905
## [31,] -0.3495627870 -0.34595050 -0.143038997 -0.0622339343 0.012541488
## [32,] -0.4167182163 0.11679482 0.115985498 -0.1145363449 -0.504984059
## [33,] -0.0664802386 0.06096201 0.169393750 -0.0931890601 0.050359501
## [34,] 0.0993285663 0.12707445 0.146335748 -0.2927396048 -0.042211407
## [,31] [,32] [,33] [,34]
## [1,] 0.651296562 0.00000000 0.000000000 0.0000000000
## [2,] -0.070109185 0.15764093 0.093059479 0.2258279763
## [3,] 0.225000201 -0.05740939 -0.073432752 -0.0775466497
## [4,] -0.025764094 0.02612722 -0.311300738 0.0568334042
## [5,] 0.096276012 0.05232596 -0.590914052 0.2323897560
## [6,] -0.142457661 -0.09220735 0.333428012 0.1007904479
## [7,] 0.021834167 -0.19384804 -0.127244418 0.3051650186
## [8,] 0.127445792 0.16599446 -0.145728973 0.0536496859
## [9,] -0.097958479 0.32727358 0.044351960 0.2832015102
## [10,] -0.050646707 0.33296669 -0.031334215 -0.4287961063
## [11,] 0.160669878 -0.01847368 -0.283044293 -0.1436456540
## [12,] -0.157097209 -0.16600151 -0.098999596 0.0159159076
## [13,] 0.150863570 0.12052991 0.007837372 0.0373265337
## [14,] -0.038204723 -0.25680494 -0.110876783 0.2852080440
## [15,] 0.050917955 0.10383261 0.087017758 0.0929988569
## [16,] 0.240056528 0.07853062 0.159148288 0.0153738192
## [17,] -0.189096635 -0.27760088 -0.123674280 -0.0393176129
## [18,] -0.120672486 0.07211858 -0.067131708 0.0615985620
## [19,] 0.050321263 -0.01491584 -0.151743250 0.0296537932
## [20,] 0.086436246 -0.11127830 0.022780834 -0.1153217146
## [21,] 0.115068409 -0.01906276 -0.091663585 -0.1428723067
## [22,] -0.047077253 0.28257045 0.001702725 0.1986630133
## [23,] 0.302618868 -0.22526714 0.135251363 0.0013892147
## [24,] 0.141406281 -0.08455361 0.179608872 0.3125458536
## [25,] -0.074251755 0.09229777 -0.035886404 0.0615998712
## [26,] -0.177017887 0.24949327 -0.086673289 -0.1099772525
## [27,] -0.142002826 -0.20189467 -0.050841660 0.0089614469
## [28,] -0.167013296 -0.08398920 -0.014602063 -0.0327534765
## [29,] 0.087043362 -0.09702597 0.311602500 0.0003707925
## [30,] -0.048701592 -0.17747829 0.119373514 -0.1089284991
## [31,] 0.156404402 0.08999960 -0.020338660 0.2389375219
## [32,] -0.003389807 0.30219098 0.102335167 0.0216692787
## [33,] -0.101788985 0.02712896 0.097247062 0.3664431142
## [34,] 0.095853159 0.24265272 0.086870966 0.0719542285pos_idx <- which(values > 0)
k <- 2
lambda <- diag( sqrt(values[pos_idx][1:k]) )
vec <- vectors[, pos_idx][, 1:k]
lambda## [,1] [,2]
## [1,] 5092.474 0.000
## [2,] 0.000 1580.164vec## [,1] [,2]
## [1,] -0.029001990 -0.097207596
## [2,] -0.249606787 -0.299167050
## [3,] 0.030777060 -0.036672471
## [4,] -0.033858105 -0.113259566
## [5,] 0.048325010 -0.018036064
## [6,] -0.010843738 -0.115721509
## [7,] 0.094596489 0.027402873
## [8,] -0.028185268 -0.063760406
## [9,] 0.144396905 0.164782342
## [10,] 0.125673902 0.134019682
## [11,] 0.104629195 0.350442915
## [12,] -0.502938666 0.332943203
## [13,] -0.465838349 0.239869480
## [14,] 0.090799496 0.170815335
## [15,] -0.515330501 -0.051199764
## [16,] 0.021642007 0.290784490
## [17,] 0.080195520 0.042695115
## [18,] 0.071629432 0.013051856
## [19,] 0.006358853 -0.236653739
## [20,] 0.039513559 -0.143393479
## [21,] 0.018991001 -0.293204584
## [22,] 0.073101646 0.066908844
## [23,] 0.047951572 -0.069153327
## [24,] 0.146080654 0.136881070
## [25,] 0.073826773 0.009345708
## [26,] 0.056668507 -0.073203783
## [27,] -0.084781365 -0.308789104
## [28,] 0.069966740 -0.005377223
## [29,] 0.128714184 0.118825179
## [30,] 0.125551677 0.055458786
## [31,] 0.097671301 -0.006440417
## [32,] 0.125759620 0.097808161
## [33,] 0.099010718 -0.011958633
## [34,] -0.001447051 -0.308836321# membentuk koordinat MDS
X <- vec %*% lambda
colnames(X) <- c("Dim1", "Dim2")
mds_coords <- as.data.frame(X)
mds_coords$Label <- labels
mds_coords## Dim1 Dim2 Label
## 1 -147.691888 -153.603986 1
## 2 -1271.116154 -472.733132 2
## 3 156.731386 -57.948535 3
## 4 -172.421530 -178.968738 4
## 5 246.093875 -28.499947 5
## 6 -55.221456 -182.859013 6
## 7 481.730191 43.301045 7
## 8 -143.532755 -100.751927 8
## 9 735.337530 260.383196 9
## 10 639.991119 211.773134 10
## 11 532.821487 553.757430 11
## 12 -2561.202239 526.105007 12
## 13 -2372.269827 379.033220 13
## 14 462.394100 269.916316 14
## 15 -2624.307343 -80.904046 15
## 16 110.211366 459.487309 16
## 17 408.393627 67.465302 17
## 18 364.771043 20.624079 18
## 19 32.382296 -373.951821 19
## 20 201.221782 -226.585275 20
## 21 96.711185 -463.311456 21
## 22 372.268254 105.726975 22
## 23 244.192147 -109.273627 23
## 24 743.911978 216.294598 24
## 25 375.960947 14.767755 25
## 26 288.582916 -115.674015 26
## 27 -431.746925 -487.937559 27
## 28 356.303826 -8.496896 28
## 29 655.473675 187.763321 29
## 30 639.368689 87.634002 30
## 31 497.388592 -10.176917 31
## 32 640.427637 154.552977 32
## 33 504.209537 -18.896606 33
## 34 -7.369069 -488.012171 34# menghitung jarak euclidean dari koordinat
D_hat <- dist(mds_coords[,1:2])
as.matrix(D_hat)## 1 2 3 4 5 6 7
## 1 0.00000 1167.8722 319.09794 35.42493 413.18065 96.98782 659.50265
## 2 1167.87221 0.0000 1486.87419 1137.28950 1580.90777 1249.97077 1827.22784
## 3 319.09794 1486.8742 0.00000 350.69578 94.08971 246.02161 340.40520
## 4 35.42493 1137.2895 350.69578 0.00000 444.74262 117.26462 690.88228
## 5 413.18065 1580.9078 94.08971 444.74262 0.00000 338.55229 246.33282
## 6 96.98782 1249.9708 246.02161 117.26462 338.55229 0.00000 582.63663
## 7 659.50265 1827.2278 340.40520 690.88228 246.33282 582.63663 0.00000
## 8 53.01546 1187.3560 303.29966 83.38124 396.26918 120.58383 641.64243
## 9 975.25706 2136.1919 660.39394 1008.49226 568.16620 906.33723 333.82831
## 10 868.30004 2029.9950 553.43450 901.49516 461.39592 799.40919 231.14793
## 11 981.55928 2075.5418 718.07239 1016.98346 649.02726 942.54883 513.00686
## 12 2507.39637 1631.5636 2779.97873 2490.66302 2861.55519 2604.33670 3080.99618
## 13 2287.45479 1392.1370 2566.47622 2269.51508 2649.88901 2384.20554 2873.67921
## 14 742.68052 1885.8913 448.24665 777.48870 368.56214 687.70005 227.43871
## 15 2477.68226 1408.7783 2781.13347 2453.84611 2870.87954 2571.10815 3108.51992
## 16 665.12783 1666.4635 519.52282 698.21736 506.55268 663.30748 557.88641
## 17 598.41685 1764.2470 281.18057 630.93263 188.54850 526.87874 77.21504
## 18 541.27043 1708.6627 222.38290 573.07343 128.44236 466.68948 119.13726
## 19 284.56964 1307.2360 339.58912 282.77732 406.21378 210.21627 613.19938
## 20 356.46461 1492.7718 174.40684 376.66518 203.10416 260.14442 389.26032
## 21 394.52703 1367.8598 409.78229 391.51398 459.75671 318.96254 636.31428
## 22 581.04311 1742.2194 270.63964 614.60443 184.21955 515.78031 126.01156
## 23 394.38341 1558.2882 101.40833 422.40308 80.79606 308.32339 282.31782
## 24 965.28877 2129.5769 648.06662 997.94800 554.74970 893.27367 314.11154
## 25 550.05576 1717.7078 230.97459 581.59880 136.88517 474.31488 109.55036
## 26 437.92053 1600.0476 143.93421 465.32926 96.97751 350.30739 250.15783
## 27 438.70970 839.5069 728.83282 403.37500 818.87183 484.60742 1056.71893
## 28 524.46901 1692.3389 205.60794 555.52781 112.01051 446.93982 135.70114
## 29 872.70073 2036.6649 555.98398 905.48488 462.99203 801.52884 225.95607
## 30 823.20114 1990.9705 504.11610 854.44741 410.06362 745.40052 163.75380
## 31 660.83292 1827.9954 343.99049 690.75052 251.96184 578.96198 55.72323
## 32 846.22284 2011.8369 528.31710 878.61283 434.74992 773.15879 193.80885
## 33 665.67375 1832.4161 349.66572 695.30762 258.29425 582.96373 66.13523
## 34 362.65594 1263.8394 460.30826 350.35719 524.78086 308.88234 722.15775
## 8 9 10 11 12 13 14
## 1 53.01546 975.25706 868.30004 981.5593 2507.3964 2287.4548 742.6805
## 2 1187.35603 2136.19192 2029.99503 2075.5418 1631.5636 1392.1370 1885.8913
## 3 303.29966 660.39394 553.43450 718.0724 2779.9787 2566.4762 448.2466
## 4 83.38124 1008.49226 901.49516 1016.9835 2490.6630 2269.5151 777.4887
## 5 396.26918 568.16620 461.39592 649.0273 2861.5552 2649.8890 368.5621
## 6 120.58383 906.33723 799.40919 942.5488 2604.3367 2384.2055 687.7001
## 7 641.64243 333.82831 231.14793 513.0069 3080.9962 2873.6792 227.4387
## 8 0.00000 950.17449 843.55295 941.1894 2497.6139 2279.7944 710.3114
## 9 950.17449 0.00000 107.02278 356.4845 3307.2319 3109.8716 273.1099
## 10 843.55295 107.02278 0.00000 358.3833 3216.5888 3016.9010 186.8725
## 11 941.18944 356.48449 358.38330 0.0000 3094.1473 2910.3409 292.4479
## 12 2497.61393 3307.23185 3216.58879 3094.1473 0.0000 239.4276 3034.4303
## 13 2279.79445 3109.87159 3016.90105 2910.3409 239.4276 0.0000 2836.7633
## 14 710.31141 273.10986 186.87250 292.4479 3034.4303 2836.7633 0.0000
## 15 2480.85398 3376.93510 3277.39292 3220.2884 610.2805 524.4666 3106.5738
## 16 615.02364 656.06796 584.83237 432.9967 2672.2441 2483.7846 399.9623
## 17 576.99200 379.61774 272.87753 501.9585 3004.8045 2798.0643 209.5291
## 18 522.59438 441.36601 335.08813 558.9921 2969.3148 2760.4075 267.7254
## 19 324.93736 946.85108 843.95628 1054.0796 2745.3202 2519.7893 774.2586
## 20 367.00098 722.78484 620.22304 847.8756 2863.1327 