# MEAN SHIFT Manual Gaussian blob, n = 500, seed 42
set.seed(42)
X <- rbind(cbind(rnorm(167, 0), rnorm(167, 0)),
cbind(rnorm(167, 10), rnorm(167, 0)),
cbind(rnorm(166, 5), rnorm(166, 9)))
asal <- rep(1:3, times = c(167, 167, 166)) # blob asal, hanya untuk pewarnaan (tidak dipakai mean shift)
warna <- c("#e05a5a", "#5fd35f", "#7b7bd8")
tepi <- c("#a33636", "#2a8a2a", "#44449c")
print(table(Kelompok = asal))
## Kelompok
## 1 2 3
## 167 167 166
par(mfrow = c(1, 1), mar = c(4.5, 4.5, 3.5, 1))
plot(X, pch = 21, cex = 0.9, lwd = 0.6, bg = adjustcolor(warna[asal], 0.8), col = tepi[asal],
xlab = "Fitur 1", ylab = "Fitur 2", main = "Scatter plot Gaussian Blobs")
legend("topright", legend = paste("Kelompok", 1:3), pch = 21, pt.bg = warna, col = tepi, bty = "n")
# 1. Validasi data
cat("\n=== 1. VALIDASI DATA ===\n")
##
## === 1. VALIDASI DATA ===
cat("Struktur : matriks", nrow(X), "x", ncol(X), "| tipe:", typeof(X), "\n")
## Struktur : matriks 500 x 2 | tipe: double
cat("Missing :", sum(is.na(X)), "\n")
## Missing : 0
cat("Duplikat :", sum(duplicated(X)), "\n")
## Duplikat : 0
cat("Tak hingga :", sum(is.infinite(X)), "\n")
## Tak hingga : 0
# 2. Pemeriksaan pencilan (aturan 1,5 x IQR)
cat("\n=== 2. PEMERIKSAAN PENCILAN (1,5 x IQR) ===\n")
##
## === 2. PEMERIKSAAN PENCILAN (1,5 x IQR) ===
pencilan <- sapply(1:ncol(X), function(j) {
q <- quantile(X[, j], c(0.25, 0.75)); batas <- 1.5 * (q[2] - q[1])
sum(X[, j] < q[1] - batas | X[, j] > q[2] + batas)
})
names(pencilan) <- c("Fitur 1", "Fitur 2")
cat("Jumlah pencilan per fitur:\n"); print(pencilan)
## Jumlah pencilan per fitur:
## Fitur 1 Fitur 2
## 0 0
par(mfrow = c(1, 1), mar = c(4.5, 4.5, 3.5, 1))
boxplot(X, names = c("Fitur 1", "Fitur 2"), col = c("#e05a5a", "#7b7bd8"),
main = "Boxplot (aturan 1,5 x IQR)", ylab = "Nilai")
# 3. Skala fitur
cat("\n=== 3. SKALA FITUR ===\n")
##
## === 3. SKALA FITUR ===
sdv <- apply(X, 2, sd)
cat("SD Fitur 1 =", round(sdv[1], 3), "| SD Fitur 2 =", round(sdv[2], 3),
"| Rasio SD =", round(min(sdv) / max(sdv), 3), "(tanpa standardisasi)\n")
## SD Fitur 1 = 4.206 | SD Fitur 2 = 4.406 | Rasio SD = 0.955 (tanpa standardisasi)
h <- as.numeric(quantile(dist(X), 0.3)) # bandwidth, h > 0
h
## [1] 3.072614
eps <- 1e-4
eps
## [1] 1e-04
P <- X
P
## [,1] [,2]
## [1,] 1.370958e+00 0.4546502976
## [2,] -5.646982e-01 0.0848980587
## [3,] 3.631284e-01 0.8955655823
## [4,] 6.328626e-01 -0.2297781389
## [5,] 4.042683e-01 0.8366190685
## [6,] -1.061245e-01 -1.7450558613
## [7,] 1.511522e+00 1.6894589213
## [8,] -9.465904e-02 0.8647779785
## [9,] 2.018424e+00 -0.1507759889
## [10,] -6.271410e-02 -1.4490071301
## [11,] 1.304870e+00 0.6430087000
## [12,] 2.286645e+00 0.4831938638
## [13,] -1.388861e+00 -0.0063556264
## [14,] -2.787888e-01 0.1514558929
## [15,] -1.333213e-01 -0.5841089703
## [16,] 6.359504e-01 0.3688067326
## [17,] -2.842529e-01 0.2946543397
## [18,] -2.656455e+00 -0.2792593733
## [19,] -2.440467e+00 -1.3362366549
## [20,] 1.320113e+00 0.7007488184
## [21,] -3.066386e-01 0.5541966223
## [22,] -1.781308e+00 -0.8363065928
## [23,] -1.719174e-01 -1.5945881620
## [24,] 1.214675e+00 0.2049585806
## [25,] 1.895193e+00 -0.3450879780
## [26,] -4.304691e-01 0.2526117034
## [27,] -2.572694e-01 -1.2940024655
## [28,] -1.763163e+00 -0.9591704444
## [29,] 4.600974e-01 1.0857748537
## [30,] -6.399949e-01 0.4037749047
## [31,] 4.554501e-01 0.5864875367
## [32,] 7.048373e-01 1.8152284462
## [33,] 1.035104e+00 0.1288214286
## [34,] -6.089264e-01 -2.0009292377
## [35,] 5.049551e-01 0.3337771974
## [36,] -1.717009e+00 1.1713251274
## [37,] -7.844590e-01 2.0595392423
## [38,] -8.509076e-01 -1.3768615982
## [39,] -2.414208e+00 -1.1508555656
## [40,] 3.612261e-02 -0.7058213948
## [41,] 2.059986e-01 -1.0540557821
## [42,] -3.610573e-01 -0.6457437231
## [43,] 7.581632e-01 -0.1853779677
## [44,] -7.267048e-01 -1.2012220507
## [45,] -1.368281e+00 2.0369721670
## [46,] 4.328180e-01 0.1077747449
## [47,] -8.113932e-01 -0.0841081005
## [48,] 1.444101e+00 0.4956196416
## [49,] -4.314462e-01 0.0374151861
## [50,] 6.556479e-01 -0.1320880370
## [51,] 3.219253e-01 1.4767874236
## [52,] -7.838389e-01 -0.2170302101
## [53,] 1.575728e+00 -1.2836022041
## [54,] 6.428993e-01 0.3856678904
## [55,] 8.976065e-02 -0.3515128735
## [56,] 2.765507e-01 -0.5217960934
## [57,] 6.792888e-01 -1.0681312007
## [58,] 8.983289e-02 0.4283659033
## [59,] -2.993090e+00 -0.1740182344
## [60,] 2.848830e-01 0.5156677286
## [61,] -3.672346e-01 -0.2343652773
## [62,] 1.852306e-01 -0.6585034258
## [63,] 5.818237e-01 1.2502366041
## [64,] 1.399737e+00 -0.2717637151
## [65,] -7.272921e-01 0.9479519959
## [66,] 1.302543e+00 -1.2015824301
## [67,] 3.358481e-01 -0.4661160964
## [68,] 1.038506e+00 -0.2693513952
## [69,] 9.207286e-01 -0.3909654081
## [70,] 7.208782e-01 1.3487070120
## [71,] -1.043119e+00 -0.0227647013
## [72,] -9.018639e-02 0.2442258511
## [73,] 6.235182e-01 -0.9423717079
## [74,] -9.535234e-01 -0.7292172765
## [75,] -5.428288e-01 0.9980689086
## [76,] 5.809965e-01 1.2584816646
## [77,] 7.681787e-01 1.2488636888
## [78,] 4.637676e-01 -1.3806370495
## [79,] -8.857763e-01 2.0499606936
## [80,] -1.099781e+00 1.0168728298
## [81,] 1.512707e+00 -0.0267174641
## [82,] 2.579214e-01 0.7036077788
## [83,] 8.844023e-02 -0.9713852292
## [84,] -1.208965e-01 -1.0961562416
## [85,] -1.194329e+00 0.0490504509
## [86,] 6.119969e-01 -1.1984958566
## [87,] -2.171398e-01 0.1900189986
## [88,] -1.827567e-01 1.2977058996
## [89,] 9.333463e-01 -1.0338737230
## [90,] 8.217731e-01 -0.7384407542
## [91,] 1.392116e+00 0.0465639395
## [92,] -4.761739e-01 -1.0175961198
## [93,] 6.503486e-01 -0.3832839599
## [94,] 1.391110e+00 0.8727554117
## [95,] -1.110789e+00 0.9695450140
## [96,] -8.607926e-01 0.3838466650
## [97,] -1.131739e+00 -1.8515556631
## [98,] -1.459214e+00 -0.0539967368
## [99,] 7.998255e-02 1.0647732143
## [100,] 6.532043e-01 