library(psych)
library(corrplot)
## corrplot 0.95 loaded
library(factoextra)
## Loading required package: ggplot2
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(knitr)

Karakteristik Data

Import data & pilih variabel numerik

data <- read.csv("DatasetKel-12.csv")

data <- data[, !names(data) %in% "X"]
data_pca <- data[, sapply(data, is.numeric)]

head(data_pca)
##   x.radius_mean x.texture_mean x.perimeter_mean x.area_mean x.smoothness_mean
## 1        13.540          14.36            87.46       566.3           0.09779
## 2        13.080          15.71            85.63       520.0           0.10750
## 3         9.504          12.44            60.34       273.9           0.10240
## 4        13.030          18.42            82.61       523.8           0.08983
## 5         8.196          16.84            51.71       201.9           0.08600
## 6        12.050          14.63            78.04       449.3           0.10310
##   x.compactness_mean x.concavity_mean x.concave_pts_mean x.symmetry_mean
## 1            0.08129          0.06664           0.047810          0.1885
## 2            0.12700          0.04568           0.031100          0.1967
## 3            0.06492          0.02956           0.020760          0.1815
## 4            0.03766          0.02562           0.029230          0.1467
## 5            0.05943          0.01588           0.005917          0.1769
## 6            0.09092          0.06592           0.027490          0.1675
##   x.fractal_dim_mean x.radius_se x.texture_se x.perimeter_se x.area_se
## 1            0.05766      0.2699       0.7886          2.058    23.560
## 2            0.06811      0.1852       0.7477          1.383    14.670
## 3            0.06905      0.2773       0.9768          1.909    15.700
## 4            0.05863      0.1839       2.3420          1.170    14.160
## 5            0.06503      0.1563       0.9567          1.094     8.205
## 6            0.06043      0.2636       0.7294          1.848    19.870
##   x.smoothness_se x.compactness_se x.concavity_se x.concave_pts_se
## 1        0.008462         0.014600        0.02387         0.013150
## 2        0.004097         0.018980        0.01698         0.006490
## 3        0.009606         0.014320        0.01985         0.014210
## 4        0.004352         0.004899        0.01343         0.011640
## 5        0.008968         0.016460        0.01588         0.005917
## 6        0.005488         0.014270        0.02322         0.005660
##   x.symmetry_se x.fractal_dim_se x.radius_worst x.texture_worst
## 1       0.01980         0.002300         15.110           19.26
## 2       0.01678         0.002425         14.500           20.49
## 3       0.02027         0.002968         10.230           15.66
## 4       0.02671         0.001777         13.300           22.81
## 5       0.02574         0.002582          8.964           21.96
## 6       0.01428         0.002422         13.760           20.70
##   x.perimeter_worst x.area_worst x.smoothness_worst x.compactness_worst
## 1             99.70        711.2            0.14400             0.17730
## 2             96.09        630.5            0.13120             0.27760
## 3             65.13        314.9            0.13240             0.11480
## 4             84.46        545.9            0.09701             0.04619
## 5             57.26        242.2            0.12970             0.13570
## 6             89.88        582.6            0.14940             0.21560
##   x.concavity_worst x.concave_pts_worst x.symmetry_worst x.fractal_dim_worst
## 1           0.23900             0.12880           0.2977             0.07259
## 2           0.18900             0.07283           0.3184             0.08183
## 3           0.08867             0.06227           0.2450             0.07773
## 4           0.04833             0.05013           0.1987             0.06169
## 5           0.06880             0.02564           0.3105             0.07409
## 6           0.30500             0.06548           0.2747             0.08301

Pemeriksaan Missing Value

colSums(is.na(data_pca))
##       x.radius_mean      x.texture_mean    x.perimeter_mean         x.area_mean 
##                   0                   0                   0                   0 
##   x.smoothness_mean  x.compactness_mean    x.concavity_mean  x.concave_pts_mean 
##                   0                   0                   0                   0 
##     x.symmetry_mean  x.fractal_dim_mean         x.radius_se        x.texture_se 
##                   0                   0                   0                   0 
##      x.perimeter_se           x.area_se     x.smoothness_se    x.compactness_se 
##                   0                   0                   0                   0 
##      x.concavity_se    x.concave_pts_se       x.symmetry_se    x.fractal_dim_se 
##                   0                   0                   0                   0 
##      x.radius_worst     x.texture_worst   x.perimeter_worst        x.area_worst 
##                   0                   0                   0                   0 
##  x.smoothness_worst x.compactness_worst   x.concavity_worst x.concave_pts_worst 
##                   0                   0                   0                   0 
##    x.symmetry_worst x.fractal_dim_worst 
##                   0                   0
sum(is.na(data_pca))
## [1] 0

Statistik deskriptif

desc<- describe(data_pca)
desc
##                     vars   n   mean     sd median trimmed    mad    min     max
## x.radius_mean          1 569  14.13   3.52  13.37   13.82   2.82   6.98   28.11
## x.texture_mean         2 569  19.29   4.30  18.84   19.04   4.17   9.71   39.28
## x.perimeter_mean       3 569  91.97  24.30  86.24   89.74  18.84  43.79  188.50
## x.area_mean            4 569 654.89 351.91 551.10  606.13 227.28 143.50 2501.00
## x.smoothness_mean      5 569   0.10   0.01   0.10    0.10   0.01   0.05    0.16
## x.compactness_mean     6 569   0.10   0.05   0.09    0.10   0.05   0.02    0.35
## x.concavity_mean       7 569   0.09   0.08   0.06    0.08   0.06   0.00    0.43
## x.concave_pts_mean     8 569   0.05   0.04   0.03    0.04   0.03   0.00    0.20
## x.symmetry_mean        9 569   0.18   0.03   0.18    0.18   0.03   0.11    0.30
## x.fractal_dim_mean    10 569   0.06   0.01   0.06    0.06   0.01   0.05    0.10
## x.radius_se           11 569   0.41   0.28   0.32    0.36   0.16   0.11    2.87
## x.texture_se          12 569   1.22   0.55   1.11    1.16   0.47   0.36    4.88
## x.perimeter_se        13 569   2.87   2.02   2.29    2.51   1.14   0.76   21.98
## x.area_se             14 569  40.34  45.49  24.53   31.69  13.63   6.80  542.20
## x.smoothness_se       15 569   0.01   0.00   0.01    0.01   0.00   0.00    0.03
## x.compactness_se      16 569   0.03   0.02   0.02    0.02   0.01   0.00    0.14
## x.concavity_se        17 569   0.03   0.03   0.03    0.03   0.02   0.00    0.40
## x.concave_pts_se      18 569   0.01   0.01   0.01    0.01   0.01   0.00    0.05
## x.symmetry_se         19 569   0.02   0.01   0.02    0.02   0.01   0.01    0.08
## x.fractal_dim_se      20 569   0.00   0.00   0.00    0.00   0.00   0.00    0.03
## x.radius_worst        21 569  16.27   4.83  14.97   15.73   3.65   7.93   36.04
## x.texture_worst       22 569  25.68   6.15  25.41   25.39   6.42  12.02   49.54
## x.perimeter_worst     23 569 107.26  33.60  97.66  103.42  25.01  50.41  251.20
## x.area_worst          24 569 880.58 569.36 686.50  788.02 319.65 185.20 4254.00
## x.smoothness_worst    25 569   0.13   0.02   0.13    0.13   0.02   0.07    0.22
## x.compactness_worst   26 569   0.25   0.16   0.21    0.23   0.13   0.03    1.06
## x.concavity_worst     27 569   0.27   0.21   0.23    0.25   0.20   0.00    1.25
## x.concave_pts_worst   28 569   0.11   0.07   0.10    0.11   0.07   0.00    0.29
## x.symmetry_worst      29 569   0.29   0.06   0.28    0.28   0.05   0.16    0.66
## x.fractal_dim_worst   30 569   0.08   0.02   0.08    0.08   0.01   0.06    0.21
##                       range skew kurtosis    se
## x.radius_mean         21.13 0.94     0.81  0.15
## x.texture_mean        29.57 0.65     0.73  0.18
## x.perimeter_mean     144.71 0.99     0.94  1.02
## x.area_mean         2357.50 1.64     3.59 14.75
## x.smoothness_mean      0.11 0.45     0.82  0.00
## x.compactness_mean     0.33 1.18     1.61  0.00
## x.concavity_mean       0.43 1.39     1.95  0.00
## x.concave_pts_mean     0.20 1.17     1.03  0.00
## x.symmetry_mean        0.20 0.72     1.25  0.00
## x.fractal_dim_mean     0.05 1.30     2.95  0.00
## x.radius_se            2.76 3.07    17.45  0.01
## x.texture_se           4.52 1.64     5.26  0.02
## x.perimeter_se        21.22 3.43    21.12  0.08
## x.area_se            535.40 5.42    48.59  1.91
## x.smoothness_se        0.03 2.30    10.32  0.00
## x.compactness_se       0.13 1.89     5.02  0.00
## x.concavity_se         0.40 5.08    48.24  0.00
## x.concave_pts_se       0.05 1.44     5.04  0.00
## x.symmetry_se          0.07 2.18     7.78  0.00
## x.fractal_dim_se       0.03 3.90    25.94  0.00
## x.radius_worst        28.11 1.10     0.91  0.20
## x.texture_worst       37.52 0.50     0.20  0.26
## x.perimeter_worst    200.79 1.12     1.04  1.41
## x.area_worst        4068.80 1.85     4.32 23.87
## x.smoothness_worst     0.15 0.41     0.49  0.00
## x.compactness_worst    1.03 1.47     2.98  0.01
## x.concavity_worst      1.25 1.14     1.57  0.01
## x.concave_pts_worst    0.29 0.49    -0.55  0.00
## x.symmetry_worst       0.51 1.43     4.37  0.00
## x.fractal_dim_worst    0.15 1.65     5.16  0.00

Visualisasi Data

boxplot(data_pca[,1:15],
        las = 2,
        cex.axis = 0.7,
        main = "Boxplot 1")

boxplot(data_pca[,16:30],
        las = 2,
        cex.axis = 0.7,
        main = "Boxplot 2")

