Unsupervised Learning (FCM analysis)
Tardha Ghaida Abdurrahman
2023-07-20
Judul: Algoritma Fuzzy C-means untuk Pengambilan Keputusan Investasi pada Perusahaan Sektor Keuangan
Pengantar
Berinvestasi di pasar saham saat ini sudah semakin meluas dan populer. Dalam berinvestasi, berlaku hukum bahwa risiko yang harus ditanggung investor sebanding dengan imbal hasil yang ditawarkan. Investor yang bijak akan memilih perusahaan yang memiliki nilai saham yang efisien. Analisis rasio keuangan terhadap laporan keuangan merupakan salah satu tolak ukur yang dapat digunakan untuk melakukan penilaian investasi. Penelitian ini bertujuan untuk mengelompokkan perusahaan sektor keuangan berdasarkan indikator rasio keuangan. Data yang digunakan adalah perusahaan sektor keuangan yang terdaftar di BEI pada tahun 2022 melalui situs resmi www.idx.co.id. Indikator rasio keuangan yang digunakan dalam penelitian ini adalah price to book value, earning per share, return on equity, price earning ratio, dividend yield dan debt to equity ratio pada tanggal 30 Desember 2022 melalui situs resmi www.stockbit.com.
Pembatasan Masalah
- Keputusan Investasi pada penelitian ini mengacu pada analisis fundamental berdasarkan rasio keuangan diantaranya PBV, EPS, ROE, PER, DY, DER.
- Perusahaan yang diteliti adalah perusahaan sektor keuangan yang terdaftar dan tercatat di Bursa Efek Indonesia pada tahun 2022.
Rumusan Masalah
- Bagaimana hasil analisis menggunakan algoritma Fuzzy C-Means untuk pengambilan keputusan investasi pada perusahaan sektor keuangan berdasarkan indikator rasio keuangan?
- Bagaimana perbandingan hasil validitas klaster menggunakan indeks Partition Entropy dan indeks Partition Coefficient dalam pemilihan klaster optimal?
Tujuan Penelitian
- Mengetahui hasil keputusan investasi pada perusahaan sektor keuangan berdasarkan indikator rasio keuangan menggunakan algoritma Fuzzy C-Means.
- Mengetahui perbandingan hasil validitas klaster menggunakan indeks Partition Entropy dan indeks Partition Coefficient
Memanggil Fungsi Library
library(readr)## Warning: package 'readr' was built under R version 4.3.2library(ggcorrplot)## Warning: package 'ggcorrplot' was built under R version 4.3.2## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.3.2library(ppclust)## Warning: package 'ppclust' was built under R version 4.3.2library(fclust)## Warning: package 'fclust' was built under R version 4.3.2library(clusterSim)## Warning: package 'clusterSim' was built under R version 4.3.2## Loading required package: cluster## Loading required package: MASS## Registered S3 method overwritten by 'e1071':
## method from
## print.fclust fclustlibrary(factoextra)## Warning: package 'factoextra' was built under R version 4.3.2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBaMemanggil dataset
SKRIPSI <- read_csv("D:/Saham.csv")## Rows: 101 Columns: 6
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (6): PBV, EPS, ROE, PER, DY, DER
##
## â„ą Use `spec()` to retrieve the full column specification for this data.
## â„ą Specify the column types or set `show_col_types = FALSE` to quiet this message.dat <- data.frame(SKRIPSI)
str(dat)## 'data.frame': 101 obs. of 6 variables:
## $ PBV: num 0.98 0.57 0.24 1.45 4.12 2.11 0.52 1.42 -0.21 2.8 ...
## $ EPS: num 102.63 -19.61 11.95 96.73 6.57 ...
## $ ROE: num 13.48 -8.61 6.08 4.79 5.28 ...
## $ PER: num 6.64 -1.57 24.76 57.12 75.84 ...
## $ DY : num 7.34 0 0 0.66 0 11.4 2.95 0 0 0 ...
## $ DER: num 0 0 0.97 0 0 0 0.06 0 0 0 ...Analisis Deskriptif
summary(dat)## PBV EPS ROE PER
## Min. :-0.21 Min. :-547.8 Min. :-44.800 Min. :-5200.00
## 1st Qu.: 0.65 1st Qu.: 0.4 1st Qu.: 0.500 1st Qu.: 0.86
## Median : 1.33 Median : 15.9 Median : 5.080 Median : 10.55
## Mean : 2.40 Mean : 116.5 Mean : 3.753 Mean : -19.85
## 3rd Qu.: 2.57 3rd Qu.: 104.1 3rd Qu.: 10.000 3rd Qu.: 31.68
## Max. :14.73 Max. :1600.0 Max. : 43.920 Max. : 1000.00
## DY DER
## Min. : 0.000 Min. :0.0000
## 1st Qu.: 0.000 1st Qu.:0.0000
## Median : 0.000 Median :0.0000
## Mean : 1.442 Mean :0.3228
## 3rd Qu.: 1.810 3rd Qu.:0.1200
## Max. :13.890 Max. :4.9500Pembentukan Klaster berjumlah 2
# membangun matriks partisi awal
set.seed(123)
u0_c2 <- inaparc::imembrand(nrow(dat), k=2)$u
# membentuk model
fcm.c2 <- fcm(dat, centers=2, u0_c2)
summary(fcm.c2)## Summary for 'fcm.c2'
##
## Number of data objects: 101
##
## Number of clusters: 2
##
## Crisp clustering vector:
## [1] 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
## [38] 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [75] 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
##
## Initial cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 0.37 185.78 4.11 9.34 4.26 0.02
## Cluster 2 3.45 -109.87 -21.07 -5.87 0.02 0.00
##
## Final cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 2.113795 1061.8563 18.099124 -303.47383 2.845701 0.3403417
## Cluster 2 2.390535 56.5817 2.752746 16.59426 1.305454 0.3251347
##
## Distance between the final cluster prototypes
## Cluster 1
## Cluster 2 1113258
##
## Difference between the initial and final cluster prototypes
## PBV EPS ROE PER DY DER
## Cluster 1 1.743795 876.0763 13.98912 -312.81383 -1.414299 0.3203417
## Cluster 2 -1.059465 166.4517 23.82275 22.46426 1.285454 0.3251347
##
## Root Mean Squared Deviations (RMSD): 668.7093
## Mean Absolute Deviation (MAD): 4265.299
##
## Membership degrees matrix (top and bottom 5 rows):
## Cluster 1 Cluster 2
## 1 0.002329552 0.9976704
## 2 0.004945420 0.9950546
## 3 0.001712884 0.9982871
## 4 0.003061001 0.9969390
## 5 0.004765674 0.9952343
## ...