0.8131950374
## [101,] 1.200965e+00 -0.1908164741
## [102,] 1.044751e+00 -2.6999298086
## [103,] -1.003209e+00 0.0609666388
## [104,] 1.848482e+00 0.5737516975
## [105,] -6.667734e-01 0.0458035797
## [106,] 1.055138e-01 0.1574125402
## [107,] -4.222559e-01 0.4315653729
## [108,] -1.223502e-01 -0.3965497361
## [109,] 1.881930e-01 1.3099782258
## [110,] 1.191610e-01 0.4703933999
## [111,] -2.509255e-02 -1.2426702706
## [112,] 1.080727e-01 1.3815754564
## [113,] -4.854352e-01 1.2044589370
## [114,] -5.042171e-01 0.8240739637
## [115,] -1.661099e+00 -1.6626294022
## [116,] -3.823337e-01 -0.5693063436
## [117,] -5.126503e-01 0.6355138173
## [118,] 2.701891e+00 0.0437220076
## [119,] -1.362116e+00 0.3480123037
## [120,] 1.372562e-01 2.4595935489
## [121,] -1.493625e+00 -0.8183803244
## [122,] -1.470436e+00 -2.1132001149
## [123,] 1.247024e-01 0.2736952724
## [124,] -9.966391e-01 -0.6875968412
## [125,] -1.822614e-03 0.4460410530
## [126,] -4.282589e-01 -0.8123847238
## [127,] -6.136716e-01 2.2120554803
## [128,] -2.024678e+00 -0.1237059716
## [129,] -1.224748e+00 -0.4773355060
## [130,] 1.795164e-01 -0.1662614915
## [131,] 5.676206e-01 0.8625633836
## [132,] -4.928774e-01 0.0973404852
## [133,] 6.288407e-05 -1.6256167392
## [134,] 1.122890e+00 -0.0046207678
## [135,] 1.439856e+00 0.7602421677
## [136,] -1.097114e+00 0.0389909129
## [137,] -1.173196e-01 0.7350721416
## [138,] 1.201498e+00 -0.1464726270
## [139,] -4.697296e-01 -0.0578873354
## [140,] -5.246948e-02 0.4823694661
## [141,] -8.610730e-02 0.9929436368
## [142,] -8.876790e-01 -1.2463954980
## [143,] -4.446840e-01 -0.0334875248
## [144,] -2.944488e-02 -0.0709621812
## [145,] -4.138688e-01 -0.7589206537
## [146,] 1.113386e+00 -1.0343593609
## [147,] -4.809928e-01 -0.6307319540
## [148,] -4.331690e-01 0.5868077200
## [149,] 6.968626e-01 -0.4163226562
## [150,] -1.056368e+00 -0.7848878095
## [151,] -4.069848e-02 0.1634163195
## [152,] -1.551545e+00 -1.2367142351
## [153,] 1.167170e+00 1.0458737762
## [154,] -2.736457e-01 -0.4845954162
## [155,] -4.678453e-01 0.1891288117
## [156,] -1.238252e+00 0.0510063316
## [157,] -7.762034e-03 -0.0002406689
## [158,] -8.002822e-01 1.8093820424
## [159,] -5.334923e-01 -0.8253279571
## [160,] 1.287675e+00 1.1454704522
## [161,] -1.755259e-01 0.0315731876
## [162,] -1.071782e+00 -0.8352058053
## [163,] 1.632069e-01 -0.0687636490
## [164,] -3.627384e-01 0.7467716870
## [165,] 5.900135e-01 -0.4255187344
## [166,] 1.432422e+00 -0.7720822352
## [167,] -9.926925e-01 0.1527641067
## [168,] 1.098860e+01 0.9147748677
## [169,] 9.926542e+00 -0.0024562667
## [170,] 8.612973e+00 0.1360095524
## [171,] 8.693324e+00 -0.7201535449
## [172,] 9.231605e+00 -0.1981243301
## [173,] 9.472892e+00 -1.0292088060
## [174,] 9.978573e+00 -0.9669558959
## [175,] 1.067050e+01 -1.2208130889
## [176,] 9.565383e+00 0.8362077039
## [177,] 8.886120e+00 1.1149717985
## [178,] 1.060711e+01 -0.4129448529
## [179,] 1.027546e+01 -1.1289773980
## [180,] 1.115735e+01 -0.0879313318
## [181,] 8.317519e+00 2.2419036933
## [182,] 1.008732e+01 2.0413131708
## [183,] 1.135336e+01 -1.7198003367
## [184,] 1.072417e+01 -0.3569066561
## [185,] 9.167447e+00 1.5332804922
## [186,] 1.073253e+01 -0.0382440966
## [187,] 9.128073e+00 1.5974132423
## [188,] 9.546602e+00 -0.3335853933
## [189,] 1.118753e+01 0.6049859239
## [190,] 9.709855e+00 0.2242412393
## [191,] 1.082855e+01 3.2290694955
## [192,] 9.708772e+00 0.9204525668
## [193,] 8.423638e+00 -1.2065390692
## [194,] 9.151184e+00 -0.6038811692
## [195,] 8.911480e+00 0.3702352846
## [196,] 9.515709e+00 -1.9010006467
## [197,] 9.663689e+00 -1.8044099450
## [198,] 9.846642e+00 -1.1218226064
## [199,] 9.756753e+00 -0.3479296066
## [200,] 1.189220e+01 1.2389021486
## [201,] 8.614002e+00 -0.2741975649
## [202,] 9.585176e+00 0.1623807156
## [203,] 1.034908e+01 -0.0646069098
## [204,] 1.162844e+01 -0.7052370970
## [205,] 1.008852e+01 1.3621972688
## [206,] 1.123915e+01 -1.0965131881
## [207,] 8.355444e+00 -0.2284335185
## [208,] 1.144636e+01 -0.3478280806
## [209,] 9.309440e+00 0.5321286195
## [210,] 9.723569e+00 1.6072345623
## [211,] 8.890581e+00 0.5138145261
## [212,] 1.013387e+01 1.3823731606
## [213,] 1.178534e+01 0.7630970485
## [214,] 1.242216e+01 -0.6245845446
## [215,] 8.923171e+00 0.0815438004
## [216,] 1.048594e+01 1.3760791114
## [217,] 1.138852e+01 -1.5612657862
## [218,] 9.804343e+00 0.3247706606
## [219,] 9.781825e+00 -0.1567903170
## [220,] 9.695222e+00 0.8777838607
## [221,] 1.059783e+01 0.7501665752
## [222,] 1.139743e+01 0.3010534038
## [223,] 1.068762e+01 1.4928111172
## [224,] 1.032019e+01 -1.5254938002
## [225,] 9.698130e+00 0.9107175585
## [226,] 1.049835e+01 -1.5795320279
## [227,] 9.450463e+00 0.5877162571
## [228,] 9.720743e+00 0.0896422960
## [229,] 1.109651e+01 0.9672616569
## [230,] 1.044201e+01 0.0788123529
## [231,] 1.024102e+01 -1.5686998365
## [232,] 9.744392e+00 -2.0078231840
## [233,] 1.093103e+01 0.5409735242
## [234,] 1.133491e+01 -0.0733765981
## [235,] 9.130728e+00 -0.5710183936
## [236,] 1.005549e+01 -0.3110684599
## [237,] 1.004907e+01 -0.6714150671
## [238,] 9.421644e+00 -0.1573404521
## [239,] 9.001261e+00 -0.9313050710
## [240,] 9.997567e+00 -1.9830094795
## [241,] 1.065551e+01 -0.2195998042
## [242,] 1.147684e+01 1.0452758695
## [243,] 8.090847e+00 1.8773295663
## [244,] 9.297561e+00 0.0026061960
## [245,] 9.688570e+00 -0.0806699347
## [246,] 8.336843e+00 0.9629822812
## [247,] 9.249467e+00 0.0535710165
## [248,] 9.222648e+00 -0.4348984089
## [249,] 9.277430e+00 -1.7372972553
## [250,] 7.811165e+00 -1.2636955998
## [251,] 1.021342e+01 0.4063085121
## [252,] 9.368077e+00 -1.4596539678
## [253,] 1.152049e+01 1.0484573702
## [254,] 1.079596e+01 -1.3464305395
## [255,] 8.546470e+00 -0.1935705581
## [256,] 1.009840e+01 -0.0023359571
## [257,] 9.406229e+00 -0.0128297339
## [258,] 1.088828e+01 0.1519473220
## [259,] 