2643.7914 561.0034
## 21 434.93283 965.18266 866.54041 1106.6261 2836.0974 2608.7184 819.3577
## 22 555.59357 394.63635 287.96062 475.9292 2963.4383 2758.1127 187.2987
## 23 387.81854 614.71128 509.63502 723.1301 2876.4464 2661.6380 437.4895
## 24 942.37819 44.91465 104.01917 398.0457 3319.6028 3120.4283 286.5791
## 25 532.18277 435.29125 329.42837 561.3511 2981.3409 2772.2665 269.3909
## 26 432.37324 583.95951 480.32214 712.5945 2921.1566 2706.4502 422.9542
## 27 482.68014 1386.38742 1279.92870 1419.6903 2358.5721 2125.3864 1172.1052
## 28 508.27906 464.71825 359.16203 589.3118 2966.0817 2755.9561 297.9414
## 29 849.50122 107.94388 28.56888 385.9990 3234.4210 3033.7790 209.8305
## 30 805.24774 197.61655 124.14069 478.1457 3230.4661 3025.7032 254.0607
## 31 647.28974 360.30886 263.81301 565.0464 3105.2498 2895.9323 282.2709
## 32 824.48438 142.15457 57.22182 413.4529 3223.1172 3021.0491 212.1430
## 33 652.89384 362.51532 267.66615 573.3684 3113.4830 2903.8736 291.8243
## 34 410.50097 1054.37598 953.29675 1173.4947 2747.8169 2518.8337 891.7023
## 15 16 17 18 19 20 21
## 1 2477.6823 665.1278 598.41685 541.27043 284.5696 356.4646 394.5270
## 2 1408.7783 1666.4635 1764.24699 1708.66271 1307.2360 1492.7718 1367.8598
## 3 2781.1335 519.5228 281.18057 222.38290 339.5891 174.4068 409.7823
## 4 2453.8461 698.2174 630.93263 573.07343 282.7773 376.6652 391.5140
## 5 2870.8795 506.5527 188.54850 128.44236 406.2138 203.1042 459.7567
## 6 2571.1081 663.3075 526.87874 466.68948 210.2163 260.1444 318.9625
## 7 3108.5199 557.8864 77.21504 119.13726 613.1994 389.2603 636.3143
## 8 2480.8540 615.0236 576.99200 522.59438 324.9374 367.0010 434.9328
## 9 3376.9351 656.0680 379.61774 441.36601 946.8511 722.7848 965.1827
## 10 3277.3929 584.8324 272.87753 335.08813 843.9563 620.2230 866.5404
## 11 3220.2884 432.9967 501.95849 558.99206 1054.0796 847.8756 1106.6261
## 12 610.2805 2672.2441 3004.80448 2969.31484 2745.3202 2863.1327 2836.0974
## 13 524.4666 2483.7846 2798.06430 2760.40755 2519.7893 2643.7914 2608.7184
## 14 3106.5738 399.9623 209.52915 267.72538 774.2586 561.0034 819.3577
## 15 0.0000 2787.4030 3036.32815 2990.80216 2672.8032 2829.2822 2747.7586
## 16 2787.4030 0.0000 492.53824 507.34758 837.0652 692.0827 922.8975
## 17 3036.3281 492.5382 0.00000 64.00805 579.8565 359.7025 615.5241
## 18 2990.8022 507.3476 64.00805 0.00000 515.9190 296.4133 553.2176
## 19 2672.8032 837.0652 579.85653 515.91901 0.0000 224.1064 110.1061
## 20 2829.2822 692.0827 359.70254 296.41327 224.1064 0.0000 258.7697
## 21 2747.7586 922.8975 615.52409 553.21758 110.1061 258.7697 0.0000
## 22 3002.3818 440.2501 52.62127 85.43250 587.8896 373.7490 632.2471
## 23 2868.6398 584.3285 241.24422 177.23624 338.9955 124.9339 383.5276
## 24 3381.3057 678.7630 367.04594 426.65537 924.4811 700.4679 938.4739
## 25 3001.7933 518.0717 61.87819 12.62975 518.7959 297.9682 553.6607
## 26 2913.0978 602.1852 218.84839 156.14673 363.7941 141.1853 397.0725
## 27 2230.0219 1091.4819 1007.12883 945.02688 477.9212 684.8025 529.0316
## 28 2981.4905 528.7445 92.10648 30.32697 488.3467 267.6060 523.6837
## 29 3290.7667 609.2166 274.80932 335.32603 838.9081 614.8411 857.9708
## 30 3268.0248 646.7475 231.85395 282.65562 762.5575 539.1720 773.3163
## 31 3122.4971 608.6795 118.10342 136.14740 590.3923 366.8070 604.8746
## 32 3273.2147 611.6488 247.83875 306.46942 805.6280 581.5223 823.0334
## 33 3129.1313 619.7465 128.99251 144.93094 590.4957 367.3366 602.9589
## 34 2648.4152 954.7672 693.83992 630.23733 120.7888 334.4461 106.9711
## 22 23 24 25 26 27 28
## 1 581.04311 394.38341 965.28877 550.05576 437.92053 438.7097 524.46901
## 2 1742.21939 1558.28818 2129.57686 1717.70780 1600.04762 839.5069 1692.33894
## 3 270.63964 101.40833 648.06662 230.97459 143.93421 728.8328 205.60794
## 4 614.60443 422.40308 997.94800 581.59880 465.32926 403.3750 555.52781
## 5 184.21955 80.79606 554.74970 136.88517 96.97751 818.8718 112.01051
## 6 515.78031 308.32339 893.27367 474.31488 350.30739 484.6074 446.93982
## 7 126.01156 282.31782 314.11154 109.55036 250.15783 1056.7189 135.70114
## 8 555.59357 387.81854 942.37819 532.18277 432.37324 482.6801 508.27906
## 9 394.63635 614.71128 44.91465 435.29125 583.95951 1386.3874 464.71825
## 10 287.96062 509.63502 104.01917 329.42837 480.32214 1279.9287 359.16203
## 11 475.92923 723.13006 398.04567 561.35114 712.59451 1419.6903 589.31181
## 12 2963.43835 2876.44636 3319.60276 2981.34087 2921.15658 2358.5721 2966.08173
## 13 2758.11268 2661.63800 3120.42832 2772.26653 2706.45018 2125.3864 2755.95605
## 14 187.29871 437.48955 286.57914 269.39094 422.95417 1172.1052 297.94138
## 15 3002.38180 2868.63977 3381.30573 3001.79328 2913.09777 2230.0219 2981.49052
## 16 440.25014 584.32855 678.76296 518.07173 602.18515 1091.4819 528.74447
## 17 52.62127 241.24422 367.04594 61.87819 218.84839 1007.1288 92.10648
## 18 85.43250 177.23624 426.65537 12.62975 156.14673 945.0269 30.32697
## 19 587.88963 338.99552 924.48111 518.79591 363.79415 477.9212 488.34666
## 20 373.74902 124.93388 700.46787 297.96822 141.18525 684.8025 267.60602
## 21 632.24713 383.52760 938.47390 553.66069 397.07248 529.0316 523.68370
## 22 0.00000 250.25736 387.74251 91.03415 236.68890 999.4388 115.33410
## 23 250.25736 0.00000 596.41812 180.96762 44.84981 774.7774 150.74806
## 24 387.74251 596.41812 0.00000 419.52477 563.49598 1370.4440 448.07510
## 25 91.03415 180.96762 419.52477 0.00000 157.00311 951.3699 30.45729
## 26 236.68890 44.84981 563.49598 157.00311 0.00000 810.8361 126.77956
## 27 999.43884 774.77739 1370.44401 951.36988 810.83613 0.0000 922.43555
## 28 115.33410 150.74806 448.07510 30.45729 126.77956 922.4355 0.00000
## 29 294.84788 507.32972 92.92668 328.71695 476.11243 1280.0861 357.79976
## 30 267.71253 441.51683 165.77952 273.30044 405.44396 1215.9652 298.94291
## 31 170.55442 271.89814 334.75831 123.96334 233.94326 1044.7718 141.09477
## 32 272.56822 476.03260 120.50326 299.13632 443.64100 1249.9410 327.58449
## 33 181.49253 275.27631 335.81567 132.59333 236.34870 1046.9068 148.27088
## 34 704.73447 454.67123 1029.79184 632.24169 475.62935 424.3779 601.82462
## 29 30 31 32 33 34
## 1 872.70073 823.20114 660.83292 846.22284 665.67375 362.6559
## 2 2036.66490 1990.97053 1827.99543 2011.83685 1832.41614 1263.8394
## 3 555.98398 504.11610 343.99049 528.31710 349.66572 460.3083
## 4 905.48488 854.44741 690.75052 878.61283 695.30762 350.3572
## 5 462.99203 410.06362 251.96184 434.74992 258.29425 524.7809
## 6 801.52884 745.40052 578.96198 773.15879 582.96373 308.8823
## 7 225.95607 163.75380 55.72323 193.80885 66.13523 722.1578
## 8 849.50122 805.24774 647.28974 824.48438 652.89384 410.5010
## 9 107.94388 197.61655 360.30886 142.15457 362.51532 1054.3760
## 10 28.56888 124.14069 263.81301 57.22182 267.66615 953.2967
## 11 385.99902 478.14575 565.04640 413.45287 573.36837 1173.4947
## 12 3234.42097 3230.46608 3105.24978 3223.11725 3113.48296 2747.8169
## 13 3033.77898 3025.70323 2895.93232 3021.04905 2903.87356 2518.8337
## 14 209.83050 254.06072 282.27085 212.14297 291.82432 891.7023
## 15 3290.76673 3268.02483 3122.49705 3273.21470 3129.13132 2648.4152
## 16 609.21664 646.74752 608.67946 611.64879 619.74650 954.7672
## 17 274.80932 231.85395 118.10342 247.83875 128.99251 693.8399
## 18 335.32603 282.65562 136.14740 306.46942 144.93094 630.2373
## 19 838.90808 762.55751 590.39227 805.62799 590.49568 120.7888
## 20 614.84107 539.17202 366.80697 581.52227 367.33658 334.4461
## 21 857.97080 773.31628 604.87461 823.03344 602.95893 106.9711
## 22 294.84788 267.71253 170.55442 272.56822 181.49253 704.7345
## 23 507.32972 441.51683 271.89814 476.03260 275.27631 454.6712
## 24 92.92668 165.77952 334.75831 120.50326 335.81567 1029.7918
## 25 328.71695 273.30044 123.96334 299.13632 132.59333 632.2417
## 26 476.11243 405.44396 233.94326 443.64100 236.34870 475.6294
## 27 1280.08606 1215.96516 1044.77177 1249.94095 1046.90683 424.3779
## 28 357.79976 298.94291 141.09477 327.58449 148.27088 601.8246
## 29 0.00000 101.41623 253.32041 36.45971 256.10382 946.5902
## 30 101.41623 0.00000 172.41033 66.92735 172.09523 865.8165
## 31 253.32041 172.41033 0.00000 218.16532 11.07060 695.0589
## 32 36.45971 66.92735 218.16532 0.00000 220.54507 912.4311
## 33 256.10382 172.09523 11.07060 220.54507 0.00000 694.1052
## 34 946.59021 865.81652 695.05887 912.43112 694.10524 0.0000# menghiung stress
num <- sum((D - D_hat)^2)
den <- sum(D^2)
stress <- sqrt(num / den)
stress## [1] 0.02528328# menghitung R-Square
eig_pos <- values[values > 0]
R2 <- sum(eig_pos[1:2]) / sum(eig_pos)
R2## [1] 0.9806235# plot MDS
ggplot(mds_coords, aes(x = Dim1, y = Dim2)) +
geom_point(size = 3) +
geom_text(aes(label = Label), vjust = -0.8) +
theme_minimal() +
labs(title = "Plot MDS (Manual)", x = "Dimensi 1", y = "Dimensi 2")
3. HASIL DAN PEMBAHASAN
3.1 Langkah-langkah MDS
Berikut adalah langkah-langkah dari MDS:
Menghitung matriks jarak
Setelah data dibaca oleh R dengan fungsi read_excel, selanjutnya akan dihitung matriks jarak dengan jarak Euclidean seperti berikut.