## Cluster 1 Cluster 2
## 97 0.255637444 0.7443626
## 98 0.020967374 0.9790326
## 99 0.029807678 0.9701923
## 100 0.001408484 0.9985915
## 101 0.044888438 0.9551116
##
## Descriptive statistics for the membership degrees by clusters
## Size Min Q1 Mean Median Q3 Max
## Cluster 1 6 0.5201829 0.8205911 0.8107334 0.8569112 0.8970134 0.9115298
## Cluster 2 95 0.7443626 0.9777748 0.9735950 0.9950208 0.9977336 0.9997592
##
## Dunn's Fuzziness Coefficients:
## dunn_coeff normalized
## 0.9399911 0.8799822
##
## Within cluster sum of squares by cluster:
## 1 2
## 24173800 3236079
## (between_SS / total_SS = 18.65%)
##
## Available components:
## [1] "u" "v" "v0" "d" "x"
## [6] "cluster" "csize" "sumsqrs" "k" "m"
## [11] "iter" "best.start" "func.val" "comp.time" "inpargs"
## [16] "algorithm" "call"# plot clustering
fcm2.c2 <- ppclust2(fcm.c2, "kmeans")
fviz_cluster(fcm2.c2, data = dat, geom = "point",
ellipse.type = "convex",
palette = "jco",
repel = FALSE)
Pembentukan Klaster berjumlah 3
# membangun matriks partisi awal
set.seed(123)
u0_c3 <- inaparc::imembrand(nrow(dat), k=3)$u
# membentuk model
fcm.c3 <- fcm(dat, centers=3, u0_c3)
summary(fcm.c3)## Summary for 'fcm.c3'
##
## Number of data objects: 101
##
## Number of clusters: 3
##
## Crisp clustering vector:
## [1] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##
## Initial cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 0.45 10.80 0.19 48.17 0.00 0.26
## Cluster 2 0.95 1600.00 16.00 5.61 6.74 1.09
## Cluster 3 5.47 -0.14 0.39 -5200.00 0.00 0.41
##
## Final cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 2.377527 55.9369686 2.748256 29.00638 1.306422222 0.3243054
## Cluster 2 1.913402 1134.8573657 19.361329 24.74621 2.994086605 0.3332981
## Cluster 3 5.469388 -0.1034386 0.392201 -5196.38758 0.000891569 0.4100698
##
## Distance between the final cluster prototypes
## Cluster 1 Cluster 2
## Cluster 2 1164366
## Cluster 3 27307899 28548755
##
## Difference between the initial and final cluster prototypes
## PBV EPS ROE PER DY
## Cluster 1 1.927527382 45.13696862 2.558256290 -19.163619 1.306422222
## Cluster 2 0.963402152 -465.14263432 3.361328794 19.136208 -3.745913395
## Cluster 3 -0.000612035 0.03656136 0.002201011 3.612422 0.000891569
## DER
## Cluster 1 0.064305375
## Cluster 2 -0.756701879
## Cluster 3 0.000069786
##
## Root Mean Squared Deviations (RMSD): 270.2963
## Mean Absolute Deviation (MAD): 1133.832
##
## Membership degrees matrix (top and bottom 5 rows):
## Cluster 1 Cluster 2 Cluster 3
## 1 0.9972440 0.002651638 0.000104360
## 2 0.9946985 0.005051728 0.000249769
## 3 0.9983677 0.001560104 0.000072172
## 4 0.9976366 0.002274553 0.000088892
## 5 0.9962093 0.003624352 0.000166357
## ...