Uji Asumsi PCA

Matriks Korelasi

mat_corr <- cor(data_pca)
kable(round(mat_corr,3))
x.radius_mean x.texture_mean x.perimeter_mean x.area_mean x.smoothness_mean x.compactness_mean x.concavity_mean x.concave_pts_mean x.symmetry_mean x.fractal_dim_mean x.radius_se x.texture_se x.perimeter_se x.area_se x.smoothness_se x.compactness_se x.concavity_se x.concave_pts_se x.symmetry_se x.fractal_dim_se x.radius_worst x.texture_worst x.perimeter_worst x.area_worst x.smoothness_worst x.compactness_worst x.concavity_worst x.concave_pts_worst x.symmetry_worst x.fractal_dim_worst
x.radius_mean 1.000 0.324 0.998 0.987 0.171 0.506 0.677 0.823 0.148 -0.312 0.679 -0.097 0.674 0.736 -0.223 0.206 0.194 0.376 -0.104 -0.043 0.970 0.297 0.965 0.941 0.120 0.413 0.527 0.744 0.164 0.007
x.texture_mean 0.324 1.000 0.330 0.321 -0.023 0.237 0.302 0.293 0.071 -0.076 0.276 0.386 0.282 0.260 0.007 0.192 0.143 0.164 0.009 0.054 0.353 0.912 0.358 0.344 0.078 0.278 0.301 0.295 0.105 0.119
x.perimeter_mean 0.998 0.330 1.000 0.987 0.207 0.557 0.716 0.851 0.183 -0.261 0.692 -0.087 0.693 0.745 -0.203 0.251 0.228 0.407 -0.082 -0.006 0.969 0.303 0.970 0.942 0.151 0.456 0.564 0.771 0.189 0.051
x.area_mean 0.987 0.321 0.987 1.000 0.177 0.499 0.686 0.823 0.151 -0.283 0.733 -0.066 0.727 0.800 -0.167 0.213 0.208 0.372 -0.072 -0.020 0.963 0.287 0.959 0.959 0.124 0.390 0.513 0.722 0.144 0.004
x.smoothness_mean 0.171 -0.023 0.207 0.177 1.000 0.659 0.522 0.554 0.558 0.585 0.301 0.068 0.296 0.247 0.332 0.319 0.248 0.381 0.201 0.284 0.213 0.036 0.239 0.207 0.805 0.472 0.435 0.503 0.394 0.499
x.compactness_mean 0.506 0.237 0.557 0.499 0.659 1.000 0.883 0.831 0.603 0.565 0.497 0.046 0.549 0.456 0.135 0.739 0.571 0.642 0.230 0.507 0.535 0.248 0.590 0.510 0.566 0.866 0.816 0.816 0.510 0.687
x.concavity_mean 0.677 0.302 0.716 0.686 0.522 0.883 1.000 0.921 0.501 0.337 0.632 0.076 0.660 0.617 0.099 0.670 0.691 0.683 0.178 0.449 0.688 0.300 0.730 0.676 0.449 0.755 0.884 0.861 0.409 0.515
x.concave_pts_mean 0.823 0.293 0.851 0.823 0.554 0.831 0.921 1.000 0.462 0.167 0.698 0.021 0.711 0.690 0.028 0.490 0.439 0.616 0.095 0.258 0.830 0.293 0.856 0.810 0.453 0.667 0.752 0.910 0.376 0.369
x.symmetry_mean 0.148 0.071 0.183 0.151 0.558 0.603 0.501 0.462 1.000 0.480 0.303 0.128 0.314 0.224 0.187 0.422 0.343 0.393 0.449 0.332 0.186 0.091 0.219 0.177 0.427 0.473 0.434 0.430 0.700 0.438
x.fractal_dim_mean -0.312 -0.076 -0.261 -0.283 0.585 0.565 0.337 0.167 0.480 1.000 0.000 0.164 0.040 -0.090 0.402 0.560 0.447 0.341 0.345 0.688 -0.254 -0.051 -0.205 -0.232 0.505 0.459 0.346 0.175 0.334 0.767
x.radius_se 0.679 0.276 0.692 0.733 0.301 0.497 0.632 0.698 0.303 0.000 1.000 0.213 0.973 0.952 0.165 0.356 0.332 0.513 0.241 0.228 0.715 0.195 0.720 0.752 0.142 0.287 0.381 0.531 0.095 0.050
x.texture_se -0.097 0.386 -0.087 -0.066 0.068 0.046 0.076 0.021 0.128 0.164 0.213 1.000 0.223 0.112 0.397 0.232 0.195 0.230 0.412 0.280 -0.112 0.409 -0.102 -0.083 -0.074 -0.092 -0.069 -0.120 -0.128 -0.046
x.perimeter_se 0.674 0.282 0.693 0.727 0.296 0.549 0.660 0.711 0.314 0.040 0.973 0.223 1.000 0.938 0.151 0.416 0.362 0.556 0.266 0.244 0.697 0.200 0.721 0.731 0.130 0.342 0.419 0.555 0.110 0.085
x.area_se 0.736 0.260 0.745 0.800 0.247 0.456 0.617 0.690 0.224 -0.090 0.952 0.112 0.938 1.000 0.075 0.285 0.271 0.416 0.134 0.127 0.757 0.196 0.761 0.811 0.125 0.283 0.385 0.538 0.074 0.018
x.smoothness_se -0.223 0.007 -0.203 -0.167 0.332 0.135 0.099 0.028 0.187 0.402 0.165 0.397 0.151 0.075 1.000 0.337 0.269 0.328 0.414 0.427 -0.231 -0.075 -0.217 -0.182 0.314 -0.056 -0.058 -0.102 -0.107 0.101
x.compactness_se 0.206 0.192 0.251 0.213 0.319 0.739 0.670 0.490 0.422 0.560 0.356 0.232 0.416 0.285 0.337 1.000 0.801 0.744 0.395 0.803 0.205 0.143 0.261 0.199 0.227 0.679 0.639 0.483 0.278 0.591
x.concavity_se 0.194 0.143 0.228 0.208 0.248 0.571 0.691 0.439 0.343 0.447 0.332 0.195 0.362 0.271 0.269 0.801 1.000 0.772 0.309 0.727 0.187 0.100 0.227 0.188 0.168 0.485 0.663 0.440 0.198 0.439
x.concave_pts_se 0.376 0.164 0.407 0.372 0.381 0.642 0.683 0.616 0.393 0.341 0.513 0.230 0.556 0.416 0.328 0.744 0.772 1.000 0.313 0.611 0.358 0.087 0.395 0.342 0.215 0.453 0.550 0.602 0.143 0.311
x.symmetry_se -0.104 0.009 -0.082 -0.072 0.201 0.230 0.178 0.095 0.449 0.345 0.241 0.412 0.266 0.134 0.414 0.395 0.309 0.313 1.000 0.369 -0.128 -0.077 -0.104 -0.110 -0.013 0.060 0.037 -0.030 0.389 0.078
x.fractal_dim_se -0.043 0.054 -0.006 -0.020 0.284 0.507 0.449 0.258 0.332 0.688 0.228 0.280 0.244 0.127 0.427 0.803 0.727 0.611 0.369 1.000 -0.037 -0.003 -0.001 -0.023 0.171 0.390 0.380 0.215 0.111 0.591
x.radius_worst 0.970 0.353 0.969 0.963 0.213 0.535 0.688 0.830 0.186 -0.254 0.715 -0.112 0.697 0.757 -0.231 0.205 0.187 0.358 -0.128 -0.037 1.000 0.360 0.994 0.984 0.217 0.476 0.574 0.787 0.244 0.093
x.texture_worst 0.297 0.912 0.303 0.287 0.036 0.248 0.300 0.293 0.091 -0.051 0.195 0.409 0.200 0.196 -0.075 0.143 0.100 0.087 -0.077 -0.003 0.360 1.000 0.365 0.346 0.225 0.361 0.368 0.360 0.233 0.219
x.perimeter_worst 0.965 0.358 0.970 0.959 0.239 0.590 0.730 0.856 0.219 -0.205 0.720 -0.102 0.721 0.761 -0.217 0.261 0.227 0.395 -0.104 -0.001 0.994 0.365 1.000 0.978 0.237 0.529 0.618 0.816 0.269 0.139
x.area_worst 0.941 0.344 0.942 0.959 0.207 0.510 0.676 0.810 0.177 -0.232 0.752 -0.083 0.731 0.811 -0.182 0.199 0.188 0.342 -0.110 -0.023 0.984 0.346 0.978 1.000 0.209 0.438 0.543 0.747 0.209 0.080
x.smoothness_worst 0.120 0.078 0.151 0.124 0.805 0.566 0.449 0.453 0.427 0.505 0.142 -0.074 0.130 0.125 0.314 0.227 0.168 0.215 -0.013 0.171 0.217 0.225 0.237 0.209 1.000 0.568 0.519 0.548 0.494 0.618
x.compactness_worst 0.413 0.278 0.456 0.390 0.472 0.866 0.755 0.667 0.473 0.459 0.287 -0.092 0.342 0.283 -0.056 0.679 0.485 0.453 0.060 0.390 0.476 0.361 0.529 0.438 0.568 1.000 0.892 0.801 0.614 0.810
x.concavity_worst 0.527 0.301 0.564 0.513 0.435 0.816 0.884 0.752 0.434 0.346 0.381 -0.069 0.419 0.385 -0.058 0.639 0.663 0.550 0.037 0.380 0.574 0.368 0.618 0.543 0.519 0.892 1.000 0.855 0.533 0.687
x.concave_pts_worst 0.744 0.295 0.771 0.722 0.503 0.816 0.861 0.910 0.430 0.175 0.531 -0.120 0.555 0.538 -0.102 0.483 0.440 0.602 -0.030 0.215 0.787 0.360 0.816 0.747 0.548 0.801 0.855 1.000 0.503 0.511
x.symmetry_worst 0.164 0.105 0.189 0.144 0.394 0.510 0.409 0.376 0.700 0.334 0.095 -0.128 0.110 0.074 -0.107 0.278 0.198 0.143 0.389 0.111 0.244 0.233 0.269 0.209 0.494 0.614 0.533 0.503 1.000 0.538
x.fractal_dim_worst 0.007 0.119 0.051 0.004 0.499 0.687 0.515 0.369 0.438 0.767 0.050 -0.046 0.085 0.018 0.101 0.591 0.439 0.311 0.078 0.591 0.093 0.219 0.139 0.080 0.618 0.810 0.687 0.511 0.538 1.000
corrplot(mat_corr,
         method = "color",
         type = "upper",
         order = "hclust",      
         tl.cex = 0.5,          
         tl.col = "black",
         tl.srt = 45,           
         addCoef.col = NULL)

Uji Barlett

bartlett <- cortest.bartlett(mat_corr, n = nrow(data_pca))
bartlett
## $chisq
## [1] 39362.12
## 
## $p.value
## [1] 0
## 
## $df
## [1] 435

Uji KMO

kmo <- KMO(mat_corr)

kmo_table <- data.frame(
  MSA = round(kmo$MSAi, 2)
)

kable(kmo_table)
MSA
x.radius_mean 0.83
x.texture_mean 0.64
x.perimeter_mean 0.85
x.area_mean 0.86
x.smoothness_mean 0.81
x.compactness_mean 0.88
x.concavity_mean 0.89
x.concave_pts_mean 0.90
x.symmetry_mean 0.83
x.fractal_dim_mean 0.83
x.radius_se 0.83
x.texture_se 0.48
x.perimeter_se 0.84
x.area_se 0.85
x.smoothness_se 0.64
x.compactness_se 0.87
x.concavity_se 0.83
x.concave_pts_se 0.84
x.symmetry_se 0.58
x.fractal_dim_se 0.81
x.radius_worst 0.82
x.texture_worst 0.60
x.perimeter_worst 0.88
x.area_worst 0.82
x.smoothness_worst 0.75
x.compactness_worst 0.85
x.concavity_worst 0.90
x.concave_pts_worst 0.89
x.symmetry_worst 0.69
x.fractal_dim_worst 0.81
kmo$MSA
## [1] 0.8322253