1.005307e+01 0.5985111314
## [260,] 9.442976e+00 -0.1262124373
## [261,] 1.043840e+01 -0.2485355658
## [262,] 1.015261e+01 0.1603273949
## [263,] 9.835382e+00 -0.4336419416
## [264,] 1.201989e+01 1.5374124191
## [265,] 9.470614e+00 -2.1702465766
## [266,] 9.529213e+00 1.0270046193
## [267,] 8.454063e+00 -0.2484829332
## [268,] 9.959473e+00 0.4223203858
## [269,] 1.089036e+01 0.9876532936
## [270,] 7.928612e+00 0.8355681720
## [271,] 9.749935e+00 -0.6605218590
## [272,] 8.818350e+00 1.5640694933
## [273,] 1.144194e+01 -1.6229759353
## [274,] 1.135790e+01 0.8638963735
## [275,] 1.033450e+01 -0.5116027734
## [276,] 1.142934e+01 -1.9173650254
## [277,] 9.132682e+00 -1.8658138486
## [278,] 1.095065e+01 0.2451790634
## [279,] 9.414988e+00 2.2235343019
## [280,] 1.032096e+01 0.2733760641
## [281,] 9.700604e+00 1.1307847945
## [282,] 9.721457e+00 0.8386693741
## [283,] 1.054612e+01 -0.6546152779
## [284,] 8.696179e+00 0.9539609785
## [285,] 9.749086e+00 0.3529514655
## [286,] 1.017101e+01 0.2065992926
## [287,] 9.596533e+00 1.0011132343
## [288,] 1.010466e+01 0.7474519916
## [289,] 9.681119e+00 -0.6265748367
## [290,] 1.161834e+01 0.3952236859
## [291,] 1.071419e+01 -0.8921679540
## [292,] 1.296587e+01 0.6308184101
## [293,] 9.204922e+00 -0.4327051833
## [294,] 1.081437e+01 0.4521386442
## [295,] 1.209803e+01 0.3679990452
## [296,] 1.030098e+01 -0.2703874897
## [297,] 8.916925e+00 0.4655126177
## [298,] 8.993677e+00 0.5743562256
## [299,] 9.964585e+00 -0.2306999902
## [300,] 1.130912e+01 1.1722425083
## [301,] 1.075040e+01 1.3927027067
## [302,] 7.861632e+00 -0.6619912557
## [303,] 9.299646e+00 -0.7773692067
## [304,] 9.990944e+00 0.5135385789
## [305,] 8.541867e+00 -0.9133122380
## [306,] 1.069453e+01 -0.4494238053
## [307,] 7.538665e+00 0.8029326991
## [308,] 1.014329e+01 -0.5734768510
## [309,] 9.608778e+00 -1.9281251678
## [310,] 9.508836e+00 0.6643908338
## [311,] 9.716353e+00 -1.6025402238
## [312,] 1.031479e+01 -1.3546002575
## [313,] 1.039633e+01 -3.0179326794
## [314,] 9.774396e+00 0.8312378222
## [315,] 8.075050e+00 0.2510970888
## [316,] 8.560771e+00 0.4622934659
## [317,] 8.530342e+00 0.8447922232
## [318,] 1.076186e+01 -0.0419715243
## [319,] 9.756385e+00 -1.1055759057
## [320,] 1.026968e+01 0.5637756523
## [321,] 8.441072e+00 1.3033647558
## [322,] 9.464412e+00 -1.5002209378
## [323,] 1.056245e+01 -0.6069892351
## [324,] 9.821674e+00 -0.2922450657
## [325,] 9.884864e+00 -1.2896833433
## [326,] 9.927939e+00 0.6941058488
## [327,] 1.121091e+01 -0.5991819029
## [328,] 9.385103e+00 1.2569066440
## [329,] 1.067613e+01 0.0535080136
## [330,] 1.089860e+01 0.7280925177
## [331,] 8.810682e+00 1.5610980682
## [332,] 1.012126e+01 0.2656247536
## [333,] 9.988778e+00 1.0767262592
## [334,] 1.102914e+01 0.2106979317
## [335,] 3.488326e+00 6.9892646674
## [336,] 5.022402e+00 7.8718195050
## [337,] 5.718136e+00 9.3487995716
## [338,] 5.489457e+00 8.6471015179
## [339,] 4.826112e+00 9.9447745979
## [340,] 3.782301e+00 7.9952801475
## [341,] 5.646398e+00 9.7239027325
## [342,] 4.083544e+00 8.3311672590
## [343,] 3.748177e+00 7.8869598063
## [344,] 5.594928e+00 8.6571948106
## [345,] 3.767189e+00 9.0497793232
## [346,] 5.244364e+00 7.7723180385
## [347,] 5.002772e+00 8.2359940892
## [348,] 3.671790e+00 7.7538179384
## [349,] 6.179696e+00 10.0167739778
## [350,] 4.407195e+00 9.7236126241
## [351,] 6.199978e+00 7.9674728629
## [352,] 4.524966e+00 9.5573460041
## [353,] 4.424943e+00 8.7444185769
## [354,] 4.968774e+00 7.8866082429
## [355,] 4.641943e+00 9.4211974396
## [356,] 4.643399e+00 8.6770496882
## [357,] 4.122336e+00 9.8801799012
## [358,] 3.787103e+00 8.8051363932
## [359,] 5.613287e+00 10.1880549821
## [360,] 4.193797e+00 8.4902354882
## [361,] 3.623543e+00 9.2195480109
## [362,] 4.492152e+00 9.3702944214
## [363,] 4.199065e+00 9.2791083937
## [364,] 2.807214e+00 9.2019424373
## [365,] 4.709063e+00 8.9870034576
## [366,] 5.167174e+00 8.9091349939
## [367,] 5.294692e+00 10.3650313653
## [368,] 5.392741e+00 9.9081305689
## [369,] 3.999156e+00 8.3901118286
## [370,] 4.674273e+00 10.3964372212
## [371,] 3.991651e+00 9.1447983733
## [372,] 4.364569e+00 8.3593932284
## [373,] 3.790159e+00 9.1698022596
## [374,] 3.883536e+00 8.8428125126
## [375,] 5.629881e+00 9.1009395945
## [376,] 4.727478e+00 8.0266058459
## [377,] 4.741159e+00 8.1801747247
## [378,] 6.729558e+00 10.3629189690
## [379,] 4.941608e+00 9.9613709305
## [380,] 4.462936e+00 8.1162755256
## [381,] 5.747287e+00 8.0999078846
## [382,] 4.512742e+00 10.7233331328
## [383,] 6.372908e+00 10.9090421621
## [384,] 4.622328e+00 8.2228588041
## [385,] 4.383847e+00 7.6976947374
## [386,] 3.831875e+00 11.6234951668
## [387,] 5.328640e+00 9.2296289143
## [388,] 6.466511e+00 9.1867498921
## [389,] 4.643990e+00 9.0761366350
## [390,] 5.261468e+00 10.4048601863
## [391,] 5.333329e+00 8.8082777647
## [392,] 6.422193e+00 10.4593921642
## [393,] 5.663877e+00 8.7793445489
## [394,] 3.926345e+00 9.5051458863
## [395,] 4.303098e+00 7.9665029939
## [396,] 4.253870e+00 9.1704734715
## [397,] 5.141573e+00 10.2006681609
## [398,] 4.996053e+00 8.8365940852
## [399,] 5.367938e+00 10.2824758631
## [400,] 4.342657e+00 11.7271963879
## [401,] 4.623653e+00 9.9419242173
## [402,] 5.741360e+00 8.7513859627
## [403,] 4.900393e+00 9.0964788597
## [404,] 4.345710e+00 8.5660690587
## [405,] 5.971164e+00 11.1786678675
## [406,] 5.013496e+00 6.0412203809
## [407,] 4.083465e+00 9.0808882392
## [408,] 6.709689e+00 9.1101378046
## [409,] 3.831899e+00 9.2134483263
## [410,] 3.218964e+00 7.4421803874
## [411,] 2.746868e+00 9.2162115463
## [412,] 5.651126e+00 9.1876638170
## [413,] 4.467167e+00 10.2586221252
## [414,] 4.724441e+00 9.5235177809
## [415,] 5.289627e+00 10.1154542775
## [416,] 4.533516e+00 8.0424977578
## [417,] 3.391940e+00 8.8755944201
## [418,] 3.050216e+00 9.1917378290
## [419,] 4.659300e+00 9.2722172506