#matriks jarak
dist_mat <- dist(data_num)
dist_mat## 1 2 3 4 5 6 7
## 2 1193.18607
## 3 324.46726 1514.16380
## 4 156.34577 1152.94883 389.99103
## 5 419.39838 1606.70719 107.78683 468.50293
## 6 127.52647 1280.66936 272.89558 240.73014 358.25689
## 7 665.80177 1847.84767 345.96676 710.05774 265.09055 606.47259
## 8 77.72387 1205.88225 318.37713 130.25744 405.19625 167.75577 651.28105
## 9 978.88712 2152.20329 663.35134 1015.32556 570.51643 919.11642 341.45864
## 10 872.16627 2042.92756 559.63113 905.92163 467.29541 814.30891 244.97347
## 11 987.65075 2091.21998 729.54849 1043.79308 669.68724 950.02579 534.09924
## 12 2523.43773 1647.70719 2800.95466 2511.22201 2882.03175 2617.22620 3101.71727
## 13 2322.36367 1487.06355 2590.83384 2304.76832 2676.17600 2430.45016 2890.50636
## 14 749.75996 1901.34663 456.95186 783.92091 377.64666 709.21012 242.13220
## 15 2491.98876 1487.78997 2790.20770 2475.27897 2878.19926 2584.81469 3119.87788
## 16 676.29875 1671.38117 546.76229 707.10112 533.27198 682.54890 583.94178
## 17 616.06087 1789.14784 301.77806 646.55472 214.55069 568.27986 125.16789
## 18 562.24194 1736.13680 248.99197 598.06354 181.66728 519.07899 138.62179
## 19 300.60439 1333.77209 356.24711 358.23037 434.09216 254.21251 621.48773
## 20 358.10613 1510.30427 187.30456 396.25497 212.43117 277.95143 401.32530
## 21 412.47424 1383.01482 432.82560 393.40691 473.16171 363.73342 652.38256
## 22 581.29081 1760.53628 278.10070 637.21974 200.99254 520.58237 161.35365
## 23 409.05623 1576.20747 141.06736 433.20088 126.87001 360.03333 292.03596
## 24 969.05521 2144.68809 651.82129 1003.80775 558.06003 907.05513 321.85711
## 25 553.84926 1740.16493 231.62038 603.27191 147.22092 491.76010 121.84827
## 26 446.44485 1624.91846 151.26136 488.53557 115.89651 384.44766 253.63557
## 27 475.69948 914.30247 741.88476 477.99582 838.11395 543.82994 1061.64778
## 28 534.56805 1723.20457 215.93518 599.86582 160.04999 471.54427 154.78049
## 29 877.56937 2052.79151 560.57025 913.59510 469.93936 819.51754 230.87226
## 30 826.53252 2006.50069 508.24699 861.30366 413.94082 759.80853 177.73576
## 31 662.58811 1846.82809 348.80940 715.44042 270.91696 588.51338 94.19660
## 32 848.04304 2028.61578 529.47332 891.23678 440.17724 784.46925 197.60314
## 33 668.10104 1850.00865 352.33223 709.07193 267.16661 598.75037 77.29812
## 34 375.19861 1284.85057 476.98532 406.32253 549.30411 339.56295 731.72263
## 8 9 10 11 12 13 14
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9 953.58219
## 10 845.64709 112.44554
## 11 953.48991 394.98354 396.02778
## 12 2512.65577 3325.90499 3233.34100 3106.52281
## 13 2316.23747 3128.67688 3038.01366 2942.73121 700.83450
## 14 715.77441 275.13633 189.33040 342.18416 3054.98183 2856.95975
## 15 2497.50936 3385.04741 3288.19069 3235.99135 801.67699 660.82600 3117.10539
## 16 620.98712 673.65125 597.49142 464.66978 2681.17885 2526.05285 425.22229
## 17 593.93771 384.97662 285.57486 547.48790 3032.94955 2813.31477 218.09860
## 18 545.63633 450.48196 351.26628 597.90802 2998.71639 2772.08207 282.57742
## 19 353.31289 958.55777 856.77710 1056.97635 2761.59754 2548.87465 790.58776
## 20 368.79669 725.80851 622.93980 857.69692 2877.68136 2673.95718 566.64098
## 21 440.49064 969.36319 868.92980 1126.24287 2853.14020 2639.56587 823.26241
## 22 560.09821 406.79602 304.42897 486.68573 2976.61670 2788.42429 221.70927
## 23 398.15324 616.56387 510.79448 746.37859 2898.06297 2681.71438 438.45980
## 24 945.39040 46.84015 106.97663 434.07603 3337.77021 3139.07009 288.11803
## 25 540.54787 438.14039 337.05638 577.03293 3001.44915 2793.67142 279.22572
## 26 443.99324 585.20338 484.37898 731.05335 2943.88977 2725.27283 427.31370
## 27 527.70352 1395.51496 1292.18497 1434.48318 2400.32373 2138.67178 1184.17144
## 28 530.01509 480.02396 384.99740 603.52713 2988.69888 2776.22910 330.16208
## 29 854.18675 113.73654 49.87986 421.94786 3253.86140 3050.74597 213.78962
## 30 807.85333 198.49433 126.09520 505.79047 3247.98861 3045.92630 256.74501
## 31 654.77172 374.99200 284.77184 571.40616 3119.93926 2920.85809 307.00326
## 32 828.49502 151.97697 84.59905 432.99769 3240.11435 3040.83245 223.93526
## 33 657.09664 365.65968 272.81679 589.37170 3130.87799 2924.43499 298.93979
## 34 429.64753 1065.87523 964.42522 1176.25337 2760.59704 2551.63653 906.39837
## 15 16 17 18 19 20 21
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16 2811.27907
## 17 3044.73069 533.11819
## 18 3001.82345 551.75901 89.22444
## 19 2692.01393 854.05562 611.40821 542.93186
## 20 2841.47602 700.45699 382.29177 330.81415 255.98242
## 21 2763.45490 928.83099 628.30407 575.78729 226.51711 273.77180
## 22 3014.23340 459.50082 168.39240 184.78907 595.11175 376.96286 646.69313
## 23 2881.87352 601.38590 250.62721 194.56361 373.06300 153.89932 392.46656
## 24 3390.24070 694.27516 373.00804 435.75911 936.38507 703.63627 942.10880
## 25 3010.46757 544.10569 113.50771 100.07497 530.79375 305.46195 568.87257
## 26 2922.34752 626.81018 229.84342 170.97661 386.42722 164.07620 415.91345
## 27 2246.89519 1124.68573 1018.18220 950.02421 502.01096 712.17273 581.01893
## 28 2991.49210 570.77754 176.23847 129.51062 496.27412 295.81582 560.19104
## 29 3300.97258 628.26746 282.92225 342.11402 849.85940 620.24673 864.01678
## 30 3277.53322 661.25940 244.63238 298.74738 775.49017 542.05350 777.53006
## 31 3134.61242 627.24875 195.41238 198.85422 592.90134 374.66385 625.27274
## 32 3283.11361 629.47041 268.48091 321.79030 811.39017 584.71446 832.16104
## 33 3139.81098 635.93632 162.75134 173.72104 599.44307 371.88842 613.49980
## 34 2670.76206 965.03368 723.70643 657.07382 126.81877 355.13659 215.12554
## 22 23 24 25 26 27 28
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23 279.64621
## 24 400.62326 597.57928
## 25 116.83321 199.26866 423.42532
## 26 256.21866 77.58866 565.04425 160.77313
## 27 1016.95182 791.39560 1379.88115 960.83974 820.20912
## 28 153.19269 208.07210 465.17631 80.34924 154.38264 927.91756
## 29 313.63514 508.30011 97.24197 333.75890 477.31436 1287.52476 375.35450
## 30 282.37387 443.61808 166.20469 278.53007 407.79039 1226.98981 322.58797
## 31 176.39161 298.30857 351.05128 140.00000 250.44760 1055.75329 156.85025
## 32 280.56372 481.60565 132.36691 300.43635 445.31337 1257.18535 336.66007
## 33 194.44794 282.59158 339.02360 137.17143 239.28226 1056.21068 172.16852
## 34 710.88607 480.97297 1041.16185 645.07441 497.22932 462.79153 613.97313
## 29 30 31 32 33
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23
## 24
## 25
## 26
## 27
## 28
## 29
## 30 106.50822
## 31 272.50138 197.80040
## 32 59.99167 82.62566 224.73095
## 33 259.12738 176.59841 62.88084 220.85289
## 34 957.34529 877.77560 698.54348 918.80194 703.00711- Mencari nilai eigen dan vektor eigen
#nilai eigen dan vektor eigen
J <- diag(n) - (1/n) * matrix(1, n, n)
B <- -0.5 * J %*% D2 %*% J
B## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 48039.032 261526.9 -13535.380 51089.944 -31122.880 42664.0026
## [2,] 261526.885 1898707.7 -181907.527 324000.797 -308595.027 156072.8555
## [3,] -13535.380 -181907.5 30169.208 -21669.468 42080.708 4624.5908
## [4,] 51089.944 324000.8 -21669.468 78584.856 -37649.968 37092.9144
## [5,] -31122.880 -308595.0 42080.708 -37649.968 65610.208 -4592.9092
## [6,] 42664.003 156072.9 4624.591 37092.914 -4592.909 53551.9732
## [7,] -79245.292 -639535.4 73619.297 -94417.380 116049.797 -38747.3209
## [8,] 38415.973 239694.8 -18180.439 48225.885 -31869.939 30121.9438
## [9,] -149874.027 -1061419.2 100283.561 -170934.115 175277.061 -90395.0562
## [10,] -128144.233 -909249.4 86664.356 -142881.321 151795.856 -76600.2621
## [11,] -159581.674 -933120.8 53089.914 -201333.762 112690.414 -120372.7033
## [12,] 310075.650 3061809.5 -437663.762 356099.561 -650323.262 71764.6202
## [13,] 276567.591 2792909.4 -391890.821 332548.503 -598919.321 22466.5614
## [14,] -112041.880 -713197.0 55690.708 -122964.968 106505.208 -79704.9092
## [15,] 399609.885 3323188.7 -396950.527 456383.797 -628616.027 166736.8555
## [16,] -84398.792 -327131.9 -14118.203 -90431.880 10887.297 -85888.8209
## [17,] -75052.380 -560477.5 60243.208 -79030.468 100482.708 -44001.4092
## [18,] -61852.850 -485546.0 56271.738 -67361.939 88489.238 -35759.8798
## [19,] 55092.032 136133.9 27882.620 51381.944 14841.120 70718.0026
## [20,] 6858.826 -144196.3 44502.414 7742.738 57200.914 35106.7967
## [21,] 56222.473 110259.3 38686.061 79178.385 38134.561 77895.4438
## [22,] -67868.821 -523329.0 53475.767 -86670.909 89667.267 -31665.8503
## [23,] -21997.409 -255214.6 42781.179 -16892.497 62403.679 -389.4386
## [24,] -144513.968 -1049489.1 103649.620 -163522.056 178090.120 -83597.9974
## [25,] -57835.233 -493213.4 59780.356 -71156.321 93487.856 -22618.2621
## [26,] -26269.850 -321459.0 53011.738 -30673.939 75456.238 2243.1202
## [27,] 134767.444 755272.3 -36218.968 148945.356 -94519.468 102793.4144
## [28,] -50502.821 -467004.0 60129.767 -72267.909 88356.267 -16041.8503
## [29,] -127679.409 -924257.6 91330.179 -144670.497 155748.679 -75663.4386
## [30,] -108745.174 -854855.3 94740.414 -122816.262 155944.914 -53065.2033
## [31,] -69652.174 -630193.3 80090.414 -90795.262 121946.914 -20558.2033
## [32,] -118325.497 -891043.6 92157.091 -140615.586 153170.591 -63676.5268
## [33,] -71752.115 -634504.3 80423.473 -84691.203 124523.973 -25067.1445
## [34,] 79062.120 249363.0 26756.708 82173.032 7367.208 94554.0908
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] -79245.292 38415.973 -149874.03 -128144.23 -159581.67 310075.650