Eliminasi Variabel dengan MSA <0.5

kmo$MSAi[kmo$MSAi < 0.5]
## x.texture_se 
##    0.4845894
data_pca2 <- data_pca[, !names(data_pca) %in% "x.texture_se"]
mat_corr2 <- cor(data_pca2)
kmo2 <- KMO(mat_corr2)

kmo2$MSA      
## [1] 0.8398098
kmo2$MSAi     
##       x.radius_mean      x.texture_mean    x.perimeter_mean         x.area_mean 
##           0.8338378           0.7138100           0.8523631           0.8661324 
##   x.smoothness_mean  x.compactness_mean    x.concavity_mean  x.concave_pts_mean 
##           0.8119036           0.8797892           0.8914803           0.8989748 
##     x.symmetry_mean  x.fractal_dim_mean         x.radius_se      x.perimeter_se 
##           0.8328784           0.8304402           0.8327264           0.8387278 
##           x.area_se     x.smoothness_se    x.compactness_se      x.concavity_se 
##           0.8571309           0.6163082           0.8702270           0.8228154 
##    x.concave_pts_se       x.symmetry_se    x.fractal_dim_se      x.radius_worst 
##           0.8311391           0.5840236           0.8070904           0.8228654 
##     x.texture_worst   x.perimeter_worst        x.area_worst  x.smoothness_worst 
##           0.7182789           0.8835000           0.8221031           0.7502878 
## x.compactness_worst   x.concavity_worst x.concave_pts_worst    x.symmetry_worst 
##           0.8524841           0.9018163           0.8881710           0.7042633 
## x.fractal_dim_worst 
##           0.8111279

Principal Component Analysis (PCA)