## [420,] 5.174726e+00 8.3061855363
## [421,] 2.722222e+00 10.4791719209
## [422,] 5.290524e+00 8.3882329784
## [423,] 5.422306e+00 7.3856900256
## [424,] 6.294737e+00 9.4024901106
## [425,] 5.164714e+00 9.6645554473
## [426,] 5.204954e+00 9.9441270710
## [427,] 5.604604e+00 8.0537392023
## [428,] 4.980859e+00 8.7517115508
## [429,] 4.920286e+00 7.6715635315
## [430,] 5.115984e+00 9.8447637421
## [431,] 5.744173e+00 9.3476967324
## [432,] 4.568709e+00 9.9137625864
## [433,] 4.500471e+00 9.6082745534
## [434,] 4.134838e+00 8.3924520122
## [435,] 4.042243e+00 9.1796580709
## [436,] 5.326800e+00 7.0915905806
## [437,] 6.547372e+00 9.5029462577
## [438,] 4.031140e+00 9.9688991535
## [439,] 4.811560e+00 8.1242628742
## [440,] 3.969999e+00 6.8639754613
## [441,] 5.908086e+00 7.4771724184
## [442,] 4.682618e+00 7.8868817921
## [443,] 5.179004e+00 10.2409838955
## [444,] 5.348028e+00 9.0034819351
## [445,] 3.945721e+00 7.7622054140
## [446,] 4.895256e+00 9.5556991189
## [447,] 4.771657e+00 6.8168506506
## [448,] 5.675356e+00 8.7529755429
## [449,] 3.766755e+00 10.1128569276
## [450,] 3.800038e+00 8.6583267630
## [451,] 5.765867e+00 10.3054383421
## [452,] 4.411902e+00 10.7953238714
## [453,] 4.339704e+00 7.8321647725
## [454,] 5.113014e+00 7.8477123750
## [455,] 4.679601e+00 8.0855445307
## [456,] 6.866381e+00 9.5287280325
## [457,] 5.259531e+00 9.8350789270
## [458,] 5.161560e+00 10.2091369741
## [459,] 5.931075e+00 10.2994725454
## [460,] 4.940053e+00 10.0757323042
## [461,] 5.048740e+00 9.9398010235
## [462,] 3.927125e+00 9.1633746934
## [463,] 2.707029e+00 8.1118614414
## [464,] 3.792793e+00 8.2738390172
## [465,] 5.114109e+00 9.4075970056
## [466,] 3.966703e+00 10.6835363393
## [467,] 5.688808e+00 10.7059798236
## [468,] 5.725083e+00 7.0738332992
## [469,] 5.217380e+00 8.1660019848
## [470,] 4.798343e+00 10.4191325163
## [471,] 3.634310e+00 7.9358902850
## [472,] 4.691062e+00 7.3864225275
## [473,] 4.547097e+00 9.5998110887
## [474,] 5.663229e+00 10.7329647054
## [475,] 6.308630e+00 10.9345045625
## [476,] 5.501040e+00 9.5328205757
## [477,] 3.871711e+00 9.7196657560
## [478,] 6.670997e+00 9.5600933858
## [479,] 6.010353e+00 8.9819130683
## [480,] 5.223521e+00 5.6282609174
## [481,] 2.793515e+00 9.7607032448
## [482,] 4.045414e+00 8.6087731478
## [483,] 4.931427e+00 10.0099012238
## [484,] 5.761306e+00 8.3730268529
## [485,] 3.820096e+00 7.3654226305
## [486,] 8.211199e+00 10.2452426520
## [487,] 2.446175e+00 9.1813774466
## [488,] 4.764066e+00 12.4953042640
## [489,] 4.740437e+00 9.9155919133
## [490,] 4.336633e+00 10.0485065174
## [491,] 4.681009e+00 9.7638249369
## [492,] 5.742395e+00 8.3966126231
## [493,] 4.125707e+00 8.6295703373
## [494,] 2.917186e+00 10.0598259383
## [495,] 5.093768e+00 10.0551105298
## [496,] 4.998180e+00 9.5829721611
## [497,] 4.986899e+00 8.0134325645
## [498,] 5.667968e+00 10.6846218117
## [499,] 4.986832e+00 7.6331589543
## [500,] 5.776047e+00 8.5667856514
riw <- list(P)
riw
## [[1]]
## [,1] [,2]
## [1,] 1.370958e+00 0.4546502976
## [2,] -5.646982e-01 0.0848980587
## [3,] 3.631284e-01 0.8955655823
## [4,] 6.328626e-01 -0.2297781389
## [5,] 4.042683e-01 0.8366190685
## [6,] -1.061245e-01 -1.7450558613
## [7,] 1.511522e+00 1.6894589213
## [8,] -9.465904e-02 0.8647779785
## [9,] 2.018424e+00 -0.1507759889
## [10,] -6.271410e-02 -1.4490071301
## [11,] 1.304870e+00 0.6430087000
## [12,] 2.286645e+00 0.4831938638
## [13,] -1.388861e+00 -0.0063556264
## [14,] -2.787888e-01 0.1514558929
## [15,] -1.333213e-01 -0.5841089703
## [16,] 6.359504e-01 0.3688067326
## [17,] -2.842529e-01 0.2946543397
## [18,] -2.656455e+00 -0.2792593733
## [19,] -2.440467e+00 -1.3362366549
## [20,] 1.320113e+00 0.7007488184
## [21,] -3.066386e-01 0.5541966223
## [22,] -1.781308e+00 -0.8363065928
## [23,] -1.719174e-01 -1.5945881620
## [24,] 1.214675e+00 0.2049585806
## [25,] 1.895193e+00 -0.3450879780
## [26,] -4.304691e-01 0.2526117034
## [27,] -2.572694e-01 -1.2940024655
## [28,] -1.763163e+00 -0.9591704444
## [29,] 4.600974e-01 1.0857748537
## [30,] -6.399949e-01 0.4037749047
## [31,] 4.554501e-01 0.5864875367
## [32,] 7.048373e-01 1.8152284462
## [33,] 1.035104e+00 0.1288214286
## [34,] -6.089264e-01 -2.0009292377
## [35,] 5.049551e-01 0.3337771974
## [36,] -1.717009e+00 1.1713251274
## [37,] -7.844590e-01 2.0595392423
## [38,] -8.509076e-01 -1.3768615982
## [39,] -2.414208e+00 -1.1508555656
## [40,] 3.612261e-02 -0.7058213948
## [41,] 2.059986e-01 -1.0540557821
## [42,] -3.610573e-01 -0.6457437231
## [43,] 7.581632e-01 -0.1853779677
## [44,] -7.267048e-01 -1.2012220507
## [45,] -1.368281e+00 2.0369721670
## [46,] 4.328180e-01 0.1077747449
## [47,] -8.113932e-01 -0.0841081005
## [48,] 1.444101e+00 0.4956196416
## [49,] -4.314462e-01 0.0374151861
## [50,] 6.556479e-01 -0.1320880370
## [51,] 3.219253e-01 1.4767874236
## [52,] -7.838389e-01 -0.2170302101
## [53,] 1.575728e+00 -1.2836022041
## [54,] 6.428993e-01 0.3856678904
## [55,] 8.976065e-02 -0.3515128735
## [56,] 2.765507e-01 -0.5217960934
## [57,] 6.792888e-01 -1.0681312007
## [58,] 8.983289e-02 0.4283659033
## [59,] -2.993090e+00 -0.1740182344
## [60,] 2.848830e-01 0.5156677286
## [61,] -3.672346e-01 -0.2343652773
## [62,] 1.852306e-01 -0.6585034258
## [63,] 5.818237e-01 1.2502366041
## [64,] 1.399737e+00 -0.2717637151
## [65,] -7.272921e-01 0.9479519959
## [66,] 1.302543e+00 -1.2015824301
## [67,] 3.358481e-01 -0.4661160964
## [68,] 1.038506e+00 -0.2693513952
## [69,] 9.207286e-01 -0.3909654081
## [70,] 7.208782e-01 1.3487070120
## [71,] -1.043119e+00 -0.0227647013
## [72,] -9.018639e-02 0.2442258511
## [73,] 6.235182e-01 -0.9423717079
## [74,] -9.535234e-01 -0.7292172765
## [75,] -5.428288e-01 0.9980689086
## [76,] 5.809965e-01 1.2584816646
## [77,] 7.681787e-01 1.2488636888
## [78,] 4.637676e-01 -1.3806370495
## [79,] -8.857763e-01 2.0499606936
## [80,] -1.099781e+00 