## [2,] -639535.439 239694.826 -1061419.17 -909249.38 -933120.82 3061809.503
## [3,] 73619.297 -18180.439 100283.56 86664.36 53089.91 -437663.762
## [4,] -94417.380 48225.885 -170934.12 -142881.32 -201333.76 356099.561
## [5,] 116049.797 -31869.939 175277.06 151795.86 112690.41 -650323.262
## [6,] -38747.321 30121.944 -90395.06 -76600.26 -120372.70 71764.620
## [7,] 236762.385 -76285.350 365300.65 316548.44 279876.00 -1222018.674
## [8,] -76285.350 34833.914 -132026.09 -111969.29 -133028.73 330622.591
## [9,] 365300.650 -132026.086 610432.91 527067.71 531336.27 -1755680.409
## [10,] 316548.444 -111969.292 527067.71 456346.50 453880.06 -1529148.615
## [11,] 279876.003 -133028.733 531336.27 453880.06 608251.62 -1051191.056
## [12,] -1222018.674 330622.591 -1755680.41 -1529148.62 -1051191.06 6939850.267
## [13,] -1109897.733 284173.532 -1639858.47 -1437355.67 -1076473.12 6173575.208
## [14,] 234075.797 -93740.939 412375.06 355258.86 390589.41 -1051523.262
## [15,] -1267843.439 379234.826 -1943462.17 -1697331.38 -1451099.82 6629176.503
## [16,] 68158.885 -55123.850 198585.15 169946.94 316438.50 -4163.174
## [17,] 201241.297 -68270.439 321806.56 278090.36 244947.91 -1038772.762
## [18,] 180958.826 -59256.909 275935.09 238664.88 197564.44 -954039.233
## [19,] 1511.708 31255.973 -77946.03 -62606.23 -178219.67 -267031.350
## [20,] 84809.503 -3629.233 88776.77 81105.56 -16736.88 -623640.556
## [21,] 22850.150 37671.414 -47345.59 -32075.79 -212815.23 -483008.909
## [22,] 182424.856 -62376.880 299536.12 258895.91 262755.47 -883137.203
## [23,] 113385.267 -24199.468 152787.53 135364.33 63231.88 -691812.792
## [24,] 367585.708 -128464.027 605119.97 523451.77 510915.33 -1799429.350
## [25,] 182477.444 -57159.292 280752.71 242889.50 209162.06 -962903.615
## [26,] 135582.826 -31780.909 183352.09 160228.88 86273.44 -813951.233
## [27,] -221273.880 102074.385 -444621.62 -382804.82 -500852.26 813041.061
## [28,] 174761.856 -54681.880 258364.12 222420.91 190362.47 -927876.203
## [29,] 325095.267 -114035.468 532113.53 460294.33 448470.88 -1590516.792
## [30,] 311399.503 -100083.233 494329.77 429036.56 385027.12 -1595976.556
## [31,] 239784.503 -71106.233 360746.77 313465.56 266713.12 -1271245.556
## [32,] 316101.179 -108541.556 510911.44 441838.24 427625.80 -1562001.880
## [33,] 242801.561 -71063.174 365770.83 318366.62 257854.18 -1303865.497
## [34,] -23898.203 50548.061 -137398.94 -111455.14 -262230.59 -215093.262
## [,13] [,14] [,15] [,16] [,17] [,18]
## [1,] 276567.59 -112041.88 399609.88 -84398.792 -75052.38 -61852.85
## [2,] 2792909.44 -713197.03 3323188.74 -327131.939 -560477.53 -485546.00
## [3,] -391890.82 55690.71 -396950.53 -14118.203 60243.21 56271.74
## [4,] 332548.50 -122964.97 456383.80 -90431.880 -79030.47 -67361.94
## [5,] -598919.32 106505.21 -628616.03 10887.297 100482.71 88489.24
## [6,] 22466.56 -79704.91 166736.86 -85888.821 -44001.41 -35759.88
## [7,] -1109897.73 234075.80 -1267843.44 68158.885 201241.30 180958.83
## [8,] 284173.53 -93740.94 379234.83 -55123.850 -68270.44 -59256.91
## [9,] -1639858.47 412375.06 -1943462.17 198585.150 321806.56 275935.09
## [10,] -1437355.67 355258.86 -1697331.38 169946.944 278090.36 238664.88
## [11,] -1076473.12 390589.41 -1451099.82 316438.503 244947.91 197564.44
## [12,] 6173575.21 -1051523.26 6629176.50 -4163.174 -1038772.76 -954039.23
## [13,] 5898469.15 -986866.32 6211483.44 -120965.233 -917441.82 -820799.29
## [14,] -986866.32 290017.21 -1232570.03 174873.297 211918.71 177269.24
## [15,] 6211483.44 -1232570.03 6961188.74 -350778.939 -1063904.53 -952692.00
## [16,] -120965.23 174873.30 -350778.94 240543.385 68857.80 40238.33
## [17,] -917441.82 211918.71 -1063904.53 68857.797 181387.21 158898.74
## [18,] -820799.29 177269.24 -952692.00 40238.326 158898.74 144371.27
## [19,] -222892.41 -91251.88 -66621.12 -168179.792 -19962.38 1052.15
## [20,] -578829.62 31426.91 -509439.32 -78088.997 64579.41 64425.94
## [21,] -417148.97 -76601.44 -220476.67 -193821.350 10581.06 23690.59
## [22,] -861359.26 197492.27 -985145.97 91762.356 153576.77 132173.30
## [23,] -608914.85 86531.68 -634356.56 -22914.233 96933.18 90904.71
## [24,] -1676645.41 404503.12 -1965271.12 180263.208 322126.62 278243.15
## [25,] -881545.67 177544.86 -979343.38 43765.944 155771.36 138697.88
## [26,] -714954.29 103077.24 -740096.00 -26806.674 113646.74 106936.27
## [27,] 886169.00 -332229.47 1180218.30 -288294.380 -203760.97 -155194.44
## [28,] -836130.26 158864.27 -925558.97 25737.356 143522.77 132158.30
## [29,] -1470925.85 355520.68 -1734250.56 156276.767 284036.18 247029.71
## [30,] -1480785.62 320862.91 -1681704.32 110453.003 269584.41 236373.94
## [31,] -1190631.62 223722.91 -1306463.32 49391.003 197440.41 178253.94
## [32,] -1456852.94 337178.59 -1691579.64 139398.679 271896.09 237654.62
## [33,] -1199517.56 227733.97 -1321204.26 45472.061 204857.47 184504.00
## [34,] -180760.32 -140340.79 39538.97 -219943.703 -45752.29 -18257.76
## [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 55092.032 6858.826 56222.47 -67868.82 -21997.4092 -144513.97
## [2,] 136133.885 -144196.321 110259.33 -523328.97 -255214.5562 -1049489.12
## [3,] 27882.620 44502.414 38686.06 53475.77 42781.1791 103649.62
## [4,] 51381.944 7742.738 79178.38 -86670.91 -16892.4974 -163522.06
## [5,] 14841.120 57200.914 38134.56 89667.27 62403.6791 178090.12
## [6,] 70718.003 35106.797 77895.44 -31665.85 -389.4386 -83598.00
## [7,] 1511.708 84809.503 22850.15 182424.86 113385.2673 367585.71
## [8,] 31255.973 -3629.233 37671.41 -62376.88 -24199.4680 -128464.03
## [9,] -77946.027 88776.767 -47345.59 299536.12 152787.5320 605119.97
## [10,] -62606.233 81105.561 -32075.79 258895.91 135364.3261 523451.77
## [11,] -178219.674 -16736.880 -212815.23 262755.47 63231.8849 510915.33
## [12,] -267031.350 -623640.556 -483008.91 -883137.20 -691812.7915 -1799429.35
## [13,] -222892.409 -578829.615 -417148.97 -861359.26 -608914.8503 -1676645.41
## [14,] -91251.880 31426.914 -76601.44 197492.27 86531.6791 404503.12
## [15,] -66621.115 -509439.321 -220476.67 -985145.97 -634356.5562 -1965271.12
## [16,] -168179.792 -78088.997 -193821.35 91762.36 -22914.2327 180263.21
## [17,] -19962.380 64579.414 10581.06 153576.77 96933.1791 322126.62
## [18,] 1052.150 64425.944 23690.59 132173.30 90904.7085 278243.15
## [19,] 152508.032 90449.826 167869.47 -23763.82 44312.5908 -61153.97
## [20,] 90449.826 93918.620 126754.27 52969.97 72763.3849 100407.83
## [21,] 167869.473 126754.267 234540.91 -14774.38 77902.0320 -25513.53
## [22,] -23763.821 52969.973 -14774.38 154122.33 75606.7379 297812.18
## [23,] 44312.591 72763.385 77902.03 75606.74 75293.1497 160096.59
## [24,] -61153.968 100407.826 -25513.53 297812.18 160096.5908 602001.03
## [25,] 6902.767 71825.561 26982.21 141755.91 89312.3261 282875.77
## [26,] 50958.150 82865.944 80145.59 93604.30 84003.7085 190730.15
## [27,] 174139.444 17257.238 172371.88 -216141.41 -51613.9974 -427142.56
## [28,] 21469.179 71564.973 28722.62 133686.33 84358.7379 261165.18
## [29,] -51511.409 87971.385 -22626.97 261242.74 141827.1497 529637.59
## [30,] -15625.174 108861.620 23807.27 246006.97 148061.3849 496001.83
## [31,] 26327.826 102612.620 47627.27 187343.97 118992.3849 365221.83
## [32,] -35679.497 93257.297 -11732.06 254946.65 138918.0614 509483.50
## [33,] 23995.885 105216.679 56487.33 185564.03 125125.4438 370939.88
## [34,] 193642.120 109327.914 219560.56 -50188.73 47408.6791 -115578.88
## [,25] [,26] [,27] [,28] [,29] [,30]
## [1,] -57835.233 -26269.85 134767.44 -50502.821 -127679.41 -108745.17
## [2,] -493213.380 -321459.00 755272.30 -467003.968 -924257.56 -854855.32
## [3,] 59780.356 53011.74 -36218.97 60129.767 91330.18 94740.41
## [4,] -71156.321 -30673.94 148945.36 -72267.909 -144670.50 -122816.26
## [5,] 93487.856 75456.24 -94519.47 88356.267 155748.68 155944.91
## [6,] -22618.262 2243.12 102793.41 -16041.850 -75663.44 -53065.20
## [7,] 182477.444 135582.83 -221273.88 174761.856 325095.27 311399.50
## [8,] -57159.292 -31780.91 102074.38 -54681.880 -114035.47 -100083.23
## [9,] 280752.708 183352.09 -444621.62 258364.120 532113.53 494329.77
## [10,] 242889.503 160228.88 -382804.82 222420.914 460294.33 429036.56
## [11,] 209162.061 86273.44 -500852.26 190362.473 448470.88 385027.12
## [12,] -962903.615 -813951.23 813041.06 -927876.203 -1590516.79 -1595976.56
## [13,] -881545.674 -714954.29 886169.00 -836130.262 -1470925.85 -1480785.62
## [14,] 177544.856 103077.24 -332229.47 158864.267 355520.68 320862.91
## [15,] -979343.380 -740096.00 1180218.30 -925558.968 -1734250.56 -1681704.32
## [16,] 43765.944 -26806.67 -288294.38 25737.356 156276.77 110453.00
## [17,] 155771.356 113646.74 -203760.97 143522.767 284036.18 269584.41
## [18,] 138697.885 106936.27 -155194.44 132158.297 247029.71 236373.94
## [19,] 6902.767 50958.15 174139.44 21469.179 -51511.41 -15625.17
## [20,] 71825.561 82865.94 17257.24 71564.973 87971.38 108861.62
## [21,] 26982.208 80145.59 172371.88 28722.620 -22626.97 23807.27
## [22,] 141755.914 93604.30 -216141.41 133686.326 261242.74 246006.97
## [23,] 89312.326 84003.71 -51614.00 84358.738 141827.15 148061.38
## [24,] 282875.767 190730.15 -427142.56 261165.179 529637.59 496001.83
## [25,] 143039.503 107962.88 -166193.82 136650.914 249187.33 241543.56
## [26,] 107962.885 98734.27 -63111.44 105809.297 168817.71 175033.94
## [27,] -166193.821 -63111.44 447785.86 -138263.409 -371602.00 -320045.76
## [28,] 136650.914 105809.30 -138263.41 136718.326 231278.74 225140.97
## [29,] 249187.326 168817.71 -371602.00 231278.738 466730.15 436506.38
## [30,] 241543.561 175033.94 -320045.76 225140.973 436506.38 417626.62
## [31,] 187559.561 143844.94 -207574.76 