Standarisasi Data

data_std <- scale(data_pca2)
kable(round(data_std,3))
x.radius_mean x.texture_mean x.perimeter_mean x.area_mean x.smoothness_mean x.compactness_mean x.concavity_mean x.concave_pts_mean x.symmetry_mean x.fractal_dim_mean x.radius_se x.perimeter_se x.area_se x.smoothness_se x.compactness_se x.concavity_se x.concave_pts_se x.symmetry_se x.fractal_dim_se x.radius_worst x.texture_worst x.perimeter_worst x.area_worst x.smoothness_worst x.compactness_worst x.concavity_worst x.concave_pts_worst x.symmetry_worst x.fractal_dim_worst
-0.167 -1.146 -0.186 -0.252 0.102 -0.436 -0.278 -0.029 0.268 -0.728 -0.488 -0.400 -0.369 0.473 -0.607 -0.266 0.219 -0.090 -0.565 -0.240 -1.044 -0.225 -0.297 0.509 -0.489 -0.159 0.216 0.123 -0.629
-0.297 -0.832 -0.261 -0.383 0.792 0.429 -0.541 -0.459 0.567 0.752 -0.793 -0.734 -0.564 -0.981 -0.363 -0.494 -0.860 -0.455 -0.518 -0.366 -0.844 -0.332 -0.439 -0.051 0.148 -0.399 -0.636 0.458 -0.117
-1.312 -1.593 -1.302 -1.083 0.429 -0.746 -0.743 -0.726 0.012 0.886 -0.461 -0.473 -0.542 0.854 -0.623 -0.399 0.391 -0.033 -0.313 -1.250 -1.630 -1.254 -0.994 0.001 -0.886 -0.880 -0.796 -0.729 -0.344
-0.311 -0.202 -0.385 -0.373 -0.464 -1.263 -0.793 -0.507 -1.257 -0.590 -0.798 -0.839 -0.575 -0.896 -1.149 -0.612 -0.025 0.746 -0.763 -0.614 -0.466 -0.679 -0.588 -1.549 -1.322 -1.073 -0.981 -1.477 -1.232
-1.683 -0.570 -1.657 -1.287 -0.737 -0.850 -0.915 -1.108 -0.155 0.316 -0.897 -0.876 -0.706 0.642 -0.504 -0.531 -0.953 0.629 -0.458 -1.511 -0.605 -1.488 -1.121 -0.117 -0.754 -0.975 -1.353 0.330 -0.546
-0.589 -1.083 -0.573 -0.584 0.479 -0.254 -0.287 -0.552 -0.498 -0.335 -0.511 -0.504 -0.450 -0.517 -0.626 -0.287 -0.994 -0.758 -0.519 -0.519 -0.810 -0.517 -0.523 0.746 -0.246 0.157 -0.747 -0.249 -0.052
-0.181 0.700 -0.208 -0.267 -0.629 -0.518 -0.518 -0.389 -0.010 -0.796 -0.618 -0.559 -0.443 -0.861 -0.651 -0.363 0.007 -0.500 -0.695 -0.232 0.999 -0.246 -0.319 -0.708 -0.529 -0.211 0.207 -0.048 -0.818
-0.672 0.537 -0.710 -0.645 -0.710 -1.035 -0.906 -0.973 -1.155 -0.555 0.004 -0.114 -0.261 -0.394 -0.878 -0.670 -0.705 0.426 -0.766 -0.681 0.007 -0.723 -0.639 -1.045 -1.069 -1.040 -1.178 -0.756 -1.014
-0.138 -0.686 -0.196 -0.236 -1.387 -0.828 -0.881 -0.817 -1.673 -0.463 -0.786 -0.701 -0.567 -0.854 -0.765 -0.699 -0.622 -0.882 -0.470 -0.331 -0.405 -0.333 -0.393 -1.028 -0.611 -0.801 -0.437 -0.897 -0.205
-0.621 -0.244 -0.669 -0.617 -0.978 -1.076 -0.867 -0.913 0.206 -0.240 -0.641 -0.666 -0.503 0.056 -0.955 -0.622 -0.615 -0.070 -0.438 -0.656 -0.707 -0.702 -0.621 -0.787 -1.050 -0.864 -0.786 -0.187 -0.546
-0.740 -0.125 -0.767 -0.699 -0.080 -0.939 -0.733 -0.674 0.395 -0.528 -0.289 -0.338 -0.371 0.429 -0.936 -0.610 -0.507 1.408 -0.532 -0.710 -0.522 -0.757 -0.658 -0.327 -1.062 -0.870 -0.783 0.655 -0.752
-0.306 0.005 -0.385 -0.363 -1.121 -1.258 -1.105 -1.153 0.027 -1.103 -0.004 -0.134 -0.162 0.150 -0.943 -1.034 -1.236 0.164 -0.304 -0.422 -0.558 -0.507 -0.450 -1.326 -1.223 -1.296 -1.575 -0.746 -1.166
-1.563 -1.744 -1.549 -1.223 0.082 -0.977 -0.855 -1.060 -0.469 1.285 -0.899 -0.900 -0.704 1.022 -0.834 -0.400 -0.981 0.043 -0.381 -1.399 -1.672 -1.409 -1.064 1.793 -0.829 -0.745 -1.071 0.516 0.350
-1.123 -1.025 -1.128 -0.975 1.212 -0.449 -0.978 -0.928 3.397 0.963 0.399 0.221 -0.126 0.158 -0.809 -0.803 -0.584 2.575 0.816 -1.086 -1.339 -1.113 -0.899 -0.213 -0.989 -1.201 -1.351 1.061 -0.207
-1.569 0.393 -1.535 -1.231 1.987 -0.279 -0.738 -1.022 0.060 0.676 -0.169 -0.185 -0.482 1.628 0.343 -0.063 -0.411 1.576 -0.282 -1.387 0.222 -1.345 -1.066 1.381 -0.537 -0.873 -1.321 0.115 -0.378
-1.406 -1.262 -1.349 -1.120 -1.362 -0.319 -0.363 -0.699 1.931 0.968 0.017 -0.128 -0.370 0.565 0.776 0.372 0.616 2.586 0.766 -1.295 -1.049 -1.240 -1.002 -1.489 -0.550 -0.635 -0.970 0.616 0.053
-1.323 0.400 -1.311 -1.095 0.572 -0.504 -0.841 -0.873 -0.345 0.877 -0.613 -0.597 -0.575 1.159 -0.443 -0.489 -0.399 0.272 0.167 -1.212 0.957 -1.197 -0.966 0.982 -0.558 -0.854 -0.752 -0.037 0.452
-0.799 -0.058 -0.830 -0.741 -1.064 -1.086 -0.649 -0.686 -1.078 -0.868 -0.478 -0.512 -0.488 0.746 -0.908 -0.373 -0.459 0.156 -0.623 -0.815 -0.299 -0.871 -0.727 -0.148 -1.035 -0.613 -0.685 -0.809 -0.971
-1.447 -0.456 -1.365 -1.149 0.728 0.700 2.812 -0.133 1.092 2.502 -0.280 -0.485 -0.498 0.835 3.383 9.008 3.472 2.592 2.178 -1.233 -0.493 -1.243 -0.976 0.693 1.158 4.697 0.919 2.145 1.858
-0.382 -0.651 -0.436 -0.433 0.139 -0.985 -0.656 -0.523 -0.808 -0.888 -0.607 -0.690 -0.484 0.307 -1.109 -0.531 -0.508 0.242 -0.714 -0.581 -0.963 -0.643 -0.572 -0.121 -1.167 -0.807 -0.849 -0.837 -1.099
-1.487 -1.081 -1.365 -1.168 0.105 0.923 -0.034 -0.521 0.330 3.825 0.436 0.149 -0.327 3.387 3.808 0.822 0.950 0.589 6.854 -1.352 -1.628 -1.330 -1.047 -0.511 -0.068 -0.617 -1.015 -1.045 1.354
-0.516 -0.644 -0.526 -0.523 -0.330 -0.683 -0.691 -0.675 -0.334 -0.518 -0.558 -0.557 -0.454 -0.728 -0.407 -0.452 -0.621 -0.808 -0.563 -0.447 -0.401 -0.522 -0.473 -0.647 -0.445 -0.488 -0.426 -0.457 -0.435
-0.169 -1.941 -0.167 -0.272 2.328 0.007 -0.251 0.429 2.157 0.512 0.018 -0.106 -0.169 2.118 0.163 -0.672 -0.576 0.626 0.895 -0.453 -2.146 -0.473 -0.483 0.558 -0.740 -0.895 -0.617 -0.308 -0.666
-0.360 -0.300 -0.361 -0.422 0.212 -0.168 -0.626 -0.664 -0.341 -0.400 -0.504 -0.538 -0.439 -0.582 -0.495 -0.370 -0.586 -0.370 -0.358 -0.420 -0.139 -0.458 -0.454 -0.152 -0.255 -0.475 -0.538 -0.197 -0.264
-0.760 0.391 -0.747 -0.720 0.984 -0.203 -0.538 -0.685 0.111 1.027 -0.289 -0.390 -0.345 1.109 -0.470 -0.200 -0.695 -0.288 0.068 -0.654 1.055 -0.676 -0.624 1.022 -0.551 -0.463 -0.811 -0.224 0.253
-0.223 -0.797 -0.225 -0.383 0.813 0.931 0.352 0.540 0.476 0.881 -0.430 -0.658 -0.602 -0.082 0.574 0.262 0.330 0.096 0.305 -0.153 -0.405 -0.315 -0.467 0.930 1.429 1.024 0.855 1.012 0.977
-0.604 -0.846 -0.618 -0.601 0.062 -0.619 -0.593 -0.781 0.975 -0.442 -0.642 -0.705 -0.531 -0.357 -0.411 -0.392 -0.773 -0.099 -0.449 -0.538 -0.126 -0.580 -0.549 0.234 -0.343 -0.218 -0.582 0.773 -0.261
-0.501 0.584 -0.502 -0.536 -0.614 -0.187 -0.359 -0.296 0.432 0.176 -0.387 -0.328 -0.426 0.024 -0.031 -0.161 0.184 -0.116 0.252 -0.505 0.785 -0.470 -0.537 -0.086 -0.051 -0.138 0.090 0.115 0.480
0.145 -0.942 0.156 -0.008 1.197 0.560 0.136 0.560 1.110 0.094 0.383 0.469 0.053 -0.511 1.041 0.413 0.719 0.451 0.395 0.015 -1.210 0.064 -0.135 -0.204 0.347 -0.057 0.382 0.404 0.043
0.140 1.100 0.107 0.022 -0.471 -0.346 -0.725 -0.499 -0.462 -0.586 -0.119 -0.290 -0.145 -0.724 -0.408 -0.685 -0.517 0.037 -0.341 -0.033 0.559 -0.130 -0.135 -0.914 -0.494 -0.864 -0.687 -0.612 -0.636
-0.243 -1.053 -0.298 -0.293 -1.622 -1.019 -0.705 -0.578 -1.553 -1.362 0.002 -0.082 -0.088 -0.853 -0.843 -0.607 -0.158 -1.192 -0.892 0.019 -0.541 -0.082 -0.088 -1.391 -0.829 -0.658 -0.221 -1.412 -1.212
-0.192 -0.230 -0.221 -0.284 0.415 -0.430 -0.615 -0.544 -0.633 -0.807 -0.397 -0.379 -0.332 -0.385 -0.590 -0.436 -0.394 -0.206 -0.747 -0.242 0.043 -0.288 -0.318 0.067 -0.503 -0.643 -0.540 -0.360 -0.992
-0.553 -0.337 -0.584 -0.579 0.579 -0.639 -0.802 -0.503 0.322 0.503 -0.141 -0.226 -0.349 -0.536 -0.764 -0.682 0.550 0.201 -0.146 -0.712 -0.774 -0.748 -0.677 -0.804 -1.021 -1.066 -0.849 -1.089 -0.564
-1.232 0.151 -1.229 -1.024 0.429 -0.972 -1.028 -1.056 -1.684 0.864 -0.253 -0.363 -0.446 1.362 -0.606 -0.881 -1.061 -0.306 0.708 -1.107 0.100 -1.144 -0.904 -0.034 -1.014 -1.206 -1.381 -1.563 0.329
-0.717 -1.500 -0.726 -0.688 -0.464 -0.551 -0.588 -0.397 -0.699 0.428 -0.626 -0.688 -0.540 -0.296 -0.680 -0.496 -0.796 -0.488 -0.470 -0.664 -1.386 -0.723 -0.646 0.470 -0.440 -0.383 -0.458 -0.208 0.200
-2.028 -1.362 -1.983 -1.453 1.468 -0.543 -1.114 -1.261 0.432 2.179 -0.653 -0.649 -0.671 1.049 -0.817 -1.057 -1.912 0.732 0.115 -1.725 -0.999 -1.692 -1.221 1.140 -0.852 -1.305 -1.744 0.051 0.547
-0.553 0.286 -0.607 -0.557 -1.154 -1.211 -0.815 -0.805 -0.265 -0.854 -0.767 -0.832 -0.564 -0.653 -1.082 -0.702 -0.810 -0.735 -0.855 -0.606 1.165 -0.675 -0.584 -0.879 -1.053 -0.756 -0.613 -0.334 -0.840
-1.206 0.026 -1.153 -1.013 0.294 -0.140 -0.342 -0.480 0.487 0.060 -0.811 -0.662 -0.628 0.672 -0.196 -0.053 -0.110 -0.539 -0.085 -1.140 0.188 -1.043 -0.912 1.031 -0.153 -0.037 -0.260 -0.451 0.053
-1.032 0.000 -1.011 -0.906 0.251 -0.351 -0.738 -0.951 1.479 0.285 -0.181 -0.279 -0.378 0.185 -0.184 -0.102 -0.516 0.793 -0.130 -0.978 -0.385 -0.983 -0.839 -0.458 -0.672 -0.922 -1.256 -0.121 -0.467
-0.706 -0.223 -0.691 -0.689 1.268 -0.050 -0.227 -0.363 -0.039 0.340 -0.358 -0.352 -0.433 0.499 -0.133 -0.081 0.354 -0.592 0.017 -0.647 0.583 -0.647 -0.630 1.596 0.075 0.072 0.109 -0.153 0.389
-0.501 -0.174 -0.533 -0.535 -0.824 -0.685 -0.782 -0.766 -0.765 -0.303 -1.029 -0.998 -0.684 -1.194 -0.838 -0.670 -1.011 -0.972 -0.922 -0.616 0.295 -0.646 -0.591 -0.612 -0.368 -0.376 -0.459 0.133 -0.670
-0.791 0.458 -0.802 -0.734 -0.624 -0.731 -0.470 -0.771 -1.184 0.353 -0.616 -0.628 -0.526 0.690 -0.553 -0.247 -0.869 -0.588 -0.498 -0.674 0.565 -0.693 -0.637 1.644 -0.220 0.191 -0.484 -0.116 0.242