## Cluster 1 Cluster 2 Cluster 3
## 97 0.6908985 0.292080607 0.017020912
## 98 0.9804362 0.018810262 0.000753528
## 99 0.9708386 0.027900928 0.001260466
## 100 0.9986778 0.001264182 0.000058007
## 101 0.9546413 0.044079216 0.001279442
##
## Descriptive statistics for the membership degrees by clusters
## Size Min Q1 Mean Median Q3 Max
## Cluster 1 95 0.6908985 0.9778678 0.9729181 0.9947128 0.9978004 0.9995914
## Cluster 2 5 0.8790367 0.9105789 0.9361474 0.9285542 0.9812236 0.9813436
## Cluster 3 1 0.9999991 0.9999991 0.9999991 0.9999991 0.9999991 0.9999991
##
## Dunn's Fuzziness Coefficients:
## dunn_coeff normalized
## 0.9494391 0.9241587
##
## Within cluster sum of squares by cluster:
## 1 2 3
## 3236078.8 394149.7 0.0
## (between_SS / total_SS = 89.97%)
##
## Available components:
## [1] "u" "v" "v0" "d" "x"
## [6] "cluster" "csize" "sumsqrs" "k" "m"
## [11] "iter" "best.start" "func.val" "comp.time" "inpargs"
## [16] "algorithm" "call"# plot clustering
fcm2.c3 <- ppclust2(fcm.c3, "kmeans")
fviz_cluster(fcm2.c3, data = dat, geom = "point",
ellipse.type = "convex",
palette = "jco",
repel = FALSE)
Pembentukan Klaster berjumlah 4
# membangun matriks partisi awal
set.seed(123)
u0_c4 <- inaparc::imembrand(nrow(dat), k=4)$u
# membentuk model
fcm.c4 <- fcm(dat, centers=4, u0_c4)
summary(fcm.c4)## Summary for 'fcm.c4'
##
## Number of data objects: 101
##
## Number of clusters: 4
##
## Crisp clustering vector:
## [1] 2 2 2 2 2 1 1 2 2 1 3 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 1 3 1 1 2 2 2 1 2
## [38] 2 2 2 1 2 3 2 1 2 2 2 3 2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 2 2 1 2 2
## [75] 2 3 2 2 2 2 2 2 2 4 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1
##
## Initial cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 8.07 0.86 0.56 1000.00 0.00 0.92
## Cluster 2 0.56 -0.31 0.18 -402.88 0.00 0.01
## Cluster 3 0.95 1600.00 16.00 5.61 6.74 1.09
## Cluster 4 5.47 -0.14 0.39 -5200.00 0.00 0.41
##
## Final cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 1.748265 254.1628263 10.5891072 21.32079 3.222146141 0.2599974
## Cluster 2 2.409380 8.6108794 0.7100191 27.55971 0.777232718 0.3658496
## Cluster 3 1.865157 1261.4603417 21.0853580 13.27730 2.983704935 0.3751214
## Cluster 4 5.469855 -0.1284736 0.3906754 -5198.70569 0.000217286 0.4100275
##
## Distance between the final cluster prototypes
## Cluster 1 Cluster 2 Cluster 3
## Cluster 2 60438.71
## Cluster 3 1014823.24 1570256.08
## Cluster 4 27313468.78 27313936.53 28756823.20
##
## Difference between the initial and final cluster prototypes
## PBV EPS ROE PER DY
## Cluster 1 -6.321735459 253.30282632 10.029107239 -978.679214 3.222146141
## Cluster 2 1.849380229 8.92087935 0.530019079 430.439711 0.777232718
## Cluster 3 0.915156821 -338.53965829 5.085357984 7.667297 -3.756295065
## Cluster 4 -0.000145471 0.01152644 0.000675375 1.294306 0.000217286
## DER
## Cluster 1 -0.660002577
## Cluster 2 0.355849555
## Cluster 3 -0.714878608
## Cluster 4 0.000027489
##