1.0168728298
## [81,] 1.512707e+00 -0.0267174641
## [82,] 2.579214e-01 0.7036077788
## [83,] 8.844023e-02 -0.9713852292
## [84,] -1.208965e-01 -1.0961562416
## [85,] -1.194329e+00 0.0490504509
## [86,] 6.119969e-01 -1.1984958566
## [87,] -2.171398e-01 0.1900189986
## [88,] -1.827567e-01 1.2977058996
## [89,] 9.333463e-01 -1.0338737230
## [90,] 8.217731e-01 -0.7384407542
## [91,] 1.392116e+00 0.0465639395
## [92,] -4.761739e-01 -1.0175961198
## [93,] 6.503486e-01 -0.3832839599
## [94,] 1.391110e+00 0.8727554117
## [95,] -1.110789e+00 0.9695450140
## [96,] -8.607926e-01 0.3838466650
## [97,] -1.131739e+00 -1.8515556631
## [98,] -1.459214e+00 -0.0539967368
## [99,] 7.998255e-02 1.0647732143
## [100,] 6.532043e-01 0.8131950374
## [101,] 1.200965e+00 -0.1908164741
## [102,] 1.044751e+00 -2.6999298086
## [103,] -1.003209e+00 0.0609666388
## [104,] 1.848482e+00 0.5737516975
## [105,] -6.667734e-01 0.0458035797
## [106,] 1.055138e-01 0.1574125402
## [107,] -4.222559e-01 0.4315653729
## [108,] -1.223502e-01 -0.3965497361
## [109,] 1.881930e-01 1.3099782258
## [110,] 1.191610e-01 0.4703933999
## [111,] -2.509255e-02 -1.2426702706
## [112,] 1.080727e-01 1.3815754564
## [113,] -4.854352e-01 1.2044589370
## [114,] -5.042171e-01 0.8240739637
## [115,] -1.661099e+00 -1.6626294022
## [116,] -3.823337e-01 -0.5693063436
## [117,] -5.126503e-01 0.6355138173
## [118,] 2.701891e+00 0.0437220076
## [119,] -1.362116e+00 0.3480123037
## [120,] 1.372562e-01 2.4595935489
## [121,] -1.493625e+00 -0.8183803244
## [122,] -1.470436e+00 -2.1132001149
## [123,] 1.247024e-01 0.2736952724
## [124,] -9.966391e-01 -0.6875968412
## [125,] -1.822614e-03 0.4460410530
## [126,] -4.282589e-01 -0.8123847238
## [127,] -6.136716e-01 2.2120554803
## [128,] -2.024678e+00 -0.1237059716
## [129,] -1.224748e+00 -0.4773355060
## [130,] 1.795164e-01 -0.1662614915
## [131,] 5.676206e-01 0.8625633836
## [132,] -4.928774e-01 0.0973404852
## [133,] 6.288407e-05 -1.6256167392
## [134,] 1.122890e+00 -0.0046207678
## [135,] 1.439856e+00 0.7602421677
## [136,] -1.097114e+00 0.0389909129
## [137,] -1.173196e-01 0.7350721416
## [138,] 1.201498e+00 -0.1464726270
## [139,] -4.697296e-01 -0.0578873354
## [140,] -5.246948e-02 0.4823694661
## [141,] -8.610730e-02 0.9929436368
## [142,] -8.876790e-01 -1.2463954980
## [143,] -4.446840e-01 -0.0334875248
## [144,] -2.944488e-02 -0.0709621812
## [145,] -4.138688e-01 -0.7589206537
## [146,] 1.113386e+00 -1.0343593609
## [147,] -4.809928e-01 -0.6307319540
## [148,] -4.331690e-01 0.5868077200
## [149,] 6.968626e-01 -0.4163226562
## [150,] -1.056368e+00 -0.7848878095
## [151,] -4.069848e-02 0.1634163195
## [152,] -1.551545e+00 -1.2367142351
## [153,] 1.167170e+00 1.0458737762
## [154,] -2.736457e-01 -0.4845954162
## [155,] -4.678453e-01 0.1891288117
## [156,] -1.238252e+00 0.0510063316
## [157,] -7.762034e-03 -0.0002406689
## [158,] -8.002822e-01 1.8093820424
## [159,] -5.334923e-01 -0.8253279571
## [160,] 1.287675e+00 1.1454704522
## [161,] -1.755259e-01 0.0315731876
## [162,] -1.071782e+00 -0.8352058053
## [163,] 1.632069e-01 -0.0687636490
## [164,] -3.627384e-01 0.7467716870
## [165,] 5.900135e-01 -0.4255187344
## [166,] 1.432422e+00 -0.7720822352
## [167,] -9.926925e-01 0.1527641067
## [168,] 1.098860e+01 0.9147748677
## [169,] 9.926542e+00 -0.0024562667
## [170,] 8.612973e+00 0.1360095524
## [171,] 8.693324e+00 -0.7201535449
## [172,] 9.231605e+00 -0.1981243301
## [173,] 9.472892e+00 -1.0292088060
## [174,] 9.978573e+00 -0.9669558959
## [175,] 1.067050e+01 -1.2208130889
## [176,] 9.565383e+00 0.8362077039
## [177,] 8.886120e+00 1.1149717985
## [178,] 1.060711e+01 -0.4129448529
## [179,] 1.027546e+01 -1.1289773980
## [180,] 1.115735e+01 -0.0879313318
## [181,] 8.317519e+00 2.2419036933
## [182,] 1.008732e+01 2.0413131708
## [183,] 1.135336e+01 -1.7198003367
## [184,] 1.072417e+01 -0.3569066561
## [185,] 9.167447e+00 1.5332804922
## [186,] 1.073253e+01 -0.0382440966
## [187,] 9.128073e+00 1.5974132423
## [188,] 9.546602e+00 -0.3335853933
## [189,] 1.118753e+01 0.6049859239
## [190,] 9.709855e+00 0.2242412393
## [191,] 1.082855e+01 3.2290694955
## [192,] 9.708772e+00 0.9204525668
## [193,] 8.423638e+00 -1.2065390692
## [194,] 9.151184e+00 -0.6038811692
## [195,] 8.911480e+00 0.3702352846
## [196,] 9.515709e+00 -1.9010006467
## [197,] 9.663689e+00 -1.8044099450
## [198,] 9.846642e+00 -1.1218226064
## [199,] 9.756753e+00 -0.3479296066
## [200,] 1.189220e+01 1.2389021486
## [201,] 8.614002e+00 -0.2741975649
## [202,] 9.585176e+00 0.1623807156
## [203,] 1.034908e+01 -0.0646069098
## [204,] 1.162844e+01 -0.7052370970
## [205,] 1.008852e+01 1.3621972688
## [206,] 1.123915e+01 -1.0965131881
## [207,] 8.355444e+00 -0.2284335185
## [208,] 1.144636e+01 -0.3478280806
## [209,] 9.309440e+00 0.5321286195
## [210,] 9.723569e+00 1.6072345623
## [211,] 8.890581e+00 0.5138145261
## [212,] 1.013387e+01 1.3823731606
## [213,] 1.178534e+01 0.7630970485
## [214,] 1.242216e+01 -0.6245845446
## [215,] 8.923171e+00 0.0815438004
## [216,] 1.048594e+01 1.3760791114
## [217,] 1.138852e+01 -1.5612657862
## [218,] 9.804343e+00 0.3247706606
## [219,] 9.781825e+00 -0.1567903170
## [220,] 9.695222e+00 0.8777838607
## [221,] 1.059783e+01 0.7501665752
## [222,] 1.139743e+01 0.3010534038
## [223,] 1.068762e+01 1.4928111172
## [224,] 1.032019e+01 -1.5254938002
## [225,] 9.698130e+00 0.9107175585
## [226,] 1.049835e+01 -1.5795320279
## [227,] 9.450463e+00 0.5877162571
## [228,] 9.720743e+00 0.0896422960
## [229,] 1.109651e+01 0.9672616569
## [230,] 1.044201e+01 0.0788123529
## [231,] 1.024102e+01 -1.5686998365
## [232,] 9.744392e+00 -2.0078231840
## [233,] 1.093103e+01 0.5409735242
## [234,] 1.133491e+01 -0.0733765981
## [235,] 9.130728e+00 -0.5710183936
## [236,] 1.005549e+01 -0.3110684599
## [237,] 1.004907e+01 -0.6714150671
## [238,] 9.421644e+00 -0.1573404521
## [239,] 9.001261e+00 -0.9313050710
## [240,] 9.997567e+00 -1.9830094795
## [241,] 1.065551e+01 -0.2195998042
## [242,] 1.147684e+01 1.0452758695
## [243,] 8.090847e+00 1.8773295663
## [244,] 9.297561e+00 0.0026061960
## [245,] 9.688570e+00 -0.0806699347
## [246,] 8.336843e+00 0.9629822812
## [247,] 9.249467e+00 0.0535710165
## [248,] 9.222648e+00 -0.4348984089
## [249,] 9.277430e+00 -1.7372972553
## [250,] 7.811165e+00 -1.2636955998
## [251,] 1.021342e+01 0.4063085121
## [252,] 9.368077e+00 -1.4596539678
## [253,] 1.152049e+01 1.0484573702
## [254,] 1.079596e+01 -1.3464305395
## [255,] 8.546470e+00 -0.1935705581
## [256,] 1.009840e+01 -0.0023359571
## [257,] 9.406229e+00 -0.0128297339
## [258,] 1.088828e+01 0.1519473220
## [259,] 1.005307e+01 0.5985111314
## [260,] 9.442976e+00 -0.1262124373
## [261,] 1.043840e+01 -0.2485355658
## [262,] 1.015261e+01 0.1603273949
## [263,] 9.835382e+00 -0.4336419416
## [264,] 1.201989e+01 1.5374124191
## [265,] 9.470614e+00 -2.1702465766
## [266,] 9.529213e+00 1.0270046193
## [267,] 8.454063e+00 -0.2484829332
## [268,] 9.959473e+00 0.4223203858
## [269,] 1.089036e+01 0.9876532936
## [270,] 7.928612e+00 0.8355681720
## [271,] 9.749935e+00 -0.6605218590
## [272,] 8.818350e+00 1.5640694933
## [273,] 1.144194e+01 -1.6229759353
## [274,] 1.135790e+01 0.8638963735
## [275,] 1.033450e+01 -0.5116027734
## [276,] 1.142934e+01 -1.9173650254
## [277,] 9.132682e+00 -1.8658138486
## [278,] 1.095065e+01 0.2451790634
## [279,] 9.414988e+00 2.2235343019
## [280,] 1.032096e+01 0.2733760641
## [281,] 9.700604e+00 1.1307847945
## [282,] 9.721457e+00 0.8386693741
## [283,] 1.054612e+01 -0.6546152779
## [284,] 8.696179e+00 0.9539609785
## [285,] 9.749086e+00 0.3529514655
## [286,] 1.017101e+01 0.2065992926
## [287,] 9.596533e+00 1.0011132343
## [288,] 1.010466e+01 0.7474519916
## [289,] 9.681119e+00 -0.6265748367
## [290,] 1.161834e+01 0.3952236859
## [291,] 1.071419e+01 -0.8921679540
## [292,] 1.296587e+01 0.6308184101
## [293,] 9.204922e+00 -0.4327051833
## [294,] 1.081437e+01 0.4521386442
## [295,] 1.209803e+01 0.3679990452
## [296,] 1.030098e+01 -0.2703874897
## [297,] 8.916925e+00 0.4655126177
## [298,] 8.993677e+00 0.5743562256
## [299,] 9.964585e+00 -0.2306999902
## [300,] 1.130912e+01 1.1722425083
## [301,] 1.075040e+01 1.3927027067
## [302,] 7.861632e+00 -0.6619912557
## [303,] 9.299646e+00 -0.7773692067
## [304,] 9.990944e+00 0.5135385789
## [305,] 8.541867e+00 -0.9133122380
## [306,] 1.069453e+01 -0.4494238053
## [307,] 7.538665e+00 0.8029326991
## [308,] 1.014329e+01 -0.5734768510
## [309,] 9.608778e+00 -1.9281251678
## [310,] 9.508836e+00 0.6643908338
## [311,] 9.716353e+00 -1.6025402238
## [312,] 1.031479e+01 -1.3546002575
## [313,] 1.039633e+01 -3.0179326794
## [314,] 9.774396e+00 0.8312378222
## [315,] 8.075050e+00 0.2510970888
## [316,] 8.560771e+00 0.4622934659
## [317,] 8.530342e+00 0.8447922232
## [318,] 1.076186e+01 -0.0419715243
## [319,] 9.756385e+00 -1.1055759057
## [320,] 1.026968e+01 0.5637756523
## [321,] 8.441072e+00 1.3033647558
## [322,] 9.464412e+00 -1.5002209378
## [323,] 1.056245e+01 -0.6069892351
## [324,] 9.821674e+00 -0.2922450657
## [325,] 9.884864e+00 -1.2896833433
## [326,] 9.927939e+00 0.6941058488
## [327,] 1.121091e+01 -0.5991819029
## [328,] 9.385103e+00 1.2569066440
## [329,] 1.067613e+01 0.0535080136
## [330,] 1.089860e+01 0.7280925177
## [331,] 8.810682e+00 1.5610980682
## [332,] 1.012126e+01 0.2656247536
## [333,] 9.988778e+00 1.0767262592
## [334,] 1.102914e+01 0.2106979317
## [335,] 3.488326e+00 6.9892646674
## [336,] 5.022402e+00 7.8718195050
## [337,] 5.718136e+00 9.3487995716
## [338,] 5.489457e+00 8.6471015179
## [339,] 4.826112e+00 9.9447745979
## [340,] 3.782301e+00 7.9952801475
## [341,] 5.646398e+00 9.7239027325
## [342,] 4.083544e+00 8.3311672590
## [343,] 3.748177e+00 7.8869598063
## [344,] 5.594928e+00 8.6571948106
## [345,] 3.767189e+00 9.0497793232
## [346,] 5.244364e+00 7.7723180385
## [347,] 5.002772e+00 8.2359940892
## [348,] 3.671790e+00 7.7538179384
## [349,] 6.179696e+00 10.0167739778
## [350,] 4.407195e+00 9.7236126241
## [351,] 6.199978e+00 7.9674728629
## [352,] 4.524966e+00 9.5573460041
## [353,] 4.424943e+00 8.7444185769
## [354,] 4.968774e+00 7.8866082429
## [355,] 4.641943e+00 9.4211974396
## [356,] 4.643399e+00 8.6770496882
## [357,] 4.122336e+00 9.8801799012
## [358,] 3.787103e+00 8.8051363932
## [359,] 5.613287e+00 10.1880549821
## [360,] 4.193797e+00 8.4902354882
## [361,] 3.623543e+00 9.2195480109
## [362,] 4.492152e+00 9.3702944214
## [363,] 4.199065e+00 9.2791083937
## [364,] 2.807214e+00 9.2019424373
## [365,] 4.709063e+00 8.9870034576
## [366,] 5.167174e+00 8.9091349939
## [367,] 5.294692e+00 10.3650313653
## [368,] 5.392741e+00 9.9081305689
## [369,] 3.999156e+00 8.3901118286
## [370,] 4.674273e+00 10.3964372212
## [371,] 3.991651e+00 9.1447983733
## [372,] 4.364569e+00 8.3593932284
## [373,] 3.790159e+00 9.1698022596
## [374,] 3.883536e+00 8.8428125126
## [375,] 5.629881e+00 9.1009395945
## [376,] 4.727478e+00 8.0266058459
## [377,] 4.741159e+00 8.1801747247
## [378,] 6.729558e+00 10.3629189690
## [379,] 4.941608e+00 9.9613709305
## [380,] 4.462936e+00 8.1162755256
## [381,] 5.747287e+00 8.0999078846
## [382,] 4.512742e+00 10.7233331328
## [383,] 6.372908e+00 10.9090421621
## [384,] 4.622328e+00 8.2228588041
## [385,] 4.383847e+00 7.6976947374
## [386,] 3.831875e+00 11.6234951668
## [387,] 5.328640e+00 9.2296289143
## [388,] 6.466511e+00 9.1867498921
## [389,] 4.643990e+00 9.0761366350
## [390,] 5.261468e+00 10.4048601863
## [391,] 5.333329e+00 8.8082777647
## [392,] 6.422193e+00 10.4593921642
## [393,] 5.663877e+00 8.7793445489
## [394,] 3.926345e+00 9.5051458863
## [395,] 4.303098e+00 7.9665029939
## [396,] 4.253870e+00 9.1704734715
## [397,] 5.141573e+00 10.2006681609
## [398,] 4.996053e+00 8.8365940852
## [399,] 5.367938e+00 10.2824758631
## [400,] 