181897.973 322076.38 315090.62
## [32,] 243632.238 167458.62 -349121.09 228932.650 448809.06 422643.30
## [33,] 189519.620 148147.00 -206489.70 180946.032 327199.44 320627.68
## [34,] -11111.144 51178.24 242234.53 5307.267 -99460.32 -51002.09
## [,31] [,32] [,33] [,34]
## [1,] -69652.174 -118325.50 -71752.115 79062.120
## [2,] -630193.321 -891043.64 -634504.262 249362.973
## [3,] 80090.414 92157.09 80423.473 26756.708
## [4,] -90795.262 -140615.59 -84691.203 82173.032
## [5,] 121946.914 153170.59 124523.973 7367.208
## [6,] -20558.203 -63676.53 -25067.144 94554.091
## [7,] 239784.503 316101.18 242801.561 -23898.203
## [8,] -71106.233 -108541.56 -71063.174 50548.061
## [9,] 360746.767 510911.44 365770.826 -137398.939
## [10,] 313465.561 441838.24 318366.620 -111455.144
## [11,] 266713.120 427625.80 257854.179 -262230.586
## [12,] -1271245.556 -1562001.88 -1303865.497 -215093.262
## [13,] -1190631.615 -1456852.94 -1199517.556 -180760.321
## [14,] 223722.914 337178.59 227733.973 -140340.792
## [15,] -1306463.321 -1691579.64 -1321204.262 39538.973
## [16,] 49391.003 139398.68 45472.061 -219943.703
## [17,] 197440.414 271896.09 204857.473 -45752.292
## [18,] 178253.944 237654.62 184504.003 -18257.762
## [19,] 26327.826 -35679.50 23995.885 193642.120
## [20,] 102612.620 93257.30 105216.679 109327.914
## [21,] 47627.267 -11732.06 56487.326 219560.561
## [22,] 187343.973 254946.65 185564.032 -50188.733
## [23,] 118992.385 138918.06 125125.444 47408.679
## [24,] 365221.826 509483.50 370939.885 -115578.880
## [25,] 187559.561 243632.24 189519.620 -11111.144
## [26,] 143844.944 167458.62 148147.003 51178.238
## [27,] -207574.762 -349121.09 -206489.703 242234.532
## [28,] 181897.973 228932.65 180946.032 5307.267
## [29,] 322076.385 448809.06 327199.444 -99460.321
## [30,] 315090.620 422643.30 320627.679 -51002.086
## [31,] 251679.620 317831.30 251270.679 7287.914
## [32,] 317831.297 434486.97 320263.356 -79425.409
## [33,] 251270.679 320263.36 254815.738 5727.973
## [34,] 7287.914 -79425.41 5727.973 250859.208eigen_decomp <- eigen(B)
values <- eigen_decomp$values
vectors <- eigen_decomp$vectors
values## [1] 2.593329e+07 2.496920e+06 3.433420e+05 1.164946e+05 9.142386e+04
## [6] 1.050316e+04 1.526936e-09 1.253976e-09 9.334625e-10 7.057659e-10
## [11] 6.746188e-10 5.278365e-10 1.609695e-10 1.244778e-10 1.037466e-10
## [16] 1.935234e-11 -8.800055e-11 -1.062780e-10 -1.363508e-10 -1.646751e-10
## [21] -1.728773e-10 -1.908670e-10 -2.237440e-10 -2.445036e-10 -2.550743e-10
## [26] -3.077544e-10 -3.753473e-10 -4.919893e-10 -5.207728e-10 -6.251737e-10
## [31] -6.504843e-10 -6.592162e-10 -8.339437e-10 -9.270070e-10vectors## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.029001990 -0.097207596 0.0628064825 -0.099668539 -0.014121155
## [2,] -0.249606787 -0.299167050 0.3159157898 0.438548329 0.003080997
## [3,] 0.030777060 -0.036672471 -0.0345681474 -0.124940875 -0.013415713
## [4,] -0.033858105 -0.113259566 0.0669477209 0.265975053 0.274184254
## [5,] 0.048325010 -0.018036064 -0.0226623623 -0.123033665 0.154678396
## [6,] -0.010843738 -0.115721509 0.1372673681 -0.299645194 0.037356298
## [7,] 0.094596489 0.027402873 -0.0669991493 0.020399129 -0.112358444
## [8,] -0.028185268 -0.063760406 0.0884834530 0.022673476 0.096615382
## [9,] 0.144396905 0.164782342 -0.0423838010 0.016427551 0.117428349
## [10,] 0.125673902 0.134019682 0.0007361369 0.084317101 0.108720957
## [11,] 0.104629195 0.350442915 0.1099222998 -0.177661202 -0.263190260
## [12,] -0.502938666 0.332943203 0.5413808772 -0.038292621 -0.121821280
## [13,] -0.465838349 0.239869480 -0.5568329311 0.346508825 -0.268264994
## [14,] 0.090799496 0.170815335 -0.0364794892 0.099116953 0.123160344
## [15,] -0.515330501 -0.051199764 -0.2484710380 -0.496490449 0.432573539
## [16,] 0.021642007 0.290784490 0.2028379543 0.157837134 0.050879062
## [17,] 0.080195520 0.042695115 -0.1375620717 0.089815354 0.161215434
## [18,] 0.071629432 0.013051856 -0.1642557498 0.115439690 -0.025065032
## [19,] 0.006358853 -0.236653739 0.0463769693 -0.088014593 -0.330339296
## [20,] 0.039513559 -0.143393479 0.0622979799 -0.045693185 0.074806838
## [21,] 0.018991001 -0.293204584 0.0628131485 0.153928347 0.262402016
## [22,] 0.073101646 0.066908844 0.0712739170 -0.142121154 -0.037823044
## [23,] 0.047951572 -0.069153327 -0.0395036413 0.151233035 0.075494155
## [24,] 0.146080654 0.136881070 -0.0357171617 0.047814143 0.109082678
## [25,] 0.073826773 0.009345708 -0.0423208223 -0.082227910 -0.002300992
## [26,] 0.056668507 -0.073203783 -0.0756718309 -0.014542579 0.019122847
## [27,] -0.084781365 -0.308789104 -0.2120917221 -0.020584352 -0.292137218
## [28,] 0.069966740 -0.005377223 -0.0764519699 -0.181886065 -0.202607796
## [29,] 0.128714184 0.118825179 -0.0542386824 0.077193464 0.028390344
## [30,] 0.125551677 0.055458786 -0.0191530138 0.033805205 0.095905765
## [31,] 0.097671301 -0.006440417 0.0308560025 -0.118154431 -0.156075988
## [32,] 0.125759620 0.097808161 -0.0203938271 -0.030397500 -0.046167316
## [33,] 0.099010718 -0.011958633 -0.0168734057 -0.005343188 -0.027384566
## [34,] -0.001447051 -0.308836321 0.1027147174 -0.032335289 -0.312024561
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.098604987 0.000000000 0.000000000 0.000000000 0.73601735
## [2,] 0.518409826 0.032089999 -0.101580690 -0.016389586 0.11463138
## [3,] 0.010726977 0.126418970 -0.608002977 0.194975915 -0.21552126
## [4,] -0.128298252 0.043656142 0.250032511 0.033632405 0.02488252
## [5,] -0.101715951 0.128112997 -0.049905165 -0.011008966 -0.11105806
## [6,] -0.028400650 0.482205683 0.002483104 0.014036185 0.05497054
## [7,] -0.087030782 -0.280694289 0.145323850 -0.377487490 -0.01730996
## [8,] -0.213752264 0.165656473 0.076043773 -0.230566067 -0.15357064
## [9,] 0.017799531 0.051755846 -0.364308294 -0.478996317 0.12461465
## [10,] -0.009597772 -0.444925834 -0.196600832 0.070180727 0.07962442
## [11,] 0.581142167 0.114719974 -0.020365593 -0.151666311 -0.05240049
## [12,] -0.330616076 -0.095759969 -0.269090027 0.001401874 0.06515581
## [13,] -0.104402327 0.246309819 -0.043638025 0.098851928 -0.04486862
## [14,] 0.186662477 -0.004315357 -0.085862063 0.304992919 0.10385017
## [15,] 0.245607589 -0.218653601 0.022293491 -0.126149254 -0.07695147
## [16,] 0.017471719 0.122339540 0.074680891 -0.231929232 -0.16578514
## [17,] 0.150289156 0.082912969 -0.109017616 0.016363368 0.22325761
## [18,] -0.037498086 0.065513792 -0.126353472 -0.151025507 0.13547275
## [19,] 0.013835671 -0.087105442 0.052595274 0.059693039 -0.09589414
## [20,] 0.003969032 0.132367726 -0.094121468 0.003414284 -0.10340484
## [21,] -0.107117045 0.109678202 -0.283930415 -0.056142287 -0.13363097
## [22,] -0.112324296 0.110292830 0.058055928 0.196953914 0.01227428
## [23,] 0.011400296 -0.035440359 -0.100667975 -0.114132593 -0.24820300
## [24,] -0.044132915 -0.232222582 -0.081163308 0.280932271 -0.09559208
## [25,] 0.082614094 0.082615845 -0.067659018 0.162971798 0.07334836
## [26,] -0.068696788 0.036546001 -0.142639103 0.061489268 0.14485815
## [27,] -0.009834239 -0.057486471 -0.219934392 -0.202479876 0.08992258
## [28,] -0.087291597 0.028641524 -0.047108884 -0.141696574 0.11614750
## [29,] -0.069976415 -0.116020263 -0.069503725 -0.132192419 -0.05000722
## [30,] -0.072095464 0.189930445 -0.041234055 -0.181421814 0.05376099
## [31,] -0.005909755 -0.062049294 -0.046652890 0.097194511 -0.15782235
## [32,] -0.026701674 0.237877942 0.070538279 0.107142508 0.01403375
## [33,] -0.076681649 -0.147660359 -0.195830897 0.104476878 0.08231215
## [34,] -0.019249549 -0.140612682 -0.028654943 -0.023531537 -0.14737458
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000000 0.0000000000 0.0000000000 0.000000000 0.00000000
## [2,] -0.085166388 0.0233951652 0.0803469226 0.020032720 -0.06579868
## [3,] -0.091470770 -0.0626912265 -0.0404716628 -0.087131904 0.04586359
## [4,] 0.295386267 -0.1887403847 0.1090399217 0.078636509 0.05493143
## [5,] -0.320424404 0.0954683782 0.0514307970 -0.055664749 -0.06141728
## [6,] -0.067965448 -0.5671409888 -0.1533100278 -0.060550323 0.04894095
## [7,] -0.062986932 -0.1488503919 -0.1209736197 0.025340016 0.08919321
## [8,] 0.305959463 -0.1656264424 -0.3113180829 -0.030357529 -0.06765720
## [9,] -0.031206391 -0.0665361077 0.0909082807 0.011370215 -0.05440884
## [10,] -0.005344126 -0.4128415710 -0.0679842615 -0.003343218 -0.16629876
## [11,] 0.237604587 -0.1215052465 0.0513473866 0.061892530 0.15102818
## [12,] 0.022894912 0.1157725514 -0.0326291606 0.055905893 -0.01566915
## [13,] 0.104761575 -0.1540854325 -0.0152649274 0.054763464 -0.04650044
## [14,] 0.238260828 -0.0194544416 0.0032241761 -0.203849819 -0.06939201
## [15,] 0.120183411 0.1016137192 0.0200563819 0.024518065 0.00620927
## [16,] -0.002008415 0.0242880932 0.0104294921 -0.035543428 0.11933112
## [17,] -0.044399784 0.0510795322 -0.3444202878 0.233438228 -0.21784960
## [18,] -0.075151305 0.0534254839 -0.0695074780 0.268009863 0.14237836
## [19,] 0.079086573 -0.0248787527 -0.0995001547 0.012374799 0.16812420
## [20,] 0.232722574 0.1146401775 -0.0002803059 0.580332297 0.24954546
## [21,] 0.036767803 -0.0402536635 0.1919757885 0.059256708 -0.01211154
## [22,] 0.107186574 0.0011083087 0.2186491951 0.252875872 -0.13240395
## [23,] 0.083262525 0.0939655651 -0.0085911459 -0.347604081 -0.08172804
## [24,] 0.046100576 -0.1865722399 0.3397394241 0.252830083 0.14136022
## [25,] 0.174338442 0.1604333198 -0.2943474960 0.057244609 -0.29628578
## [26,] 0.278896818 0.2159091099 -0.0930967387 -0.203607120 0.44405989
## [27,] -0.099833756 -0.0718521997 0.1507955913 0.053976544 0.06032584
## [28,] 0.261104214 0.0011023622 0.4761483932 -0.074195234 -0.21454770
## [29,] 0.003448137 0.2139633901 -0.2190272385 0.242454349 0.05602015
## [30,] 0.292826804 0.2104928161 0.1651346180 -0.080613824 -0.31501183
## [31,] -0.054265660 0.0113609572 -0.1447697706 0.167817814 -0.34337400
## [32,] -0.246678246 0.3191348235 0.0865882886 -0.091061862 0.10772359
## [33,] 0.261620923 0.0008748017 -0.1887409410 -0.229647982 0.26099304
## [34,] 0.240482066 0.0860858764 -0.0858544578 0.029694327 -0.24427812
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.00000000 0.000000000 0.0000000000 0.000000000 0.000000000