-1.234 -0.535 -1.213 -1.036 0.522 -0.384 -0.570 -0.802 -0.830 1.112 -0.008 -0.059 -0.384 2.268 0.215 -0.155 -0.254 1.484 0.319 -1.080 -0.685 -1.059 -0.902 0.628 -0.494 -0.682 -0.932 -0.594 0.041
-0.425 0.342 -0.404 -0.496 0.211 0.314 0.222 0.291 -0.279 1.119 -0.226 -0.077 -0.437 1.955 0.834 0.633 1.808 0.109 0.792 -0.608 -0.034 -0.543 -0.620 -0.161 -0.186 -0.242 -0.062 -1.091 0.051
0.038 0.084 0.241 -0.071 -1.279 2.252 2.653 0.749 -0.393 2.109 -0.153 0.264 -0.244 -0.581 2.735 3.697 1.803 0.619 3.471 -0.201 -0.317 -0.008 -0.301 -1.878 1.049 1.947 0.546 -0.813 1.343
-1.026 0.209 -0.960 -0.911 1.126 0.492 -0.302 -0.470 0.403 2.128 -0.258 -0.408 -0.449 1.612 0.670 0.464 0.591 0.282 1.133 -1.057 -0.476 -1.031 -0.889 -0.104 -0.314 -0.684 -0.810 -0.837 0.350
-1.533 -0.804 -1.487 -1.205 1.325 -0.423 -0.596 -0.765 -0.593 1.917 -0.861 -0.748 -0.690 0.406 -0.187 0.023 -0.226 -0.419 0.004 -1.374 -0.986 -1.273 -1.047 1.753 -0.114 -0.127 -0.146 0.041 0.983
-0.624 0.521 -0.635 -0.615 0.094 -0.489 -0.696 -0.743 -0.451 -0.121 -0.337 -0.428 -0.342 0.254 -0.023 -0.449 -0.662 -0.939 0.023 -0.538 0.077 -0.587 -0.523 0.772 -0.091 -0.584 -0.641 -0.748 0.081
-1.469 -0.821 -1.368 -1.164 -0.124 0.378 0.048 -0.666 -1.848 1.251 -0.332 0.205 -0.514 3.767 2.352 2.012 1.829 0.399 0.683 -1.418 -1.400 -1.307 -1.072 -0.634 -0.422 -0.565 -1.158 -2.018 -0.372
-0.771 -1.969 -0.767 -0.715 -0.187 -0.710 -0.673 -0.585 -0.528 -0.236 -0.953 -0.872 -0.656 -0.333 -0.569 -0.555 -0.865 -0.859 -0.600 -0.714 -1.579 -0.700 -0.650 0.982 -0.097 -0.297 -0.381 0.186 0.071
0.106 -1.953 0.095 -0.040 0.977 0.105 -0.005 0.228 0.162 0.173 -0.405 -0.464 -0.355 -1.073 -0.710 -0.102 0.033 -0.174 -0.373 -0.118 -1.578 -0.133 -0.237 -0.047 -0.480 -0.078 0.114 -0.019 -0.215
-0.215 -0.674 -0.242 -0.288 -1.793 -0.589 -0.099 -0.539 -1.421 -0.647 -0.870 -0.813 -0.564 -0.374 0.403 0.586 -0.230 -1.024 0.106 -0.416 -0.476 -0.454 -0.436 -1.308 -0.007 0.281 -0.378 -1.378 -0.424
-0.079 -0.484 -0.145 -0.188 -0.605 -0.814 -0.936 -0.967 -0.721 -0.552 -0.673 -0.678 -0.493 -0.813 -0.911 -0.754 -1.132 -0.977 -0.789 -0.161 -0.341 -0.207 -0.272 -0.730 -0.758 -0.916 -0.967 -0.868 -0.671
0.276 -0.674 0.313 0.056 1.325 1.446 0.314 0.939 0.691 0.265 0.093 -0.035 -0.011 0.654 0.914 0.005 1.748 0.361 0.449 -0.033 -1.195 -0.041 -0.207 0.273 0.216 -0.365 0.421 -0.502 -0.341
-0.550 -1.395 -0.530 -0.566 0.728 -0.175 -0.756 -0.518 0.249 0.271 -0.738 -0.442 -0.552 -0.089 -0.051 -0.719 -0.600 0.735 0.132 -0.606 -1.280 -0.473 -0.589 0.452 0.027 -0.829 -0.498 0.918 0.469
0.449 -1.246 0.413 0.304 -0.124 -0.184 -0.219 0.268 0.016 -0.789 -0.337 -0.442 -0.273 -0.607 -0.577 -0.501 0.143 -0.466 -0.554 0.255 -1.046 0.209 0.074 -0.441 -0.377 -0.486 0.347 -0.287 -0.733
-0.686 -0.609 -0.710 -0.657 0.621 -0.822 -0.663 -0.591 -1.724 -0.474 0.158 0.194 -0.131 -0.154 -0.652 -0.175 0.206 -0.841 -0.033 -0.608 -0.032 -0.628 -0.586 -0.231 -0.963 -0.803 -0.683 -1.921 -0.582
-0.765 -0.907 -0.778 -0.725 0.002 -0.671 -0.674 -0.520 -0.283 -0.587 -0.827 -0.852 -0.608 -0.635 -0.573 -0.582 -0.518 -0.669 -0.834 -0.817 -0.595 -0.813 -0.735 -0.586 -0.569 -0.634 -0.454 -0.363 -0.902
-0.808 -1.372 -0.781 -0.767 1.425 0.175 -0.532 -0.025 -0.148 -0.294 -0.241 -0.502 -0.308 1.408 0.531 -0.332 1.273 -0.574 -0.133 -0.900 -1.612 -0.915 -0.784 0.190 -0.458 -0.889 -0.434 -1.291 -0.892
-1.246 -1.702 -1.265 -1.041 -0.274 -1.199 -1.114 -1.261 0.333 0.201 -0.744 -0.815 -0.617 -0.333 -1.107 -1.057 -1.912 0.269 -0.217 -1.169 -1.884 -1.212 -0.944 -0.393 -1.158 -1.305 -1.744 0.330 -0.135
-0.765 -0.460 -0.753 -0.730 0.913 -0.180 -0.859 -0.781 -0.608 0.400 -0.436 -0.460 -0.417 -0.126 -0.454 -0.673 -0.369 0.276 -0.102 -0.722 0.176 -0.732 -0.663 0.391 -0.477 -0.935 -0.770 -0.512 -0.165
-0.348 -0.783 -0.339 -0.405 -0.682 -0.175 -0.500 -0.465 -0.123 -0.063 -0.688 -0.582 -0.521 -0.572 -0.550 -0.556 -0.683 0.060 -0.721 -0.370 -0.628 -0.300 -0.416 -0.051 0.003 -0.303 -0.204 1.048 -0.153
-0.958 -1.004 -0.976 -0.851 -1.310 -1.003 -0.832 -1.058 -1.505 -0.838 -0.551 -0.524 -0.497 -0.165 -0.428 -0.388 -1.002 -0.464 -0.542 -0.894 -0.807 -0.877 -0.772 -1.085 -0.839 -0.837 -1.224 -0.971 -0.900
-0.632 -1.079 -0.570 -0.631 1.340 0.478 -0.649 -0.487 0.669 2.208 -0.032 0.077 -0.336 1.042 1.225 -0.133 -0.113 1.298 2.127 -0.645 -1.492 -0.625 -0.652 0.439 -0.016 -0.853 -0.824 -0.281 1.088
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2.163 0.395 2.277 2.376 -0.167 1.737 1.640 1.543 -0.331 -0.121 2.747 2.968 2.560 -0.451 1.347 1.040 0.618 -0.158 0.310 2.466 0.407 2.638 2.641 -0.226 1.387 1.479 1.057 -0.110 0.257
1.079 1.207 0.956 0.978 -0.555 -0.645 -0.399 -0.038 -0.998 -1.090 0.058 -0.050 0.120 -0.532 -0.770 -0.519 -0.531 -0.768 -0.395 0.962 1.466 0.828 0.772 -0.038 -0.468 -0.308 -0.015 -0.641 -0.247
1.329 0.161 1.191 1.271 -0.507 -0.862 -0.108 0.245 -0.954 -1.818 -0.277 -0.249 -0.079 0.177 -0.801 -0.188 0.459 -0.150 -0.801 0.764 -0.224 0.647 0.624 -0.353 -0.879 -0.245 0.225 -0.539 -1.471
1.428 1.700 1.409 1.373 0.401 0.776 1.296 1.230 0.330 -0.085 0.833 0.720 0.644 0.117 -0.055 0.265 0.184 -0.749 -0.132 1.542 1.663 1.564 1.481 2.007 0.825 1.453 1.104 0.577 0.734
1.496 -0.258 1.450 1.393 0.522 0.755 0.926 1.178 0.297 -0.549 0.237 0.018 0.282 -0.462 -0.195 -0.043 0.518 -0.522 -0.692 1.556 0.484 1.343 1.313 0.851 0.767 0.764 1.682 1.114 -0.336
0.600 -0.121 0.693 0.427 0.728 1.436 1.330 1.072 0.235 0.573 -0.425 -0.199 -0.269 -0.825 0.521 0.226 0.048 -0.806 0.108 0.472 -0.096 0.584 0.264 0.181 1.375 1.104 0.891 -0.211 1.238
-0.672 -0.267 -0.698 -0.636 0.236 -0.856 -0.777 -0.355 -0.703 0.010 0.865 0.629 0.193 -0.481 -0.862 -0.635 0.409 -0.580 -0.392 -0.602 -0.372 -0.660 -0.574 -0.818 -1.109 -1.011 -0.654 -1.492 -0.819
1.533 -0.091 1.545 1.597 1.325 1.133 1.642 1.476 -0.072 0.386 2.545 2.162 2.037 -0.328 0.366 0.811 0.897 -0.206 0.375 1.999 0.092 1.900 2.059 0.750 1.000 1.629 1.269 0.109 0.850
1.692 1.063 1.759 1.683 0.828 1.505 1.750 2.038 1.595 1.684 2.405 2.442 1.989 0.307 1.220 1.477 1.226 0.825 0.806 1.533 0.611 1.534 1.432 0.102 0.539 1.059 1.182 0.636 0.595
1.161 -0.098 1.100 1.057 0.078 0.139 0.304 0.788 -0.017 -0.872 -0.004 -0.158 0.188 -0.739 -0.496 -0.259 -0.059 -0.943 -0.508 1.153 -0.110 1.001 1.062 0.483 0.140 0.542 0.958 -0.143 -0.109
1.712 0.086 1.610 1.759 -1.149 -0.354 0.335 0.730 0.425 -1.677 0.676 0.496 0.759 -0.834 -0.654 -0.180 0.109 0.168 -0.834 1.405 -0.431 1.278 1.364 -1.181 -0.639 -0.056 0.424 0.249 -1.363
1.763 0.516 1.808 1.731 1.468 1.575 2.104 2.615 2.763 0.553 0.595 0.567 0.631 -0.518 -0.065 0.000 0.307 0.863 -0.170 1.868 1.006 1.900 1.857 1.175 1.239 1.257 2.341 4.295 1.022
0.608 0.330 0.614 0.451 1.460 0.522 0.740 0.927 0.497 -0.004 0.117 0.200 0.090 -0.115 -0.260 0.019 0.344 -0.627 -0.380 0.623 0.765 0.671 0.422 1.166 0.257 0.419 0.665 0.327 -0.108
0.605 0.602 0.639 0.489 1.432 0.454 1.143 0.796 0.209 0.357 0.597 0.047 0.382 1.172 0.675 0.878 0.010 2.380 0.904 0.302 -0.076 0.192 0.166 0.448 -0.271 0.298 -0.151 -0.266 -0.244
0.540 -0.879 0.569 0.393 -0.103 0.620 0.396 0.554 -0.108 -0.430 -0.245 -0.117 -0.155 -0.400 0.389 0.174 0.453 -0.710 -0.255 0.515 -0.602 0.507 0.333 0.488 1.230 1.071 1.270 0.191 0.404
0.832 0.398 0.816 0.749 1.105 0.024 0.778 1.299 -0.309 -0.296 1.482 1.588 1.029 -0.195 -0.419 0.435 0.915 -0.272 -0.023 0.977 1.216 1.070 0.846 0.549 -0.311 0.574 1.036 -0.449 -0.440
1.317 0.498 1.273 1.242 -0.370 0.679 0.216 0.309 0.516 -0.279 0.855 0.743 1.053 0.169 0.753 0.240 1.031 0.138 0.246 1.711 1.414 1.602 1.743 0.763 1.452 0.917 1.372 1.258 0.817
2.662 1.158 2.598 3.103 0.749 0.454 1.781 2.373 -0.053 -1.096 2.177 1.779 2.721 -0.249 -0.322 0.130 0.197 -0.696 -0.256 2.980 0.822 2.831 3.557 0.838 0.086 1.005 1.435 -0.497 -0.364
1.576 0.556 1.561 1.532 0.114 0.560 1.223 1.582 0.986 -0.800 0.784 1.141 0.601 -0.761 0.458 0.383 1.015 2.059 -0.192 1.341 1.462 1.498 1.158 -0.463 0.582 0.964 1.687 1.850 -0.264
0.460 -0.016 0.623 0.295 1.987 2.501 2.541 1.940 2.055 1.874 0.416 0.302 0.239 0.762 2.240 2.241 1.788 4.220 1.336 0.226 -0.245 0.361 0.061 0.991 1.591 1.989 1.504 2.173 1.166
3.292 -0.425 3.384 3.851 1.318 2.499 3.111 3.669 0.527 -0.225 2.126 2.154 2.479 -0.224 0.947 0.357 0.532 0.340 -0.155 3.489 -0.341 3.632 4.133 0.904 2.157 1.787 2.449 1.276 0.233
0.270 1.500 0.248 0.175 0.429 -0.126 0.435 0.428 -0.600 0.261 0.895 0.647 0.506 1.159 -0.065 0.571 0.918 0.080 0.405 0.464 1.227 0.415 0.298 1.473 -0.119 0.627 0.578 -0.399 0.578
1.791 0.579 1.722 1.813 -0.346 0.166 0.115 0.746 -0.706 -1.024 0.624 0.669 0.706 -0.277 -0.358 -0.270 0.456 -0.737 -0.714 1.664 0.113 1.605 1.580 0.015 -0.106 -0.010 0.942 -0.472 -0.919
1.723 1.753 1.717 1.646 0.191 1.185 0.945 1.999 0.231 -0.368 2.059 2.108 1.391 0.466 1.187 0.899 2.198 2.003 0.186 1.639 1.323 1.569 1.388 -0.200 0.555 0.470 1.530 0.598 -0.422