4.342657e+00 11.7271963879
## [401,] 4.623653e+00 9.9419242173
## [402,] 5.741360e+00 8.7513859627
## [403,] 4.900393e+00 9.0964788597
## [404,] 4.345710e+00 8.5660690587
## [405,] 5.971164e+00 11.1786678675
## [406,] 5.013496e+00 6.0412203809
## [407,] 4.083465e+00 9.0808882392
## [408,] 6.709689e+00 9.1101378046
## [409,] 3.831899e+00 9.2134483263
## [410,] 3.218964e+00 7.4421803874
## [411,] 2.746868e+00 9.2162115463
## [412,] 5.651126e+00 9.1876638170
## [413,] 4.467167e+00 10.2586221252
## [414,] 4.724441e+00 9.5235177809
## [415,] 5.289627e+00 10.1154542775
## [416,] 4.533516e+00 8.0424977578
## [417,] 3.391940e+00 8.8755944201
## [418,] 3.050216e+00 9.1917378290
## [419,] 4.659300e+00 9.2722172506
## [420,] 5.174726e+00 8.3061855363
## [421,] 2.722222e+00 10.4791719209
## [422,] 5.290524e+00 8.3882329784
## [423,] 5.422306e+00 7.3856900256
## [424,] 6.294737e+00 9.4024901106
## [425,] 5.164714e+00 9.6645554473
## [426,] 5.204954e+00 9.9441270710
## [427,] 5.604604e+00 8.0537392023
## [428,] 4.980859e+00 8.7517115508
## [429,] 4.920286e+00 7.6715635315
## [430,] 5.115984e+00 9.8447637421
## [431,] 5.744173e+00 9.3476967324
## [432,] 4.568709e+00 9.9137625864
## [433,] 4.500471e+00 9.6082745534
## [434,] 4.134838e+00 8.3924520122
## [435,] 4.042243e+00 9.1796580709
## [436,] 5.326800e+00 7.0915905806
## [437,] 6.547372e+00 9.5029462577
## [438,] 4.031140e+00 9.9688991535
## [439,] 4.811560e+00 8.1242628742
## [440,] 3.969999e+00 6.8639754613
## [441,] 5.908086e+00 7.4771724184
## [442,] 4.682618e+00 7.8868817921
## [443,] 5.179004e+00 10.2409838955
## [444,] 5.348028e+00 9.0034819351
## [445,] 3.945721e+00 7.7622054140
## [446,] 4.895256e+00 9.5556991189
## [447,] 4.771657e+00 6.8168506506
## [448,] 5.675356e+00 8.7529755429
## [449,] 3.766755e+00 10.1128569276
## [450,] 3.800038e+00 8.6583267630
## [451,] 5.765867e+00 10.3054383421
## [452,] 4.411902e+00 10.7953238714
## [453,] 4.339704e+00 7.8321647725
## [454,] 5.113014e+00 7.8477123750
## [455,] 4.679601e+00 8.0855445307
## [456,] 6.866381e+00 9.5287280325
## [457,] 5.259531e+00 9.8350789270
## [458,] 5.161560e+00 10.2091369741
## [459,] 5.931075e+00 10.2994725454
## [460,] 4.940053e+00 10.0757323042
## [461,] 5.048740e+00 9.9398010235
## [462,] 3.927125e+00 9.1633746934
## [463,] 2.707029e+00 8.1118614414
## [464,] 3.792793e+00 8.2738390172
## [465,] 5.114109e+00 9.4075970056
## [466,] 3.966703e+00 10.6835363393
## [467,] 5.688808e+00 10.7059798236
## [468,] 5.725083e+00 7.0738332992
## [469,] 5.217380e+00 8.1660019848
## [470,] 4.798343e+00 10.4191325163
## [471,] 3.634310e+00 7.9358902850
## [472,] 4.691062e+00 7.3864225275
## [473,] 4.547097e+00 9.5998110887
## [474,] 5.663229e+00 10.7329647054
## [475,] 6.308630e+00 10.9345045625
## [476,] 5.501040e+00 9.5328205757
## [477,] 3.871711e+00 9.7196657560
## [478,] 6.670997e+00 9.5600933858
## [479,] 6.010353e+00 8.9819130683
## [480,] 5.223521e+00 5.6282609174
## [481,] 2.793515e+00 9.7607032448
## [482,] 4.045414e+00 8.6087731478
## [483,] 4.931427e+00 10.0099012238
## [484,] 5.761306e+00 8.3730268529
## [485,] 3.820096e+00 7.3654226305
## [486,] 8.211199e+00 10.2452426520
## [487,] 2.446175e+00 9.1813774466
## [488,] 4.764066e+00 12.4953042640
## [489,] 4.740437e+00 9.9155919133
## [490,] 4.336633e+00 10.0485065174
## [491,] 4.681009e+00 9.7638249369
## [492,] 5.742395e+00 8.3966126231
## [493,] 4.125707e+00 8.6295703373
## [494,] 2.917186e+00 10.0598259383
## [495,] 5.093768e+00 10.0551105298
## [496,] 4.998180e+00 9.5829721611
## [497,] 4.986899e+00 8.0134325645
## [498,] 5.667968e+00 10.6846218117
## [499,] 4.986832e+00 7.6331589543
## [500,] 5.776047e+00 8.5667856514
norma <- numeric(0)
for (it in 1:200) {
D2 <- pmax(outer(rowSums(P^2), rowSums(X^2), "+") - 2 * P %*% t(X), 0)
W <- exp(-0.5 * D2 / h^2) # bobot kernel Gaussian
Pn <- (W %*% X) / rowSums(W) # p + m(p)
norma[it] <- max(sqrt(rowSums((Pn - P)^2))) # maks ||m(p)||
P <- Pn
riw[[it + 1]] <- P
cat("iterasi", it, "| maks ||m|| =", format(norma[it], digits = 3), "\n")
if (norma[it] < eps) break # kriteria henti
}
## iterasi 1 | maks ||m|| = 3.22
## iterasi 2 | maks ||m|| = 1.26
## iterasi 3 | maks ||m|| = 0.475
## iterasi 4 | maks ||m|| = 0.114
## iterasi 5 | maks ||m|| = 0.0244
## iterasi 6 | maks ||m|| = 0.00507
## iterasi 7 | maks ||m|| = 0.00105
## iterasi 8 | maks ||m|| = 0.000218
## iterasi 9 | maks ||m|| = 4.5e-05
Tit <- length(riw) - 1
Tit
## [1] 9
kl <- cutree(hclust(dist(P), "single"), h = h / 2)
cat("Konvergen:", Tit, "iterasi | kluster:", length(unique(kl)), "\n")
## Konvergen: 9 iterasi | kluster: 3
print(table(kl))
## kl
## 1 2 3
## 167 167 166
sel <- sort(unique(pmin(c(0, 1, 2, 3, 4, Tit), Tit)))
par(mfrow = c(2, 3), mar = c(4, 4, 3, 1))
for (t in sel) {
plot(X, pch = 16, cex = 0.4, col = "grey85", xlab = "x1", ylab = "x2",
main = if (t == 0) "Iterasi 0: data awal" else
paste0("Iterasi ", t, " (maks ||m|| = ", format(norma[t], digits = 2), ")"))
if (t > 0) # jejak pergeseran p -> p + m(p)
segments(riw[[t]][, 1], riw[[t]][, 2], riw[[t + 1]][, 1], riw[[t + 1]][, 2],
col = adjustcolor("red3", 0.2))
points(riw[[t + 1]], pch = 16, cex = 0.5, col = adjustcolor(kl + 1, 0.7))
}
par(mfrow = c(1, 2))
plot(norma, type = "b", pch = 19, col = "blue", log = "y", xlab = "Iterasi",
ylab = "maks ||m(p)|| (skala log)", main = "Cek konvergensi")
abline(h = eps, col = "red", lty = 2, lwd = 2)
plot(X, col = kl + 1, pch = 16, cex = 0.5, xlab = "x1", ylab = "x2",
main = paste0("Hasil: ", length(unique(kl)), " kluster"))
points(do.call(rbind, lapply(split(as.data.frame(P), kl), colMeans)),
pch = 24, bg = "gold", cex = 2) # mode
d <- 2; n <- nrow(X)
dens <- function(p) sum(exp(-0.5 * colSums((t(X) - p)^2) / h^2)) * (2 * pi)^(-d / 2) / (n * h^d)
lingk <- function(c, r, ...) {
t <- seq(0, 2 * pi, length.out = 200); lines(c[1] + r * cos(t), c[2] + r * sin(t), ...)