## [2,] -0.04403487 0.082724599 -0.0333704417 -0.060271923 0.061426566
## [3,] 0.02623884 0.255880432 0.0505548479 -0.041988439 0.066878073
## [4,] -0.02834791 0.110230383 -0.1312790638 0.038451790 -0.092337903
## [5,] 0.05574049 0.101224821 -0.0129759670 -0.040130859 -0.276055192
## [6,] -0.04257826 0.094707542 -0.1411110354 -0.039643271 -0.044254067
## [7,] -0.09057878 0.058734118 -0.1040147590 0.066102923 0.133580439
## [8,] 0.02649476 0.047451422 0.0587118305 0.178330523 0.194361208
## [9,] 0.09520011 -0.139591444 -0.0747261987 0.180142030 -0.028514656
## [10,] 0.06840047 0.007692870 -0.1558086355 -0.080796110 -0.189065817
## [11,] -0.11451248 -0.061653799 -0.0083043214 0.114267610 0.064726882
## [12,] -0.03606755 -0.020243087 -0.1027278317 0.050970625 0.057308211
## [13,] -0.03963518 -0.033443921 0.0093688932 0.007872011 -0.073332657
## [14,] 0.26489368 0.198115815 -0.2751208853 0.016729867 -0.155104390
## [15,] -0.01147930 0.082851889 0.0149295283 -0.069341009 -0.013553623
## [16,] 0.04638147 0.113892636 0.3594238589 -0.208606729 -0.283738804
## [17,] -0.50829929 0.088358024 0.2293140014 0.057003809 -0.168195684
## [18,] 0.19573977 0.232585871 -0.1485726393 -0.557010319 0.339336461
## [19,] 0.14717296 0.143192785 0.1683115407 -0.082140422 0.078476813
## [20,] 0.17162319 -0.239052299 -0.2771556580 -0.080586834 -0.312408145
## [21,] -0.11614997 -0.035354089 0.2633047339 0.085218168 0.153733912
## [22,] -0.24577892 0.040423837 -0.1418360393 0.092819272 -0.018796967
## [23,] -0.20916577 -0.101735154 -0.4749325060 -0.017659234 0.086592956
## [24,] -0.06104498 -0.020465219 0.2052041226 0.185593385 0.260014699
## [25,] 0.39432720 -0.064016274 0.1151726107 0.258852031 0.288773830
## [26,] -0.35966126 -0.009672119 -0.1080677638 0.008325749 0.175541829
## [27,] 0.10049297 -0.196077453 -0.0371812336 0.298150149 -0.186808622
## [28,] -0.13227639 0.358759607 0.0473239558 -0.176054574 -0.018242930
## [29,] -0.02724297 0.463218376 -0.1054599007 0.225122335 -0.083038919
## [30,] 0.14355725 -0.194862159 0.1091144321 -0.160861546 0.008079303
## [31,] -0.27290084 -0.332368524 -0.1134269795 -0.353882397 0.091843685
## [32,] -0.03022161 0.036728041 -0.1543288088 0.197418300 -0.094457675
## [33,] -0.01486881 -0.226980569 0.2718155395 -0.201827092 -0.317516343
## [34,] -0.04456938 0.257332884 -0.0006988779 0.068013769 -0.272806467
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.00000000 0.0000000000 0.000000000 0.000000000 0.000000000
## [2,] 0.16929816 0.0365795229 0.075791473 0.107300343 -0.022391071
## [3,] 0.12576922 0.0113549102 0.018302162 -0.437817892 -0.076679305
## [4,] 0.18016863 0.0612590259 -0.368174306 -0.389102868 0.112047768
## [5,] 0.07653175 -0.0776431725 -0.135466750 0.407444862 -0.027351354
## [6,] 0.02435475 -0.0912399645 -0.158405758 0.187233643 -0.051665170
## [7,] 0.12710171 -0.3364721465 0.171152105 -0.025854483 -0.156537166
## [8,] -0.02417595 0.3477239483 0.363174354 0.135997048 -0.078441483
## [9,] -0.21475582 0.0074058897 -0.255908155 -0.245800317 0.052099900
## [10,] 0.15020917 0.0941838671 0.012756469 0.241238847 -0.054468153
## [11,] 0.16487760 -0.1129604495 -0.021886300 0.071549246 -0.023755560
## [12,] 0.01557947 0.0004866872 -0.090555114 0.080637422 -0.014535331
## [13,] 0.03766797 -0.1382521831 -0.039086214 0.081393592 -0.019943970
## [14,] -0.31381425 0.0923796879 0.290507888 -0.010249354 -0.208935933
## [15,] 0.05885774 0.0868090468 -0.012818443 0.015434045 -0.058469847
## [16,] -0.22401596 0.2628665804 0.039130255 0.052475838 0.119786404
## [17,] -0.07895679 0.1589586983 -0.131518118 0.051495214 0.003769359
## [18,] 0.02324184 0.0553817397 0.003322629 0.141960236 -0.017164978
## [19,] 0.12308635 0.3619254321 -0.330732691 0.017492321 -0.091435567
## [20,] -0.10434270 -0.0956544933 0.053601596 0.080454534 0.106834015
## [21,] 0.01256548 -0.2866161295 0.246189086 0.135592385 0.024554989
## [22,] 0.29077722 0.1508013809 0.274389926 -0.080559925 -0.013285711
## [23,] 0.09148142 0.1448409168 -0.208506761 0.222301535 0.290450446
## [24,] -0.11433363 0.1066413644 -0.251315531 0.299452022 -0.125941077
## [25,] 0.04797871 -0.0955572695 -0.130368050 0.151506779 0.395791590
## [26,] -0.25075168 0.0078313239 -0.067871412 0.124941845 -0.155020741
## [27,] 0.01768661 0.4170947759 0.125057950 0.054444681 -0.031152457
## [28,] -0.04236678 0.0168721027 0.091382869 0.098703501 0.398739333
## [29,] 0.28044771 0.0109660631 0.010978897 0.007402113 0.008672042
## [30,] 0.30843592 0.0164216932 -0.166859909 0.064671270 -0.564691249
## [31,] -0.10882333 0.1358545542 0.038852611 -0.143951171 -0.013726752
## [32,] 0.18772471 0.0974117845 0.006435964 0.089872921 -0.095562251
## [33,] 0.38426483 -0.1142725854 0.095251616 0.042135534 0.196760945
## [34,] -0.27466245 -0.2996310666 -0.188438476 0.074706396 -0.223597700
## [,26] [,27] [,28] [,29] [,30]
## [1,] 0.0000000000 0.00000000 0.000000000 0.0000000000 0.000000000
## [2,] -0.0933168728 0.09698469 -0.207102211 0.1431773058 0.087034815
## [3,] -0.0004775527 0.27726690 -0.231477708 -0.0348039568 -0.032631486
## [4,] -0.1488145786 -0.10463820 -0.087373732 -0.2888477831 -0.086388137
## [5,] 0.0234569739 -0.04042486 -0.133530767 0.0525550295 0.261635701
## [6,] -0.0168774354 -0.13795850 -0.074467647 -0.0337650709 -0.044556665
## [7,] 0.0338809313 0.10523848 -0.334572798 0.1139323170 -0.400128163
## [8,] -0.2257849142 0.29344582 0.111647846 0.0210442552 0.162521657
## [9,] 0.0270737452 -0.03407468 0.193222473 0.2395042769 0.032326811
## [10,] -0.0445372386 -0.01856765 -0.102659433 0.0550207295 -0.135534846
## [11,] -0.0434804363 -0.08475536 0.141378788 -0.1899756317 0.058193083
## [12,] -0.0377805605 -0.02744337 0.063207422 -0.0555513879 -0.091924374
## [13,] -0.0218316434 -0.05244342 -0.023447416 0.1338779297 -0.015775767
## [14,] -0.0156363318 -0.20669133 0.112653986 0.0592096527 -0.147867455
## [15,] -0.0248269735 -0.04000226 0.003502137 -0.0502509437 -0.137097039
## [16,] 0.2052357606 -0.12295116 -0.316023369 -0.1402555897 -0.235821887
## [17,] 0.0467251402 0.19030940 0.118341111 0.0346305457 -0.192663991
## [18,] 0.1202228771 0.05355515 0.226774840 -0.3487863374 -0.055509559
## [19,] 0.0603234926 -0.20300488 0.186516824 0.4937964156 -0.242308928
## [20,] -0.0832614491 0.19799389 -0.104187775 0.2397031196 -0.080166879
## [21,] -0.0137972304 -0.43491568 0.250871640 -0.0003351395 -0.277478361
## [22,] 0.5897226905 -0.02711922 0.008781913 0.0614608043 -0.036484534
## [23,] 0.2213175727 0.09132579 0.117326786 -0.0142472082 -0.085496429
## [24,] -0.1134289791 0.17977540 -0.038769443 -0.0974323855 0.054429473
## [25,] 0.0971246308 -0.07220104 -0.308645005 -0.0947283686 -0.180608435
## [26,] 0.0477431812 -0.15632828 -0.368107556 0.0385857517 0.078424479
## [27,] 0.0409884452 -0.14143280 -0.146955340 -0.3833414139 -0.006123818
## [28,] -0.2867935965 0.09366380 -0.111967167 0.1595260331 -0.016123894
## [29,] -0.1534011291 -0.38886988 -0.036178680 0.0367835837 0.325917761
## [30,] 0.0190349271 0.02011845 -0.153449661 0.0336761022 0.021400905
## [31,] -0.3495627870 -0.34595050 -0.143038997 -0.0622339343 0.012541488
## [32,] -0.4167182163 0.11679482 0.115985498 -0.1145363449 -0.504984059
## [33,] -0.0664802386 0.06096201 0.169393750 -0.0931890601 0.050359501
## [34,] 0.0993285663 0.12707445 0.146335748 -0.2927396048 -0.042211407
## [,31] [,32] [,33] [,34]
## [1,] 0.651296562 0.00000000 0.000000000 0.0000000000
## [2,] -0.070109185 0.15764093 0.093059479 0.2258279763
## [3,] 0.225000201 -0.05740939 -0.073432752 -0.0775466497
## [4,] -0.025764094 0.02612722 -0.311300738 0.0568334042
## [5,] 0.096276012 0.05232596 -0.590914052 0.2323897560
## [6,] -0.142457661 -0.09220735 0.333428012 0.1007904479
## [7,] 0.021834167 -0.19384804 -0.127244418 0.3051650186
## [8,] 0.127445792 0.16599446 -0.145728973 0.0536496859
## [9,] -0.097958479 0.32727358 0.044351960 0.2832015102
## [10,] -0.050646707 0.33296669 -0.031334215 -0.4287961063
## [11,] 0.160669878 -0.01847368 -0.283044293 -0.1436456540
## [12,] -0.157097209 -0.16600151 -0.098999596 0.0159159076
## [13,] 0.150863570 0.12052991 0.007837372 0.0373265337
## [14,] -0.038204723 -0.25680494 -0.110876783 0.2852080440
## [15,] 0.050917955 0.10383261 0.087017758 0.0929988569
## [16,] 0.240056528 0.07853062 0.159148288 0.0153738192
## [17,] -0.189096635 -0.27760088 -0.123674280 -0.0393176129
## [18,] -0.120672486 0.07211858 -0.067131708 0.0615985620
## [19,] 0.050321263 -0.01491584 -0.151743250 0.0296537932
## [20,] 0.086436246 -0.11127830 0.022780834 -0.1153217146
## [21,] 0.115068409 -0.01906276 -0.091663585 -0.1428723067
## [22,] -0.047077253 0.28257045 0.001702725 0.1986630133
## [23,] 0.302618868 -0.22526714 0.135251363 0.0013892147
## [24,] 0.141406281 -0.08455361 0.179608872 0.3125458536
## [25,] -0.074251755 0.09229777 -0.035886404 0.0615998712
## [26,] -0.177017887 0.24949327 -0.086673289 -0.1099772525
## [27,] -0.142002826 -0.20189467 -0.050841660 0.0089614469
## [28,] -0.167013296 -0.08398920 -0.014602063 -0.0327534765
## [29,] 0.087043362 -0.09702597 0.311602500 0.0003707925
## [30,] -0.048701592 -0.17747829 0.119373514 -0.1089284991
## [31,] 0.156404402 0.08999960 -0.020338660 0.2389375219
## [32,] -0.003389807 0.30219098 0.102335167 0.0216692787
## [33,] -0.101788985 0.02712896 0.097247062 0.3664431142
## [34,] 0.095853159 0.24265272 0.086870966 0.0719542285pos_idx <- which(values > 0)
k <- 2