## Root Mean Squared Deviations (RMSD): 574.9348
## Mean Absolute Deviation (MAD): 3079.61
##
## Membership degrees matrix (top and bottom 5 rows):
## Cluster 1 Cluster 2 Cluster 3 Cluster 4
## 1 0.288654541 0.7061112 0.004987196 0.000247095
## 2 0.022348215 0.9765568 0.001032268 0.000062762
## 3 0.000910361 0.9990535 0.000034226 0.000001959
## 4 0.247767362 0.7472381 0.004760462 0.000234084
## 5 0.035335386 0.9631435 0.001439414 0.000081691
## ...
## Cluster 1 Cluster 2 Cluster 3 Cluster 4
## 97 0.399018814 0.431250372 0.159116401 0.010614413
## 98 0.306559394 0.680482568 0.012340605 0.000617433
## 99 0.253711416 0.729493695 0.015909730 0.000885159
## 100 0.001574346 0.998364953 0.000057437 0.000003263
## 101 0.997677774 0.002196795 0.000120857 0.000004574
##
## Descriptive statistics for the membership degrees by clusters
## Size Min Q1 Mean Median Q3 Max
## Cluster 1 20 0.5080985 0.8710967 0.8852387 0.9126160 0.9710421 0.9976778
## Cluster 2 75 0.4312504 0.8261656 0.8906046 0.9549092 0.9806690 0.9993276
## Cluster 3 5 0.5719862 0.6804897 0.8290930 0.8989000 0.9968610 0.9972282
## Cluster 4 1 0.9999998 0.9999998 0.9999998 0.9999998 0.9999998 0.9999998
##
## Dunn's Fuzziness Coefficients:
## dunn_coeff normalized
## 0.8284412 0.7712549
##
## Within cluster sum of squares by cluster:
## 1 2 3 4
## 149003.8 1982511.7 394149.7 0.0
## (between_SS / total_SS = 93.24%)
##
## Available components:
## [1] "u" "v" "v0" "d" "x"
## [6] "cluster" "csize" "sumsqrs" "k" "m"
## [11] "iter" "best.start" "func.val" "comp.time" "inpargs"
## [16] "algorithm" "call"# plot clustering
fcm2.c4 <- ppclust2(fcm.c4, "kmeans")
fviz_cluster(fcm2.c4, data = dat, geom = "point",
ellipse.type = "convex",
palette = "jco",
repel = FALSE)
Pembentukan Klaster berjumlah 5
# membangun matriks partisi awal
set.seed(123)
u0_c5 <- inaparc::imembrand(nrow(dat), k=5)$u
# membentuk model
fcm.c5 <- fcm(dat, centers=5, u0_c5)
summary(fcm.c5)## Summary for 'fcm.c5'
##
## Number of data objects: 101
##
## Number of clusters: 5
##
## Crisp clustering vector:
## [1] 5 5 5 5 5 2 5 5 5 2 4 5 5 5 5 1 1 5 5 5 5 2 5 1 2 1 5 5 5 4 2 2 5 5 5 2 5
## [38] 5 5 1 2 5 4 5 2 5 5 5 4 1 5 2 5 5 1 5 5 5 5 5 5 5 2 2 5 5 5 2 5 5 5 2 5 5
## [75] 5 4 5 5 1 5 5 5 5 3 5 1 2 2 2 5 5 5 1 5 5 5 1 1 1 5 2
##
## Initial cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 1.22 1.60 0.98 81.90 0.00 0.30
## Cluster 2 0.60 372.61 8.39 7.11 0.00 0.26
## Cluster 3 5.47 -0.14 0.39 -5200.00 0.00 0.41
## Cluster 4 2.18 845.40 17.93 11.74 3.63 0.02
## Cluster 5 1.65 -547.81 2.69 -7.92 1.16 0.00
##
## Final cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 3.840929 10.8070396 2.1540459 154.551630 0.175391499 0.1093614