}
label_bg <- function(x, y, teks, cex = 0.72) { # teks dengan latar putih
w <- strwidth(teks, cex = cex); hh <- strheight(teks, cex = cex)
rect(x - w / 2 - 0.05 * u, y - hh / 2 - 0.05 * u, x + w / 2 + 0.05 * u, y + hh / 2 + 0.05 * u,
col = adjustcolor("white", 0.9), border = "grey40")
text(x, y, teks, cex = cex, font = 2)
}
u <- mean(apply(X, 2, sd))
# KDE pada grid: f(x) = 1/(n h^d) * sum K((x - xi)/h)
gx <- seq(min(X[, 1]) - 0.5 * u, max(X[, 1]) + 0.5 * u, length.out = 120)
gy <- seq(min(X[, 2]) - 0.5 * u, max(X[, 2]) + 0.5 * u, length.out = 120)
Kx <- exp(-0.5 * outer(gx, X[, 1], "-")^2 / h^2)
Ky <- exp(-0.5 * outer(gy, X[, 2], "-")^2 / h^2)
f <- (Kx %*% t(Ky)) * (2 * pi)^(-d / 2) / (n * h^d)
fz <- f^0.6
mode_k <- do.call(rbind, lapply(split(as.data.frame(P), kl), colMeans))
f_mode <- apply(mode_k, 1, dens)
jauh <- sqrt(rowSums((X - P)^2))
rep_i <- which.max(jauh)
rep_k <- sapply(sort(unique(kl)), function(k) { idx <- which(kl == k); idx[which.max(jauh[idx])] })
jejak <- t(sapply(riw, function(M) M[rep_i, ]))
p0 <- jejak[1, ]; p1 <- jejak[2, ]; pT <- jejak[Tit + 1, ]
m1 <- p1 - p0
cat("\n--- NOMINAL UNTUK ANOTASI ---\n")
##
## --- NOMINAL UNTUK ANOTASI ---
cat("1. KDE f(mode) :", sprintf("%.4f", f_mode), "\n")
## 1. KDE f(mode) : 0.0052 0.0052 0.0051
cat("2. Kernel Gaussian K(0) :", sprintf("%.4f", (2 * pi)^(-d / 2)), "\n")
## 2. Kernel Gaussian K(0) : 0.1592
cat("3. m(p) titik contoh :", sprintf("(%.4f, %.4f), ||m|| = %.4f", m1[1], m1[2], sqrt(sum(m1^2))), "\n")
## 3. m(p) titik contoh : (-3.0464, -1.0552), ||m|| = 3.2239
cat("4. Iterasi :", Tit, "| dari", sprintf("(%.3f, %.3f)", p0[1], p0[2]),
"ke", sprintf("(%.3f, %.3f)", pT[1], pT[2]), "\n")
## 4. Iterasi : 9 | dari (8.211, 10.245) ke (4.806, 8.977)
cat("5. Kriteria henti :", sprintf("maks ||m|| = %.2e < eps = %g", norma[Tit], eps), "\n")
## 5. Kriteria henti : maks ||m|| = 4.50e-05 < eps = 0.0001
cat("6. Bandwidth h :", sprintf("%.4f", h), "\n")
## 6. Bandwidth h : 3.0726
col_titik <- "#08519c"; col_jejak <- "#e31a1c"; col_eps <- "#7b2cbf"; col_box <- "#08519c"
xl <- c(min(gx) - 3.4 * u, max(gx) + 3.4 * u); yl <- c(min(gy) - 1 * u, max(gy) + 0.3 * u)
par(mfrow = c(1, 1), mar = c(4.5, 4.5, 4, 1))
image(gx, gy, fz, xlim = xl, ylim = yl, xlab = "x1", ylab = "x2",
col = colorRampPalette(c("#ffffff", "#c7e9c0", "#74c476", "#31a354", "#006d2c", "#00441b"))(80),
main = sprintf("Mean Shift: h = %.3f \u2192 %d puncak", h, length(unique(kl))))
contour(gx, gy, fz, add = TRUE, drawlabels = FALSE, nlevels = 8,
col = adjustcolor("#00441b", 0.55), lwd = 1)
points(X, pch = 21, bg = "white", col = col_titik, lwd = 0.6, cex = 0.5)
for (i in rep_k) {
jj <- t(sapply(riw, function(M) M[i, ]))
q0 <- jj[1, ]; q1 <- jj[2, ]; qT <- jj[Tit + 1, ]
lines(jj, col = col_jejak, lwd = 3)
points(jj, pch = 21, bg = col_jejak, col = "white", cex = 1.1)
lingk(q0, h, lty = 2, lwd = 2.5, col = "black")
arrows(q0[1], q0[2], q1[1], q1[2], col = col_jejak, lwd = 4, length = 0.12)
points(q0[1], q0[2], pch = 21, bg = "white", col = "black", cex = 1.8, lwd = 2.5)
lingk(qT, 0.28 * u, col = col_eps, lwd = 3.5)
}
points(mode_k, pch = 24, bg = "#ffd400", col = "black", cex = 2.6, lwd = 1.5)
for (i in seq_len(nrow(mode_k)))
label_bg(mode_k[i, 1], mode_k[i, 2] - 0.55 * u,
sprintf("(%.2f, %.2f) f = %.3f", mode_k[i, 1], mode_k[i, 2], f_mode[i]))
kotak <- function(x, y, no, teks, target, kanan = FALSE) {
w <- strwidth(teks, cex = 0.75); hh <- strheight(teks, cex = 0.75); pad <- 0.1 * u
x0 <- if (kanan) x - w else x
xc <- x0 - pad - 0.18 * u # posisi lingkaran nomor
segments(if (kanan) xc else x0 + w + pad, y, target[1], target[2], col = "grey20", lwd = 1.3)
rect(x0 - pad, y - hh / 2 - pad, x0 + w + pad, y + hh / 2 + pad,
col = "#fffbe6", border = col_box, lwd = 2)
text(x0, y, teks, adj = c(0, 0.5), cex = 0.75)
points(xc, y, pch = 21, bg = col_box, col = "white", cex = 2.6)
text(xc, y, no, col = "white", font = 2, cex = 0.85)
}
ys <- seq(max(gy) - 0.2 * u, min(gy) + 1.0 * u, length.out = 3)
xk <- xl[1] + 0.45 * u; xr <- xl[2] - 0.35 * u
kotak(xk, ys[1], 1, sprintf("Kepadatan (KDE)\nf(mode) = %s",
paste(sprintf("%.3f", f_mode), collapse = ", ")), mode_k[kl[rep_i], ])
kotak(xk, ys[2], 2, sprintf("Kernel (pembobot titik)\nGaussian, d = %d\nK(0) = %.4f",
d, (2 * pi)^(-d / 2)), p0)
kotak(xk, ys[3], 3, sprintf("Vektor mean shift m(p)\nm = (%.3f, %.3f)\n||m|| = %.3f",
m1[1], m1[2], sqrt(sum(m1^2))), (p0 + p1) / 2)
kotak(xr, ys[1], 4, sprintf("Pergeseran titik (iterasi)\n%d iterasi\n(%.2f, %.2f) -> (%.2f, %.2f)",
Tit, p0[1], p0[2], pT[1], pT[2]), jejak[min(3, Tit + 1), ], kanan = TRUE)
kotak(xr, ys[2], 5, sprintf("Kriteria henti\nmaks ||m|| = %.1e\n< eps = %g",
norma[Tit], eps), pT, kanan = TRUE)
kotak(xr, ys[3], 6, sprintf("Bandwidth (h) = radius\nh = %.4f\n(kuantil 30%% jarak)", h),
p0 + h * c(cos(pi / 4), sin(pi / 4)), kanan = TRUE)
legend("bottom", ncol = 3, bty = "o", bg = "white", cex = 0.8,
legend = c("titik data", "mode (puncak)", "jejak iterasi", "radius h", "vektor m(p)", "lingkaran eps (diperbesar)"),
pch = c(21, 24, 21, NA, NA, NA), lty = c(NA, NA, 1, 2, 1, 1), lwd = c(NA, NA, 3, 2.5, 4, 3.5),
col = c(col_titik, "black", col_jejak, "black", col_jejak, col_eps),
pt.bg = c("white", "#ffd400", col_jejak, NA, NA, NA), pt.cex = c(1, 1.6, 1, NA, NA, NA))