2.152 -0.474 2.014 2.532 -0.179 -0.354 0.351 0.921 -0.345 -1.736 2.891 2.407 4.040 -0.491 -0.802 -0.362 0.028 -0.957 -0.753 2.996 0.124 2.745 3.974 0.172 -0.581 0.067 1.025 -0.632 -1.052
2.237 0.607 2.273 2.350 0.707 1.724 1.957 2.608 0.045 -0.198 2.174 2.322 1.975 -1.020 0.153 0.128 0.472 -0.649 0.000 2.357 0.020 2.611 2.365 -0.130 0.853 0.975 1.956 -0.258 0.099
0.631 0.930 0.701 0.527 0.075 0.859 1.158 1.000 1.326 -0.087 0.094 0.052 0.113 -0.468 0.765 0.955 0.772 1.382 0.110 0.644 0.871 0.656 0.500 0.400 1.349 2.092 1.676 3.109 0.675
2.055 -0.974 2.030 2.078 0.266 0.893 1.310 1.974 0.589 -0.137 -0.230 -0.227 -0.028 -0.871 0.071 0.082 0.265 -0.459 0.216 1.328 -0.624 1.334 1.149 -0.577 0.189 0.624 1.247 -0.276 0.150
1.848 -0.451 1.763 1.933 -0.135 0.062 0.802 1.044 -0.878 -1.136 0.752 0.620 0.806 -0.276 -0.365 -0.168 0.085 -0.941 -0.788 1.883 -0.408 1.772 1.871 1.044 0.326 0.689 1.470 -0.342 -0.742
-0.865 -0.107 -0.768 -0.833 1.795 2.103 1.005 0.380 1.402 2.366 -0.699 -0.567 -0.579 0.121 1.117 0.463 0.258 -0.383 0.242 -0.627 1.162 -0.461 -0.654 3.768 4.345 2.723 2.096 2.026 3.120
0.134 0.930 0.082 0.028 -0.678 -0.719 -0.061 0.098 -0.673 -1.223 0.038 0.024 -0.161 0.423 -0.450 0.066 0.642 -0.380 -0.349 -0.099 0.982 -0.151 -0.215 -0.051 -0.611 -0.022 0.324 -0.685 -0.863
1.539 0.911 1.520 1.475 0.330 0.520 1.214 1.371 0.647 -0.561 0.741 1.245 0.654 1.398 0.865 1.418 3.665 0.863 0.924 0.942 0.775 1.034 0.759 -0.318 -0.082 0.531 1.033 -0.525 -0.439
0.387 0.158 0.429 0.255 1.396 0.982 1.258 1.088 0.428 0.658 0.872 0.895 0.584 0.076 0.212 0.591 0.745 -0.245 0.165 1.020 0.607 1.037 0.840 1.565 0.871 1.357 1.483 0.463 0.994
2.123 0.695 2.158 2.137 1.446 1.976 2.411 2.765 1.278 0.462 0.790 0.639 0.894 -0.608 0.658 0.506 0.176 -0.011 0.088 2.061 0.498 1.927 2.108 0.781 2.018 2.076 1.941 1.499 0.928
1.073 0.402 1.335 0.964 1.894 2.902 2.886 1.827 1.099 1.183 -0.008 0.127 0.026 0.039 0.653 0.986 -0.208 -0.560 0.493 0.937 0.342 1.260 0.744 2.406 2.145 3.026 1.244 0.556 1.985
1.096 0.319 1.063 0.957 0.515 0.493 0.393 1.013 0.658 -0.299 0.175 0.096 0.208 0.063 0.125 -0.225 0.487 -0.774 -0.173 0.995 -0.043 0.918 0.823 0.693 0.758 0.278 1.260 0.257 0.060
0.285 2.446 0.195 0.184 -0.936 -1.104 -0.526 -0.555 0.147 -1.396 0.227 0.088 0.111 -0.070 -0.626 -0.232 -0.439 1.327 -0.773 0.205 1.828 0.084 0.089 -0.769 -0.989 -0.563 -0.743 0.537 -1.234
0.390 0.416 0.450 0.421 1.112 0.999 0.795 0.925 0.997 0.827 3.479 3.244 2.993 0.385 0.749 0.432 1.555 -0.044 0.763 1.428 0.321 1.483 1.524 0.847 0.928 0.714 1.503 0.165 1.155
0.219 0.753 0.417 0.086 0.221 2.237 2.314 1.242 0.837 0.876 -0.549 0.297 -0.355 -0.025 2.047 1.569 1.709 -0.672 0.752 0.017 0.308 0.540 -0.084 0.417 2.890 3.018 2.022 -0.056 1.747
1.718 0.058 1.722 1.691 1.204 0.844 1.562 1.984 -0.320 -0.321 0.101 0.070 0.267 0.681 0.093 0.781 1.184 0.480 0.079 1.192 -0.099 1.153 1.051 1.495 0.254 1.240 1.562 0.212 -0.177
1.332 0.623 1.306 1.293 0.387 0.654 0.886 0.993 0.479 -0.209 1.493 0.805 1.397 0.344 0.860 0.706 1.061 0.398 0.272 1.322 0.855 1.132 1.269 0.290 0.585 0.570 0.855 0.172 -0.045
-0.042 0.077 -0.035 -0.157 0.685 0.170 0.299 0.405 -0.520 0.374 -0.665 -0.625 -0.472 -0.575 -0.423 -0.333 -0.361 -1.006 -0.359 0.159 0.833 0.198 -0.020 1.267 0.652 0.646 1.036 0.450 1.193
0.892 1.425 0.841 0.778 -0.928 0.124 0.396 0.218 -1.257 -1.236 0.378 0.206 0.397 0.356 0.983 0.581 0.911 -0.557 -0.021 0.851 1.592 0.760 0.709 0.492 1.004 1.109 0.902 -0.648 -0.249
1.107 -0.567 1.051 0.952 -0.490 0.357 0.253 0.351 -0.334 -0.708 -0.384 -0.467 -0.100 -0.974 -0.552 -0.071 -0.331 -0.918 -0.514 0.851 -0.595 0.775 0.723 -0.266 0.078 0.752 0.592 -0.095 -0.094
1.028 2.032 1.042 0.928 0.257 0.512 1.016 0.877 -0.360 -0.515 -0.056 0.003 0.079 -0.775 -0.298 0.168 -0.113 -0.989 -0.468 1.088 2.093 1.135 0.977 0.339 0.775 1.763 1.253 0.115 0.377
1.979 0.286 1.898 2.072 0.034 0.249 0.858 1.716 -0.940 -0.876 0.934 0.829 0.913 -0.524 -0.264 -0.001 0.464 -1.240 -0.601 1.947 1.040 1.814 2.005 0.194 0.355 0.804 1.725 -1.023 -0.537
1.550 1.328 1.470 1.523 0.486 -0.107 0.962 1.075 -0.542 -1.259 0.224 0.025 0.348 1.618 -0.346 0.569 0.518 -0.500 -0.751 1.070 0.860 0.968 0.949 0.895 -0.443 0.602 0.487 -0.982 -1.275
0.838 1.828 0.791 0.784 0.186 0.126 0.149 0.397 -0.068 0.002 1.889 1.575 1.646 0.566 -0.184 -0.155 0.451 -0.011 0.235 1.384 1.434 1.334 1.348 1.210 -0.063 -0.040 0.622 0.177 0.368
3.772 1.623 3.907 5.246 0.856 1.789 3.446 3.092 0.910 -0.930 7.724 7.807 11.032 0.203 1.578 1.612 2.299 -0.432 0.288 4.091 0.926 4.284 5.925 0.146 1.089 1.971 2.250 -0.420 -0.536
0.985 0.939 1.112 0.925 -0.247 1.819 1.565 1.322 -0.422 1.543 1.889 1.452 1.419 -0.092 2.500 1.127 1.834 -0.461 2.836 1.097 0.519 1.081 0.977 -0.511 1.425 1.171 1.293 -0.969 2.129
0.602 0.051 0.734 0.457 0.444 1.609 1.691 1.109 1.238 0.422 -0.326 0.101 -0.159 0.718 1.632 1.620 1.678 0.870 0.968 0.232 -0.427 0.442 0.104 0.234 1.220 1.522 0.957 0.674 0.411
1.508 -0.109 1.487 1.455 0.892 0.766 1.716 1.816 0.042 -0.233 0.580 0.378 0.602 -0.584 0.159 0.353 -0.006 -0.408 -0.221 1.591 0.767 1.388 1.509 0.834 0.751 1.541 1.390 0.590 0.340
0.727 0.212 0.623 0.576 -1.521 -0.629 -0.656 -0.666 0.125 -1.352 -0.569 -0.540 -0.382 -1.457 -0.615 -0.585 -1.053 -0.113 -0.792 0.602 0.144 0.596 0.357 -1.378 0.240 -0.117 -0.414 2.871 -0.427
1.102 0.295 1.088 1.001 0.266 0.465 0.354 0.740 1.110 -0.287 1.261 1.230 1.086 0.318 0.085 0.181 0.759 1.020 0.076 1.088 0.062 1.075 0.958 -0.064 -0.137 -0.085 0.522 0.566 -0.426
1.238 -0.411 1.207 1.174 0.344 0.518 0.756 1.106 0.074 0.591 1.396 0.982 1.219 0.311 0.372 0.413 0.638 -0.529 0.552 1.341 -0.455 1.165 1.264 0.387 0.347 0.389 0.786 -0.632 0.582
1.834 0.453 1.886 1.890 0.863 1.137 1.631 1.628 0.133 -0.082 0.668 0.663 0.764 -0.125 0.136 0.289 0.485 -1.134 -0.026 1.571 0.827 1.665 1.545 0.615 0.670 1.178 1.471 -0.680 0.335
-0.087 1.209 0.015 -0.168 1.411 1.207 0.588 0.481 1.690 1.356 0.252 0.053 -0.028 0.879 0.730 0.095 0.707 0.459 1.209 -0.054 1.182 -0.038 -0.163 2.060 0.905 0.316 0.570 1.213 1.902
2.543 0.126 2.475 2.919 -0.209 0.439 0.988 1.324 -1.118 -1.127 3.194 3.348 3.075 -0.429 0.451 0.261 1.582 0.178 -0.339 3.004 -0.294 3.102 3.340 -0.546 0.688 0.514 1.701 0.012 -0.619
0.378 1.084 0.487 0.217 1.560 1.565 1.433 0.935 -0.017 1.138 -0.260 0.035 -0.172 0.832 1.336 0.937 1.396 0.061 0.833 0.174 1.733 0.311 0.051 1.788 1.541 1.529 1.547 0.181 1.260
-0.206 0.286 -0.137 -0.279 1.012 0.806 0.699 0.845 1.110 1.480 -0.053 0.112 -0.147 -0.542 -0.158 0.087 0.250 -0.422 0.079 0.029 0.648 0.180 -0.064 1.096 0.835 1.143 1.377 1.106 1.492
0.262 -0.051 0.218 0.134 -0.299 -0.348 -0.175 -0.144 -0.914 -0.517 -0.069 -0.117 -0.041 -0.696 -0.513 -0.074 -0.385 -1.091 -0.785 0.271 0.388 0.195 0.152 -0.340 -0.281 0.069 -0.040 -1.000 -0.798
1.187 0.300 1.187 1.128 0.742 0.387 0.854 1.175 0.176 -0.480 0.504 0.174 0.594 -0.288 -0.375 -0.092 -0.217 -0.599 -0.404 1.157 0.085 1.040 1.076 0.737 -0.004 0.497 0.554 0.280 -0.294
1.635 0.226 1.586 1.589 0.522 0.505 0.656 1.170 -0.035 -0.130 0.370 0.390 0.426 -0.650 -0.137 -0.046 -0.003 -1.206 -0.153 1.544 -0.073 1.584 1.344 0.409 0.487 0.701 0.710 -0.569 0.411
2.980 0.537 3.026 3.370 0.472 2.012 1.784 2.530 0.654 0.650 2.114 2.069 2.189 -0.683 0.371 0.126 0.676 -0.212 0.365 2.824 0.204 2.930 3.094 0.080 1.046 0.928 2.022 0.414 0.707
1.800 0.321 1.759 1.830 -0.341 0.510 0.797 1.355 1.293 -1.219 1.545 1.139 1.320 -0.700 0.302 0.299 0.842 0.922 -0.407 1.440 0.240 1.331 1.343 -0.993 -0.005 0.177 0.710 0.516 -1.112
1.823 0.365 1.886 1.856 0.586 1.317 1.502 2.146 1.150 -0.041 1.058 0.910 1.043 -0.820 0.038 0.270 0.391 -0.129 -0.418 1.662 -0.032 1.575 1.631 -0.244 0.376 0.820 1.524 0.285 -0.457
0.040 0.758 0.074 -0.071 0.529 0.209 0.721 0.321 0.417 -0.422 -0.730 -0.480 -0.479 -0.309 0.020 0.482 0.156 -0.730 -0.015 -0.203 1.398 -0.088 -0.267 0.247 0.121 0.725 0.329 -0.328 -0.024
0.310 2.634 0.470 0.176 0.600 1.976 2.085 1.169 1.154 1.235 -0.523 -0.249 -0.389 -0.805 1.282 1.381 0.694 0.100 0.887 0.259 2.784 0.638 0.060 0.409 3.416 4.303 1.841 1.921 3.153
1.928 1.349 2.100 1.967 0.963 2.258 2.868 2.538 1.231 0.849 2.009 2.914 1.725 -0.214 0.984 1.542 2.341 0.003 0.914 1.660 0.607 2.138 1.648 0.365 1.044 1.858 2.124 0.046 0.819
2.109 0.721 2.059 2.342 1.041 0.219 1.946 2.319 -0.312 -0.930 2.780 2.377 2.602 1.085 0.192 0.665 2.065 -1.137 0.168 1.900 0.118 1.751 2.014 0.378 -0.273 0.664 1.628 -1.359 -0.708
1.703 2.083 1.615 1.722 0.102 -0.018 0.692 1.263 -0.217 -1.058 1.299 1.156 1.290 -0.424 -0.070 0.252 0.808 -0.189 -0.490 1.535 2.046 1.421 1.494 -0.691 -0.394 0.236 0.733 -0.531 -0.973
0.702 2.044 0.672 0.577 -0.840 -0.039 0.047 0.106 -0.808 -0.895 0.185 0.276 0.181 -0.379 0.661 0.510 0.612 -0.891 0.037 0.561 1.374 0.578 0.428 -0.809 0.350 0.326 0.414 -1.104 -0.318
1.837 2.334 1.981 1.734 1.524 3.269 3.294 2.657 2.135 1.043 1.157 1.437 1.009 -0.173 2.016 1.301 0.785 0.326 0.903 1.960 2.236 2.302 1.652 1.429 3.901 3.195 2.288 1.917 2.218