lambda <- diag( sqrt(values[pos_idx][1:k]) )
vec <- vectors[, pos_idx][, 1:k]
lambda## [,1] [,2]
## [1,] 5092.474 0.000
## [2,] 0.000 1580.164vec## [,1] [,2]
## [1,] -0.029001990 -0.097207596
## [2,] -0.249606787 -0.299167050
## [3,] 0.030777060 -0.036672471
## [4,] -0.033858105 -0.113259566
## [5,] 0.048325010 -0.018036064
## [6,] -0.010843738 -0.115721509
## [7,] 0.094596489 0.027402873
## [8,] -0.028185268 -0.063760406
## [9,] 0.144396905 0.164782342
## [10,] 0.125673902 0.134019682
## [11,] 0.104629195 0.350442915
## [12,] -0.502938666 0.332943203
## [13,] -0.465838349 0.239869480
## [14,] 0.090799496 0.170815335
## [15,] -0.515330501 -0.051199764
## [16,] 0.021642007 0.290784490
## [17,] 0.080195520 0.042695115
## [18,] 0.071629432 0.013051856
## [19,] 0.006358853 -0.236653739
## [20,] 0.039513559 -0.143393479
## [21,] 0.018991001 -0.293204584
## [22,] 0.073101646 0.066908844
## [23,] 0.047951572 -0.069153327
## [24,] 0.146080654 0.136881070
## [25,] 0.073826773 0.009345708
## [26,] 0.056668507 -0.073203783
## [27,] -0.084781365 -0.308789104
## [28,] 0.069966740 -0.005377223
## [29,] 0.128714184 0.118825179
## [30,] 0.125551677 0.055458786
## [31,] 0.097671301 -0.006440417
## [32,] 0.125759620 0.097808161
## [33,] 0.099010718 -0.011958633
## [34,] -0.001447051 -0.308836321- Membentuk koordinat objek berdasarkan vektor eigen
# membentuk koordinat MDS
X <- vec %*% lambda
colnames(X) <- c("Dim1", "Dim2")
mds_coords <- as.data.frame(X)
mds_coords$Label <- labels
mds_coords## Dim1 Dim2 Label
## 1 -147.691888 -153.603986 1
## 2 -1271.116154 -472.733132 2
## 3 156.731386 -57.948535 3
## 4 -172.421530 -178.968738 4
## 5 246.093875 -28.499947 5
## 6 -55.221456 -182.859013 6
## 7 481.730191 43.301045 7
## 8 -143.532755 -100.751927 8
## 9 735.337530 260.383196 9
## 10 639.991119 211.773134 10
## 11 532.821487 553.757430 11
## 12 -2561.202239 526.105007 12
## 13 -2372.269827 379.033220 13
## 14 462.394100 269.916316 14
## 15 -2624.307343 -80.904046 15
## 16 110.211366 459.487309 16
## 17 408.393627 67.465302 17
## 18 364.771043 20.624079 18
## 19 32.382296 -373.951821 19
## 20 201.221782 -226.585275 20
## 21 96.711185 -463.311456 21
## 22 372.268254 105.726975 22
## 23 244.192147 -109.273627 23
## 24 743.911978 216.294598 24
## 25 375.960947 14.767755 25
## 26 288.582916 -115.674015 26
## 27 -431.746925 -487.937559 27
## 28 356.303826 -8.496896 28
## 29 655.473675 187.763321 29
## 30 639.368689 87.634002 30
## 31 497.388592 -10.176917 31
## 32 640.427637 154.552977 32
## 33 504.209537 -18.896606 33
## 34 -7.369069 -488.012171 34- Menghitung matrik D yang merupakan jarak euclidean dari koordinat yang terbentuk
# menghitung jarak euclidean dari koordinat
D_hat <- dist(mds_coords[,1:2])
as.matrix(D_hat)## 1 2 3 4 5 6 7
## 1 0.00000 1167.8722 319.09794 35.42493 413.18065 96.98782 659.50265
## 2 1167.87221 0.0000 1486.87419 1137.28950 1580.90777 1249.97077 1827.22784
## 3 319.09794 1486.8742 0.00000 350.69578 94.08971 246.02161 340.40520
## 4 35.42493 1137.2895 350.69578 0.00000 444.74262 117.26462 690.88228
## 5 413.18065 1580.9078 94.08971 444.74262 0.00000 338.55229 246.33282
## 6 96.98782 1249.9708 246.02161 117.26462 338.55229 0.00000 582.63663
## 7 659.50265 1827.2278 340.40520 690.88228 246.33282 582.63663 0.00000
## 8 53.01546 1187.3560 303.29966 83.38124 396.26918 120.58383 641.64243
## 9 975.25706 2136.1919 660.39394 1008.49226 568.16620 906.33723 333.82831
## 10 868.30004 2029.9950 553.43450 901.49516 461.39592 799.40919 231.14793
## 11 981.55928 2075.5418 718.07239 1016.98346 649.02726 942.54883 513.00686
## 12 2507.39637 1631.5636 2779.97873 2490.66302 2861.55519 2604.33670 3080.99618
## 13 2287.45479 1392.1370 2566.47622 2269.51508 2649.88901 2384.20554 2873.67921
## 14 742.68052 1885.8913 448.24665 777.48870 368.56214 687.70005 227.43871
## 15 2477.68226 1408.7783 2781.13347 2453.84611 2870.87954 2571.10815 3108.51992
## 16 665.12783 1666.4635 519.52282 698.21736 506.55268 663.30748 557.88641
## 17 598.41685 1764.2470 281.18057 630.93263 188.54850 526.87874 77.21504
## 18 541.27043 1708.6627 222.38290 573.07343 128.44236 466.68948 119.13726
## 19 284.56964 1307.2360 339.58912 282.77732 406.21378 210.21627 613.19938
## 20 356.46461 1492.7718 174.40684 376.66518 203.10416 260.14442 389.26032
## 21 394.52703 1367.8598 409.78229 391.51398 459.75671 318.96254 636.31428
## 22 581.04311 1742.2194 270.63964 614.60443 184.21955 515.78031 126.01156
## 23 394.38341 1558.2882 101.40833 422.40308 80.79606 308.32339 282.31782
## 24 965.28877 2129.5769 648.06662 997.94800 554.74970 893.27367 314.11154
## 25 550.05576 1717.7078 230.97459 581.59880 136.88517 474.31488 109.55036
## 26 437.92053 1600.0476 143.93421 465.32926 96.97751 350.30739 250.15783
## 27 438.70970 839.5069 728.83282 403.37500 818.87183 484.60742 1056.71893
## 28 524.46901 1692.3389 205.60794 555.52781 112.01051 446.93982 135.70114
## 29 872.70073 2036.6649 555.98398 905.48488 462.99203 801.52884 225.95607
## 30 823.20114 1990.9705 504.11610 854.44741 410.06362 745.40052 163.75380
## 31 660.83292 1827.9954 343.99049 690.75052 251.96184 578.96198 55.72323
## 32 846.22284 2011.8369 528.31710 878.61283 434.74992 773.15879 193.80885
## 33 665.67375 1832.4161 349.66572 695.30762 258.29425 582.96373 66.13523
## 34 362.65594 1263.8394 460.30826 350.35719 524.78086 308.88234 722.15775
## 8 9 10 11 12 13 14
## 1 53.01546 975.25706 868.30004 981.5593 2507.3964 2287.4548 742.6805
## 2 1187.35603 2136.19192 2029.99503 2075.5418 1631.5636 1392.1370 1885.8913
## 3 303.29966 660.39394 553.43450 718.0724 2779.9787 2566.4762 448.2466
## 4 83.38124 1008.49226 901.49516 1016.9835 2490.6630 2269.5151 777.4887
## 5 396.26918 568.16620 461.39592 649.0273 2861.5552 2649.8890 368.5621
## 6 120.58383 906.33723 799.40919 942.5488 2604.3367 2384.2055 687.7001
## 7 641.64243 333.82831 231.14793 513.0069 3080.9962 2873.6792 227.4387
## 8 0.00000 950.17449 843.55295 941.1894 2497.6139 2279.7944 710.3114
## 9 950.17449 0.00000 107.02278 356.4845 3307.2319 3109.8716 273.1099
## 10 843.55295 107.02278 0.00000 358.3833 3216.5888 3016.9010 186.8725
## 11 941.18944 356.48449 358.38330 0.0000 3094.1473 2910.3409 292.4479
## 12 2497.61393 3307.23185 3216.58879 3094.1473 0.0000 239.4276 3034.4303
## 13 2279.79445 3109.87159 3016.90105 2910.3409 239.4276 0.0000 2836.7633
## 14 710.31141 273.10986 186.87250 292.4479 3034.4303 2836.7633 0.0000
## 15 2480.85398 3376.93510 3277.39292 3220.2884 610.2805 524.4666 3106.5738
## 16 615.02364 656.06796 584.83237 432.9967 2672.2441 2483.7846 399.9623
## 17 576.99200 379.61774 272.87753 501.9585 3004.8045 2798.0643 209.5291
## 18 522.59438 441.36601 335.08813 558.9921 2969.3148 2760.4075 267.7254
## 19 324.93736 946.85108 843.95628 1054.0796 2745.3202 2519.7893 774.2586
## 20 367.00098 722.78484 620.22304 847.8756 2863.1327 2643.7914 561.0034
## 21 434.93283 965.18266 866.54041 1106.6261 2836.0974 2608.7184 819.3577
## 22 555.59357 394.63635 287.96062 475.9292 2963.4383 2758.1127 187.2987
## 23 387.81854 614.71128 509.63502 723.1301 2876.4464 2661.6380 437.4895
## 24 942.37819 44.91465 104.01917 398.0457 3319.6028 3120.4283 286.5791
## 25 532.18277 435.29125 329.42837 561.3511 2981.3409 2772.2665 269.3909
## 26 432.37324 583.95951 480.32214 712.5945 2921.1566 2706.4502 422.9542
## 27 482.68014 1386.38742 1279.92870 1419.6903 2358.5721 2125.3864 1172.1052
## 28 508.27906 464.71825 359.16203 589.3118 2966.0817 2755.9561 297.9414
## 29 849.50122 107.94388 28.56888 385.9990 3234.4210 3033.7790 209.8305
## 30 805.24774 197.61655 124.14069 478.1457 3230.4661 3025.7032 254.0607
## 31 647.28974 360.30886 263.81301 565.0464 3105.2498 2895.9323 282.2709
## 32 824.48438 142.15457 57.22182 413.4529 3223.1172 3021.0491 212.1430
## 33 652.89384 362.51532 267.66615 573.3684 3113.4830 2903.8736 291.8243
## 34 410.50097 1054.37598 953.29675 1173.4947 2747.8169 2518.8337 891.7023
## 15 16 17 18 19 20 21
## 1 2477.6823 665.1278 598.41685 541.27043 284.5696 356.4646 394.5270
## 2 1408.7783 1666.4635 1764.24699 1708.66271 1307.2360 1492.7718 1367.8598
## 3 2781.1335 519.5228 281.18057 222.38290 339.5891 174.4068 409.7823
## 4 2453.8461 698.2174 630.93263 573.07343 282.7773 376.6652 391.5140
## 5 2870.8795 506.5527 188.54850 128.44236 406.2138 203.1042 459.7567
## 6 2571.1081 663.3075 526.87874 466.68948 210.2163 260.1444 318.9625
## 7 3108.5199 557.8864 77.21504 119.13726 613.1994 389.2603 636.3143
## 8 2480.8540 615.0236 576.99200 522.59438 324.9374 367.0010 434.9328
## 9 3376.9351 656.0680 379.61774 441.36601 946.8511 722.7848 965.1827
## 10 3277.3929 584.8324 272.87753 335.08813 843.9563 620.2230 866.5404
## 11 3220.2884 432.9967 501.95849 558.99206 1054.0796 847.8756 1106.6261
## 12 610.2805 2672.2441 3004.80448 2969.31484 2745.3202 2863.1327 2836.0974
## 13 524.4666 2483.7846 2798.06430 2760.40755 2519.7893 2643.7914 2608.7184
## 14 3106.5738 399.9623 209.52915 267.72538 774.2586 561.0034 819.3577
## 15 0.0000 2787.4030 3036.32815 2990.80216 2672.8032 2829.2822 2747.7586
## 16 2787.4030 0.0000 492.53824 507.34758 837.0652 692.0827 922.8975
## 17 3036.3281 492.5382 0.00000 64.00805 579.8565 359.7025 615.5241
## 18 