## Cluster 2 1.656613 286.8320474 11.8009561 13.018737 3.407893082 0.2952964
## Cluster 3 5.469877 -0.1221009 0.3904823 -5199.382054 0.000134235 0.4100098
## Cluster 4 1.853342 1303.7071634 21.7620982 8.980371 3.022427178 0.3896150
## Cluster 5 2.096148 11.4719204 0.7045934 5.676347 0.929526332 0.4407347
##
## Distance between the final cluster prototypes
## Cluster 1 Cluster 2 Cluster 3 Cluster 4
## Cluster 2 96329.68
## Cluster 3 28664731.22 27251621.05
## Cluster 4 1693178.33 1034150.73 28827488.86
## Cluster 5 22170.12 76006.60 27092779.72 1670330.70
##
## Difference between the initial and final cluster prototypes
## PBV EPS ROE PER DY
## Cluster 1 2.620929280 9.20703964 1.174045929 72.651630 0.175391499
## Cluster 2 1.056612982 -85.77795261 3.410956133 5.908737 3.407893082
## Cluster 3 -0.000122588 0.01789912 0.000482329 0.617946 0.000134235
## Cluster 4 -0.326657645 458.30716340 3.832098188 -2.759629 -0.607572822
## Cluster 5 0.446148145 559.28192040 -1.985406578 13.596347 -0.230473668
## DER
## Cluster 1 -0.190638607
## Cluster 2 0.035296439
## Cluster 3 0.000009834
## Cluster 4 0.369615023
## Cluster 5 0.440734727
##
## Root Mean Squared Deviations (RMSD): 327.3661
## Mean Absolute Deviation (MAD): 1474.125
##
## Membership degrees matrix (top and bottom 5 rows):
## Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5
## 1 0.18180293 0.163120898 0.000204491 0.003843170 0.6510285
## 2 0.04129432 0.011104710 0.000038861 0.000599208 0.9469629
## 3 0.02291101 0.005104688 0.000014167 0.000231648 0.9717385
## 4 0.31692979 0.140336146 0.000193649 0.003667588 0.5388728
## 5 0.42905298 0.032344475 0.000095952 0.001582481 0.5369241
## ...
## Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5
## 97 0.37240260 0.252091539 0.006927283 0.099339154 0.26923943
## 98 0.84706568 0.046374024 0.000118660 0.002213266 0.10422837
## 99 0.89158338 0.028133135 0.000118236 0.001991272 0.07817398
## 100 0.02466843 0.005647518 0.000015169 0.000249787 0.96941910
## 101 0.02108149 0.948778589 0.000058144 0.001416305 0.02866547
##
## Descriptive statistics for the membership degrees by clusters
## Size Min Q1 Mean Median Q3 Max
## Cluster 1 13 0.3724026 0.7100485 0.8012151 0.8915834 0.9653854 0.9888599
## Cluster 2 18 0.6470110 0.7767605 0.8613418 0.8873683 0.9543256 0.9962831
## Cluster 3 1 0.9999999 0.9999999 0.9999999 0.9999999 0.9999999 0.9999999
## Cluster 4 5 0.4394504 0.5476665 0.7751456 0.8903193 0.9988715 0.9994201
## Cluster 5 64 0.4038023 0.6978012 0.8182545 0.8568209 0.9561797 0.9905922
##
## Dunn's Fuzziness Coefficients:
## dunn_coeff normalized
## 0.7396368 0.6745460
##
## Within cluster sum of squares by cluster:
## 1 2 3 4 5
## 692955.4 109039.0 0.0 394149.7 748733.6
## (between_SS / total_SS = 94.84%)
##
## Available components:
## [1] "u" "v" "v0" "d" "x"
## [6] "cluster" "csize" "sumsqrs" "k" "m"
## [11] "iter" "best.start" "func.val" "comp.time" "inpargs"
## [16] "algorithm" "call"# plot clustering
fcm2.c5 <- ppclust2(fcm.c5, "kmeans")
fviz_cluster(fcm2.c5, data = dat, geom = "point",
ellipse.type = "convex",
palette = "jco",
repel = FALSE)
Validitas Klaster
# membangun model
fcm3.c2 <- ppclust2(fcm.c2,"fclust")
fcm3.c3 <- ppclust2(fcm.c3,"fclust")
fcm3.c4 <- ppclust2(fcm.c4,"fclust")
fcm3.c5 <- ppclust2(fcm.c5,"fclust")- Partition Entropy Index
PE2 <- PE(fcm3.c2$U)
PE3 <- PE(fcm3.c3$U)
PE4 <- PE(fcm3.c4$U)
PE5 <- PE(fcm3.c5$U)- Partition Coefficient Index
PC2 <- PC(fcm3.c2$U)
PC3 <- PC(fcm3.c3$U)
PC4 <- PC(fcm3.c4$U)
PC5 <- PC(fcm3.c5$U)Perbandingan Validitas Klaster
data.frame(PE2, PE3, PE4, PE5, PC2, PC3, PC4, PC5)## PE2 PE3 PE4 PE5 PC2 PC3 PC4
## 1 0.1133526 0.1037975 0.3061966 0.4911467 0.9399911 0.9494391 0.8284412
## PC5
## 1 0.7396368Berdasarkan hasil perbandingan dapat dilihat bahwa nilai terendah PE dan nilai tertinggi PC dimiliki pembentukan 3 klaster.
Profiling Model Optimum
summary(fcm.c3)## Summary for 'fcm.c3'