Menjalankan PCA

pca_res <- prcomp(data_std)
summary(pca_res)
## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     3.6439 2.3780 1.60315 1.33285 1.22156 1.09801 0.81940
## Proportion of Variance 0.4579 0.1950 0.08862 0.06126 0.05146 0.04157 0.02315
## Cumulative Proportion  0.4579 0.6529 0.74148 0.80274 0.85420 0.89577 0.91892
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.66046 0.62185 0.57086 0.52309 0.49418 0.39629 0.30793
## Proportion of Variance 0.01504 0.01333 0.01124 0.00944 0.00842 0.00542 0.00327
## Cumulative Proportion  0.93396 0.94730 0.95854 0.96797 0.97639 0.98181 0.98508
##                           PC15    PC16    PC17    PC18    PC19    PC20    PC21
## Standard deviation     0.28424 0.25068 0.23289 0.22889 0.21857 0.17618 0.16596
## Proportion of Variance 0.00279 0.00217 0.00187 0.00181 0.00165 0.00107 0.00095
## Cumulative Proportion  0.98786 0.99003 0.99190 0.99371 0.99535 0.99643 0.99738
##                           PC22    PC23    PC24    PC25    PC26    PC27    PC28
## Standard deviation     0.15602 0.13477 0.12649 0.09057 0.08319 0.03996 0.02770
## Proportion of Variance 0.00084 0.00063 0.00055 0.00028 0.00024 0.00006 0.00003
## Cumulative Proportion  0.99821 0.99884 0.99939 0.99968 0.99991 0.99997 1.00000
##                           PC29
## Standard deviation     0.01155
## Proportion of Variance 0.00000
## Cumulative Proportion  1.00000

Eigenvalue (Kaiser Rule)

eigenvalue <- pca_res$sdev^2
eigenvalue
##  [1] 1.327791e+01 5.655043e+00 2.570075e+00 1.776496e+00 1.492201e+00
##  [6] 1.205619e+00 6.714163e-01 4.362111e-01 3.867030e-01 3.258819e-01
## [11] 2.736236e-01 2.442144e-01 1.570474e-01 9.482067e-02 8.079034e-02
## [16] 6.284287e-02 5.423985e-02 5.238872e-02 4.777190e-02 3.103952e-02
## [21] 2.754293e-02 2.434090e-02 1.816173e-02 1.599933e-02 8.203097e-03
## [26] 6.921200e-03 1.596990e-03 7.672311e-04 1.333158e-04
sum(eigenvalue > 1)
## [1] 6
prop_var <- eigenvalue / sum(eigenvalue)

percent_var <- prop_var * 100

cum_percent <- cumsum(percent_var)

hasil_pca <- data.frame(
  Eigenvalue = eigenvalue,
  Percent_Variance = percent_var,
  Cumulative_Percent = cum_percent
)

round(hasil_pca, 2)
##    Eigenvalue Percent_Variance Cumulative_Percent
## 1       13.28            45.79              45.79
## 2        5.66            19.50              65.29
## 3        2.57             8.86              74.15
## 4        1.78             6.13              80.27
## 5        1.49             5.15              85.42
## 6        1.21             4.16              89.58
## 7        0.67             2.32              91.89
## 8        0.44             1.50              93.40
## 9        0.39             1.33              94.73
## 10       0.33             1.12              95.85
## 11       0.27             0.94              96.80
## 12       0.24             0.84              97.64
## 13       0.16             0.54              98.18
## 14       0.09             0.33              98.51
## 15       0.08             0.28              98.79
## 16       0.06             0.22              99.00
## 17       0.05             0.19              99.19
## 18       0.05             0.18              99.37
## 19       0.05             0.16              99.54
## 20       0.03             0.11              99.64
## 21       0.03             0.09              99.74
## 22       0.02             0.08              99.82
## 23       0.02             0.06              99.88
## 24       0.02             0.06              99.94
## 25       0.01             0.03              99.97
## 26       0.01             0.02              99.99
## 27       0.00             0.01             100.00
## 28       0.00             0.00             100.00
## 29       0.00             0.00             100.00

Scree Plot

fviz_eig(pca_res,
         addlabels = TRUE,
         ylim = c(0, 100))
## Warning in geom_bar(stat = "identity", fill = barfill, color = barcolor, :
## Ignoring empty aesthetic: `width`.

Pengambilan 6 PC

loading <- pca_res$rotation[,1:6]
round(loading, 3)
##                       PC1    PC2    PC3    PC4    PC5    PC6
## x.radius_mean       0.219  0.233  0.004 -0.024  0.078 -0.025
## x.texture_mean      0.103  0.068  0.098  0.496 -0.463  0.071
## x.perimeter_mean    0.228  0.214  0.004 -0.024  0.077 -0.024
## x.area_mean         0.221  0.231 -0.035 -0.039  0.046 -0.002
## x.smoothness_mean   0.143 -0.189  0.086 -0.371 -0.150  0.286
## x.compactness_mean  0.239 -0.155  0.058 -0.035  0.052  0.009
## x.concavity_mean    0.258 -0.061 -0.016  0.033  0.088  0.004
## x.concave_pts_mean  0.261  0.033  0.015 -0.092  0.030  0.047
## x.symmetry_mean     0.138 -0.191  0.036 -0.230 -0.225 -0.349
## x.fractal_dim_mean  0.064 -0.368 -0.001 -0.061 -0.013  0.120
## x.radius_se         0.206  0.111 -0.281 -0.100 -0.171  0.038
## x.perimeter_se      0.211  0.095 -0.279 -0.074 -0.147  0.010
## x.area_se           0.203  0.156 -0.233 -0.105 -0.126  0.053
## x.smoothness_se     0.014 -0.197 -0.313 -0.080 -0.296  0.366
## x.compactness_se    0.170 -0.231 -0.179  0.233  0.140 -0.070
## x.concavity_se      0.153 -0.195 -0.212  0.254  0.218 -0.061
## x.concave_pts_se    0.183 -0.127 -0.263  0.109  0.129  0.028
## x.symmetry_se       0.042 -0.177 -0.289 -0.096 -0.321 -0.471
## x.fractal_dim_se    0.102 -0.277 -0.246  0.201  0.138  0.053
## x.radius_worst      0.228  0.218  0.051 -0.033  0.033 -0.003
## x.texture_worst     0.104  0.053  0.224  0.455 -0.448  0.083
## x.perimeter_worst   0.237  0.198  0.051 -0.025  0.041 -0.012
## x.area_worst        0.225  0.219  0.014 -0.045  0.005  0.024
## x.smoothness_worst  0.128 -0.178  0.269 -0.258 -0.173  0.374
## x.compactness_worst 0.210 -0.150  0.242  0.094  0.113 -0.055
## x.concavity_worst   0.229 -0.103  0.173  0.130  0.166 -0.037
## x.concave_pts_worst 0.251  0.003  0.164 -0.024  0.105  0.022
## x.symmetry_worst    0.123 -0.148  0.284 -0.158 -0.182 -0.494
## x.fractal_dim_worst 0.132 -0.282  0.232  0.071  0.093  0.075