2990.8022 507.3476 64.00805 0.00000 515.9190 296.4133 553.2176
## 19 2672.8032 837.0652 579.85653 515.91901 0.0000 224.1064 110.1061
## 20 2829.2822 692.0827 359.70254 296.41327 224.1064 0.0000 258.7697
## 21 2747.7586 922.8975 615.52409 553.21758 110.1061 258.7697 0.0000
## 22 3002.3818 440.2501 52.62127 85.43250 587.8896 373.7490 632.2471
## 23 2868.6398 584.3285 241.24422 177.23624 338.9955 124.9339 383.5276
## 24 3381.3057 678.7630 367.04594 426.65537 924.4811 700.4679 938.4739
## 25 3001.7933 518.0717 61.87819 12.62975 518.7959 297.9682 553.6607
## 26 2913.0978 602.1852 218.84839 156.14673 363.7941 141.1853 397.0725
## 27 2230.0219 1091.4819 1007.12883 945.02688 477.9212 684.8025 529.0316
## 28 2981.4905 528.7445 92.10648 30.32697 488.3467 267.6060 523.6837
## 29 3290.7667 609.2166 274.80932 335.32603 838.9081 614.8411 857.9708
## 30 3268.0248 646.7475 231.85395 282.65562 762.5575 539.1720 773.3163
## 31 3122.4971 608.6795 118.10342 136.14740 590.3923 366.8070 604.8746
## 32 3273.2147 611.6488 247.83875 306.46942 805.6280 581.5223 823.0334
## 33 3129.1313 619.7465 128.99251 144.93094 590.4957 367.3366 602.9589
## 34 2648.4152 954.7672 693.83992 630.23733 120.7888 334.4461 106.9711
## 22 23 24 25 26 27 28
## 1 581.04311 394.38341 965.28877 550.05576 437.92053 438.7097 524.46901
## 2 1742.21939 1558.28818 2129.57686 1717.70780 1600.04762 839.5069 1692.33894
## 3 270.63964 101.40833 648.06662 230.97459 143.93421 728.8328 205.60794
## 4 614.60443 422.40308 997.94800 581.59880 465.32926 403.3750 555.52781
## 5 184.21955 80.79606 554.74970 136.88517 96.97751 818.8718 112.01051
## 6 515.78031 308.32339 893.27367 474.31488 350.30739 484.6074 446.93982
## 7 126.01156 282.31782 314.11154 109.55036 250.15783 1056.7189 135.70114
## 8 555.59357 387.81854 942.37819 532.18277 432.37324 482.6801 508.27906
## 9 394.63635 614.71128 44.91465 435.29125 583.95951 1386.3874 464.71825
## 10 287.96062 509.63502 104.01917 329.42837 480.32214 1279.9287 359.16203
## 11 475.92923 723.13006 398.04567 561.35114 712.59451 1419.6903 589.31181
## 12 2963.43835 2876.44636 3319.60276 2981.34087 2921.15658 2358.5721 2966.08173
## 13 2758.11268 2661.63800 3120.42832 2772.26653 2706.45018 2125.3864 2755.95605
## 14 187.29871 437.48955 286.57914 269.39094 422.95417 1172.1052 297.94138
## 15 3002.38180 2868.63977 3381.30573 3001.79328 2913.09777 2230.0219 2981.49052
## 16 440.25014 584.32855 678.76296 518.07173 602.18515 1091.4819 528.74447
## 17 52.62127 241.24422 367.04594 61.87819 218.84839 1007.1288 92.10648
## 18 85.43250 177.23624 426.65537 12.62975 156.14673 945.0269 30.32697
## 19 587.88963 338.99552 924.48111 518.79591 363.79415 477.9212 488.34666
## 20 373.74902 124.93388 700.46787 297.96822 141.18525 684.8025 267.60602
## 21 632.24713 383.52760 938.47390 553.66069 397.07248 529.0316 523.68370
## 22 0.00000 250.25736 387.74251 91.03415 236.68890 999.4388 115.33410
## 23 250.25736 0.00000 596.41812 180.96762 44.84981 774.7774 150.74806
## 24 387.74251 596.41812 0.00000 419.52477 563.49598 1370.4440 448.07510
## 25 91.03415 180.96762 419.52477 0.00000 157.00311 951.3699 30.45729
## 26 236.68890 44.84981 563.49598 157.00311 0.00000 810.8361 126.77956
## 27 999.43884 774.77739 1370.44401 951.36988 810.83613 0.0000 922.43555
## 28 115.33410 150.74806 448.07510 30.45729 126.77956 922.4355 0.00000
## 29 294.84788 507.32972 92.92668 328.71695 476.11243 1280.0861 357.79976
## 30 267.71253 441.51683 165.77952 273.30044 405.44396 1215.9652 298.94291
## 31 170.55442 271.89814 334.75831 123.96334 233.94326 1044.7718 141.09477
## 32 272.56822 476.03260 120.50326 299.13632 443.64100 1249.9410 327.58449
## 33 181.49253 275.27631 335.81567 132.59333 236.34870 1046.9068 148.27088
## 34 704.73447 454.67123 1029.79184 632.24169 475.62935 424.3779 601.82462
## 29 30 31 32 33 34
## 1 872.70073 823.20114 660.83292 846.22284 665.67375 362.6559
## 2 2036.66490 1990.97053 1827.99543 2011.83685 1832.41614 1263.8394
## 3 555.98398 504.11610 343.99049 528.31710 349.66572 460.3083
## 4 905.48488 854.44741 690.75052 878.61283 695.30762 350.3572
## 5 462.99203 410.06362 251.96184 434.74992 258.29425 524.7809
## 6 801.52884 745.40052 578.96198 773.15879 582.96373 308.8823
## 7 225.95607 163.75380 55.72323 193.80885 66.13523 722.1578
## 8 849.50122 805.24774 647.28974 824.48438 652.89384 410.5010
## 9 107.94388 197.61655 360.30886 142.15457 362.51532 1054.3760
## 10 28.56888 124.14069 263.81301 57.22182 267.66615 953.2967
## 11 385.99902 478.14575 565.04640 413.45287 573.36837 1173.4947
## 12 3234.42097 3230.46608 3105.24978 3223.11725 3113.48296 2747.8169
## 13 3033.77898 3025.70323 2895.93232 3021.04905 2903.87356 2518.8337
## 14 209.83050 254.06072 282.27085 212.14297 291.82432 891.7023
## 15 3290.76673 3268.02483 3122.49705 3273.21470 3129.13132 2648.4152
## 16 609.21664 646.74752 608.67946 611.64879 619.74650 954.7672
## 17 274.80932 231.85395 118.10342 247.83875 128.99251 693.8399
## 18 335.32603 282.65562 136.14740 306.46942 144.93094 630.2373
## 19 838.90808 762.55751 590.39227 805.62799 590.49568 120.7888
## 20 614.84107 539.17202 366.80697 581.52227 367.33658 334.4461
## 21 857.97080 773.31628 604.87461 823.03344 602.95893 106.9711
## 22 294.84788 267.71253 170.55442 272.56822 181.49253 704.7345
## 23 507.32972 441.51683 271.89814 476.03260 275.27631 454.6712
## 24 92.92668 165.77952 334.75831 120.50326 335.81567 1029.7918
## 25 328.71695 273.30044 123.96334 299.13632 132.59333 632.2417
## 26 476.11243 405.44396 233.94326 443.64100 236.34870 475.6294
## 27 1280.08606 1215.96516 1044.77177 1249.94095 1046.90683 424.3779
## 28 357.79976 298.94291 141.09477 327.58449 148.27088 601.8246
## 29 0.00000 101.41623 253.32041 36.45971 256.10382 946.5902
## 30 101.41623 0.00000 172.41033 66.92735 172.09523 865.8165
## 31 253.32041 172.41033 0.00000 218.16532 11.07060 695.0589
## 32 36.45971 66.92735 218.16532 0.00000 220.54507 912.4311
## 33 256.10382 172.09523 11.07060 220.54507 0.00000 694.1052
## 34 946.59021 865.81652 695.05887 912.43112 694.10524 0.0000- Validitas model dengan menghitung STRESS dan \(R^2\)
# menghiung stress
num <- sum((D - D_hat)^2)
den <- sum(D^2)
stress <- sqrt(num / den)
stress## [1] 0.02528328# menghitung R-Square
eig_pos <- values[values > 0]
R2 <- sum(eig_pos[1:2]) / sum(eig_pos)
R2## [1] 0.9806235- Visualisasi : plot hasil MDS
# plot MDS
ggplot(mds_coords, aes(x = Dim1, y = Dim2)) +
geom_point(size = 3) +
geom_text(aes(label = Label), vjust = -0.8) +
theme_minimal() +
labs(title = "Plot MDS (Manual)", x = "Dimensi 1", y = "Dimensi 2")
3.2 Interpretasi Hasil
Plot MDS dua dimensi yang dihasilkan menunjukkan posisi relatif dari seluruh sarana kesehatan berdasarkan kemiripan atau ketidakmiripan dalan data.
Objek yang berdekatan
Objek yang berdekatan menandakan bahwa objek tersebut memiliki karakteristik yang mirip. Terlihat bahwa sebagian besar objek berkumpul di satu cluster sebelah kanan atas. Hal ini menunjukkan bahwa sarana kesehatan memiliki profil sarana kesehatan yang sama baik dari segi rumah sakit, rumah sakit bersalin, dan lainnya.Dimensi 1
Dimensi 1 (horizontal) menunjukkan variasi terbesar yaitu membedakan objek berdasarkan kapasitas fasilitas kesehatan. Objek yang jauh ke kanan memiliki skor yang tinggi sementara objek yang jauh kek kiri memiliki skor yang rendah.Dimensi 2
Dimensi 2 (vertikal) menunjukkan variasi tambahan yaitu pemisahan objek berdasarkan pola lainnya yang tidak dijelaskan oleh dimensi 1. Titik yang tinggi ke atas memiliki skor besar dan titik yang jauh ke bawah memiliki skor rendah.Validitas Model
Berdasarkan nilai stress yang diperoleh yaitu 0.0252 atau setara dengan 2.52%, dapat disimpulkan bahwa kriteria MDS sangat baik dan cukup representatif. Koefisien determinasi (\(R^2\)) yang cukup tinggi yaitu 0.9806 atau setara 98% menunjukkan bahwa variasi jarak antar objek dapat dijelaskan oleh dimensi 1 dan 2. Sehingga, dapat disimpulkan bahwa model MDS dapat dipercaya dan menangkap struktur data dengan sangat baik.
4. PENUTUP
4.1 Kesimpulan
Berdasarkan hasil yang sudah diperoleh dapat disimpulkan bahwa:
Berdasarkan matriks jarak ketidaksamaan, dapat disimpulkan bahwa sebagian besar provinsi memiliki kemiripan yang cukup tinggi dalam ketersediaan sarana kesehatan. Namun, terdapat beberapa provinsi yang memiliki karakteristik yang berbeda dari mayoritas.
MDS berhasil memetakan seluruh provinsi dalam ruang dua dimensi dengan stress rendah dan \(R^2\) tinggi, yang menunjukkan bahwa model MDS representatif dan dapat dipercaya.
Berdasarkan plot MDS tersebut dapat diketahui visualisasi pola penyebaran ketersediaan fasilitas kesehatan di tiap provinsi. Secara keseluruhan, pemetaan ini membantu mengidentifikasi posisi relatif tiap provinsi dan memberikan gambaran mengenai disparitas sarana kesehatan antar wilayah di Indonesia.
4.2 Daftar Pustaka
Aswin, & Wahidun, A. (2016). ANALISIS ATRIBUT PRODUK SAMSUNG DAN ASUS MENGGUNAKAN METODE MULTIDIMENSIONAL SCALING (MDS) DI BANDAR LAMPUNG. Jurnal Bisnis Darmajaya, 2(2), 68.
Kuswandari, R., Arofah, I., & Setiawan, T. H. (2021). ANALISIS POSITIONING MEREK LIPSTIK BERDASARKAN PERSEPSI KONSUMEN DENGAN MENGGUNAKAN METODE MULTIDIMENSIONAL SCALING. Jurnal Syntax Admiration, 2(5), 893-894.
Mahida, M. (2020). Pendekatan Multidimensional Scaling untuk Penilaian Status Keberlanjutan ATCS Kota Pintar Semarang. Warta Penelitian Perhubungan, 32(2), 106-108.
Pradita, D., Satyahadewi, N., & Perdana, H. (2019). ANALISIS PERBANDINGAN METODE MULTIDIMENSIONAL SCALING (MDS) DAN WEIGHTED MULTIDIMENSIONAL SCALING (WMDS). Buletin Ilmiah Mat. Stat. dan Terapannya, 8(1), 149.