##
## Number of data objects: 101
##
## Number of clusters: 3
##
## Crisp clustering vector:
## [1] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##
## Initial cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 0.45 10.80 0.19 48.17 0.00 0.26
## Cluster 2 0.95 1600.00 16.00 5.61 6.74 1.09
## Cluster 3 5.47 -0.14 0.39 -5200.00 0.00 0.41
##
## Final cluster prototypes:
## PBV EPS ROE PER DY DER
## Cluster 1 2.377527 55.9369686 2.748256 29.00638 1.306422222 0.3243054
## Cluster 2 1.913402 1134.8573657 19.361329 24.74621 2.994086605 0.3332981
## Cluster 3 5.469388 -0.1034386 0.392201 -5196.38758 0.000891569 0.4100698
##
## Distance between the final cluster prototypes
## Cluster 1 Cluster 2
## Cluster 2 1164366
## Cluster 3 27307899 28548755
##
## Difference between the initial and final cluster prototypes
## PBV EPS ROE PER DY
## Cluster 1 1.927527382 45.13696862 2.558256290 -19.163619 1.306422222
## Cluster 2 0.963402152 -465.14263432 3.361328794 19.136208 -3.745913395
## Cluster 3 -0.000612035 0.03656136 0.002201011 3.612422 0.000891569
## DER
## Cluster 1 0.064305375
## Cluster 2 -0.756701879
## Cluster 3 0.000069786
##
## Root Mean Squared Deviations (RMSD): 270.2963
## Mean Absolute Deviation (MAD): 1133.832
##
## Membership degrees matrix (top and bottom 5 rows):
## Cluster 1 Cluster 2 Cluster 3
## 1 0.9972440 0.002651638 0.000104360
## 2 0.9946985 0.005051728 0.000249769
## 3 0.9983677 0.001560104 0.000072172
## 4 0.9976366 0.002274553 0.000088892
## 5 0.9962093 0.003624352 0.000166357
## ...
## Cluster 1 Cluster 2 Cluster 3
## 97 0.6908985 0.292080607 0.017020912
## 98 0.9804362 0.018810262 0.000753528
## 99 0.9708386 0.027900928 0.001260466
## 100 0.9986778 0.001264182 0.000058007
## 101 0.9546413 0.044079216 0.001279442
##
## Descriptive statistics for the membership degrees by clusters
## Size Min Q1 Mean Median Q3 Max
## Cluster 1 95 0.6908985 0.9778678 0.9729181 0.9947128 0.9978004 0.9995914
## Cluster 2 5 0.8790367 0.9105789 0.9361474 0.9285542 0.9812236 0.9813436
## Cluster 3 1 0.9999991 0.9999991 0.9999991 0.9999991 0.9999991 0.9999991
##
## Dunn's Fuzziness Coefficients:
## dunn_coeff normalized
## 0.9494391 0.9241587
##
## Within cluster sum of squares by cluster:
## 1 2 3
## 3236078.8 394149.7 0.0
## (between_SS / total_SS = 89.97%)
##
## Available components:
## [1] "u" "v" "v0" "d" "x"
## [6] "cluster" "csize" "sumsqrs" "k" "m"
## [11] "iter" "best.start" "func.val" "comp.time" "inpargs"
## [16] "algorithm" "call"Berikut merupakan ringkasan hasil pengelompokkan perusahaan keuangan berdasarkan indikator rasio keuangan menggunakan algoritma Fuzzy C-Means:
-Number of data objects menunjukkan bahwa data perusahaan terdapat 101 perusahaan.
-Number of clusters menunjukkan klaster yang dibentuk adalah 3 klaster.
-Crisp clustering vector menunjukkan data ke-1 hingga ke-101 masuk ke dalam klaster mana (sebagai contoh data ke-1 masuk kedalam klaster 1).
-Initial cluster prototypes menunjukkan pusat klaster yang terbentuk pada iterasi pertama
-Final cluster prototypes menunjukkan titik-titik pusat klaster final yang telah melalui proses iterasi.
-Distance between the final cluster prototypes menunjukkan jarak antara titik-titik pusat klaster pertama kedua dan ketiga.
-Difference between the initial and final cluster prototypes menunjukkan selisih dari pusat klaster pada iterasi pertama dengan pusat klaster pada iterasi terakhir.
-Root Mean Squared Deviations (RMSD) dan Mean Absolute Deviation (MAD) merupakan salah satu ukuran yang paling umum digunakan untuk mengevaluasi kualitas prediksi.
-Membership degrees matrix merupakan derajat keanggotaan yang terbentuk setelah melewati proses iterasi, data dengan derajat keanggotaan terbesar akan menjadi anggota tersebut (sebagai contoh data ke-1 memiliki nilai derajat keanggotaan pada klaster 1 sebesar 0.9972440, klaster 2 sebesar 0.002651638 dan klaster 3 sebesar 0.000104360, Maka data ke-1 akan menjadi anggota klaster 1).
-Dunn’s Fuzziness Coefficients merupakan koefisien salah satu nilai validitas klaster.
-Within cluster sum of squares by cluster merupakan jumlah kuadrat tiap klaster yang dapat digunakan sebagai evaluasi prediksi.