Factor Analysis

Ekstraksi Faktor dengan Metode Maximum Likelihood

Rotasi Varimax

fa_ml <- fa(data_std,
            nfactors = 6,
            rotate = "varimax",
            fm = "ml")
round(fa_ml$loadings[,1:6], 3)
##                        ML1    ML4    ML3    ML2    ML6    ML5
## x.radius_mean        0.966  0.042  0.063  0.099 -0.145 -0.168
## x.texture_mean       0.239  0.006  0.092  0.902  0.029 -0.018
## x.perimeter_mean     0.962  0.078  0.104  0.100 -0.128 -0.167
## x.area_mean          0.976  0.029  0.062  0.094 -0.074 -0.114
## x.smoothness_mean    0.181  0.809  0.054 -0.102  0.396 -0.150
## x.compactness_mean   0.454  0.614  0.570  0.060  0.095 -0.088
## x.concavity_mean     0.634  0.433  0.554  0.108  0.082 -0.095
## x.concave_pts_mean   0.794  0.436  0.307  0.074  0.076 -0.146
## x.symmetry_mean      0.150  0.511  0.299 -0.008  0.255 -0.003
## x.fractal_dim_mean  -0.313  0.599  0.501 -0.080  0.303  0.075
## x.radius_se          0.806  0.021  0.174  0.065  0.457  0.306
## x.perimeter_se       0.789  0.023  0.252  0.072  0.442  0.276
## x.area_se            0.849 -0.009  0.113  0.058  0.365  0.254
## x.smoothness_se     -0.158  0.133  0.173 -0.021  0.587 -0.018
## x.compactness_se     0.162  0.224  0.869  0.072  0.139  0.010
## x.concavity_se       0.158  0.132  0.809  0.045  0.127 -0.002
## x.concave_pts_se     0.368  0.171  0.647 -0.002  0.258 -0.062
## x.symmetry_se       -0.052  0.002  0.344 -0.037  0.476  0.020
## x.fractal_dim_se    -0.052  0.166  0.753 -0.017  0.252  0.059
## x.radius_worst       0.957  0.156  0.032  0.139 -0.184  0.026
## x.texture_worst      0.193  0.166  0.019  0.960 -0.082  0.025
## x.perimeter_worst    0.950  0.185  0.091  0.140 -0.176  0.025
## x.area_worst         0.955  0.139  0.017  0.130 -0.133  0.105
## x.smoothness_worst   0.093  0.890 -0.022  0.072  0.116 -0.017
## x.compactness_worst  0.316  0.626  0.559  0.174 -0.212  0.021
## x.concavity_worst    0.434  0.532  0.575  0.177 -0.194 -0.018
## x.concave_pts_worst  0.676  0.545  0.331  0.126 -0.155 -0.071
## x.symmetry_worst     0.107  0.587  0.193  0.100 -0.149  0.065
## x.fractal_dim_worst -0.067  0.693  0.528  0.100 -0.095  0.105
print(fa_ml$loadings, cutoff = 0.4)
## 
## Loadings:
##                     ML1    ML4    ML3    ML2    ML6    ML5   
## x.radius_mean        0.966                                   
## x.texture_mean                            0.902              
## x.perimeter_mean     0.962                                   
## x.area_mean          0.976                                   
## x.smoothness_mean           0.809                            
## x.compactness_mean   0.454  0.614  0.570                     
## x.concavity_mean     0.634  0.433  0.554                     
## x.concave_pts_mean   0.794  0.436                            
## x.symmetry_mean             0.511                            
## x.fractal_dim_mean          0.599  0.501                     
## x.radius_se          0.806                       0.457       
## x.perimeter_se       0.789                       0.442       
## x.area_se            0.849                                   
## x.smoothness_se                                  0.587       
## x.compactness_se                   0.869                     
## x.concavity_se                     0.809                     
## x.concave_pts_se                   0.647                     
## x.symmetry_se                                    0.476       
## x.fractal_dim_se                   0.753                     
## x.radius_worst       0.957                                   
## x.texture_worst                           0.960              
## x.perimeter_worst    0.950                                   
## x.area_worst         0.955                                   
## x.smoothness_worst          0.890                            
## x.compactness_worst         0.626  0.559                     
## x.concavity_worst    0.434  0.532  0.575                     
## x.concave_pts_worst  0.676  0.545                            
## x.symmetry_worst            0.587                            
## x.fractal_dim_worst         0.693  0.528                     
## 
##                   ML1   ML4   ML3   ML2   ML6   ML5
## SS loadings    10.004 4.876 4.826 1.983 1.894 0.412
## Proportion Var  0.345 0.168 0.166 0.068 0.065 0.014
## Cumulative Var  0.345 0.513 0.680 0.748 0.813 0.827

Communalities

fa_ml$communality
##       x.radius_mean      x.texture_mean    x.perimeter_mean         x.area_mean 
##           0.9970932           0.8798162           0.9973182           0.9844886 
##   x.smoothness_mean  x.compactness_mean    x.concavity_mean  x.concave_pts_mean 
##           0.8790838           0.9298101           0.9235689           0.9466415 
##     x.symmetry_mean  x.fractal_dim_mean         x.radius_se      x.perimeter_se 
##           0.4383535           0.8117822           0.9867561           0.9627484 
##           x.area_se     x.smoothness_se    x.compactness_se      x.concavity_se 
##           0.9340827           0.4180488           0.8568155           0.7147470 
##    x.concave_pts_se       x.symmetry_se    x.fractal_dim_se      x.radius_worst 
##           0.6535147           0.3490344           0.6640884           0.9954577 
##     x.texture_worst   x.perimeter_worst        x.area_worst  x.smoothness_worst 
##           0.9950051           0.9951105           0.9767705           0.8208587 
## x.compactness_worst   x.concavity_worst x.concave_pts_worst    x.symmetry_worst 
##           0.8796218           0.8716107           0.9090812           0.4302566 
## x.fractal_dim_worst 
##           0.7935857

Rasio Kuadrat Loading

load_mat <- as.data.frame(unclass(fa_ml$loadings))

cutoff <- 0.4

ratio_sq <- apply(load_mat, 1, function(x){
  
  signif_load <- abs(x[abs(x) >= cutoff])
  
  if(length(signif_load) < 2){
    return(NA)
  }
  
  signif_sq <- signif_load^2
  
  sorted_sq <- sort(signif_sq, decreasing = TRUE)
  
  return(sorted_sq[1] / sorted_sq[2])
})

hasil_ratio <- cbind(load_mat, Ratio_Squared = ratio_sq)

hasil_ratio[, sapply(hasil_ratio, is.numeric)] <-
  round(hasil_ratio[, sapply(hasil_ratio, is.numeric)], 3)

hasil_ratio
##                        ML1    ML4    ML3    ML2    ML6    ML5 Ratio_Squared
## x.radius_mean        0.966  0.042  0.063  0.099 -0.145 -0.168            NA
## x.texture_mean       0.239  0.006  0.092  0.902  0.029 -0.018            NA
## x.perimeter_mean     0.962  0.078  0.104  0.100 -0.128 -0.167            NA
## x.area_mean          0.976  0.029  0.062  0.094 -0.074 -0.114            NA
## x.smoothness_mean    0.181  0.809  0.054 -0.102  0.396 -0.150            NA
## x.compactness_mean   0.454  0.614  0.570  0.060  0.095 -0.088         1.161
## x.concavity_mean     0.634  0.433  0.554  0.108  0.082 -0.095         1.309
## x.concave_pts_mean   0.794  0.436  0.307  0.074  0.076 -0.146         3.316
## x.symmetry_mean      0.150  0.511  0.299 -0.008  0.255 -0.003            NA
## x.fractal_dim_mean  -0.313  0.599  0.501 -0.080  0.303  0.075         1.429
## x.radius_se          0.806  0.021  0.174  0.065  0.457  0.306         3.105
## x.perimeter_se       0.789  0.023  0.252  0.072  0.442  0.276         3.182
## x.area_se            0.849 -0.009  0.113  0.058  0.365  0.254            NA
## x.smoothness_se     -0.158  0.133  0.173 -0.021  0.587 -0.018            NA
## x.compactness_se     0.162  0.224  0.869  0.072  0.139  0.010            NA
## x.concavity_se       0.158  0.132  0.809  0.045  0.127 -0.002            NA
## x.concave_pts_se     0.368  0.171  0.647 -0.002  0.258 -0.062            NA
## x.symmetry_se       -0.052  0.002  0.344 -0.037  0.476  0.020            NA
## x.fractal_dim_se    -0.052  0.166  0.753 -0.017  0.252  0.059            NA
## x.radius_worst       0.957  0.156  0.032  0.139 -0.184  0.026            NA
## x.texture_worst      0.193  0.166  0.019  0.960 -0.082  0.025            NA
## x.perimeter_worst    0.950  0.185  0.091  0.140 -0.176  0.025            NA
## x.area_worst         0.955  0.139  0.017  0.130 -0.133  0.105            NA
## x.smoothness_worst   0.093  0.890 -0.022  0.072  0.116 -0.017            NA
## x.compactness_worst  0.316  0.626  0.559  0.174 -0.212  0.021         1.255
## x.concavity_worst    0.434  0.532  0.575  0.177 -0.194 -0.018         1.172
## x.concave_pts_worst  0.676  0.545  0.331  0.126 -0.155 -0.071         1.540
## x.symmetry_worst     0.107  0.587  0.193  0.100 -0.149  0.065            NA
## x.fractal_dim_worst -0.067  0.693  0.528  0.100 -0.095  0.105         1.727

problematic cross-Loading (1.0-1.5)

filter_problematic <- subset(hasil_ratio,
                             Ratio_Squared >= 1 & Ratio_Squared < 1.5)

round(filter_problematic, 3)
##                        ML1   ML4   ML3    ML2    ML6    ML5 Ratio_Squared
## x.compactness_mean   0.454 0.614 0.570  0.060  0.095 -0.088         1.161
## x.concavity_mean     0.634 0.433 0.554  0.108  0.082 -0.095         1.309
## x.fractal_dim_mean  -0.313 0.599 0.501 -0.080  0.303  0.075         1.429
## x.compactness_worst  0.316 0.626 0.559  0.174 -0.212  0.021         1.255
## x.concavity_worst    0.434 0.532 0.575  0.177 -0.194 -0.018         1.172

potential Cross-loading (1.5-2.0)

filter_potential <- subset(hasil_ratio,
                           Ratio_Squared >= 1.5 & Ratio_Squared < 2)

round(filter_potential, 3)
##                        ML1   ML4   ML3   ML2    ML6    ML5 Ratio_Squared
## x.concave_pts_worst  0.676 0.545 0.331 0.126 -0.155 -0.071         1.540
## x.fractal_dim_worst -0.067 0.693 0.528 0.100 -0.095  0.105         1.727

Ignorable Cross_Loading (>2.0)

filter_ignorable <- subset(hasil_ratio,
                           Ratio_Squared >= 2)

round(filter_ignorable, 3)
##                      ML1   ML4   ML3   ML2   ML6    ML5 Ratio_Squared
## x.concave_pts_mean 0.794 0.436 0.307 0.074 0.076 -0.146         3.316
## x.radius_se        0.806 0.021 0.174 0.065 0.457  0.306         3.105
## x.perimeter_se     0.789 0.023 0.252 0.072 0.442  0.276         3.182

Hapus variabel

data_std_new <- data_std[, 
                         !colnames(data_std) %in% 
                         c("x.compactness_mean", "x.concavity_mean", "x.fractal_dim_mean", "x.compactness_worst", "x.concavity_worst", "x.concave_pts_worst", "x.fractal_dim_worst" )]
fa_ml_new <- fa(data_std_new,
                nfactors = 6,
                rotate   = "varimax",
                fm       = "ml")
print(fa_ml_new$loadings, cutoff = 0.4)
## 
## Loadings:
##                    ML1    ML6    ML5    ML3    ML2    ML4   
## x.radius_mean       0.992                                   
## x.texture_mean                           0.898              
## x.perimeter_mean    0.989                                   
## x.area_mean         0.982                                   
## x.smoothness_mean                 0.781                     
## x.concave_pts_mean  0.805                                   
## x.symmetry_mean                                 0.654       
## x.radius_se         0.660                              0.691
## x.perimeter_se      0.653                              0.661
## x.area_se           0.727                              0.624
## x.smoothness_se            0.429                            
## x.compactness_se           0.859                            
## x.concavity_se             0.817                            
## x.concave_pts_se           0.792                            
## x.symmetry_se              0.416                0.503       
## x.fractal_dim_se           0.821                            
## x.radius_worst      0.964                                   
## x.texture_worst                          0.969              
## x.perimeter_worst   0.958                                   
## x.area_worst        0.940                                   
## x.smoothness_worst                0.944                     
## x.symmetry_worst                                0.934       
## 
##                  ML1   ML6   ML5   ML3   ML2   ML4
## SS loadings    8.114 3.567 1.980 1.912 1.791 1.610
## Proportion Var 0.369 0.162 0.090 0.087 0.081 0.073
## Cumulative Var 0.369 0.531 0.621 0.708 0.789 0.862

Communalities

fa_ml_new$communality
##      x.radius_mean     x.texture_mean   x.perimeter_mean        x.area_mean 
##          0.9965542          0.8774205          0.9967562          0.9851875 
##  x.smoothness_mean x.concave_pts_mean    x.symmetry_mean        x.radius_se 
##          0.7574168          0.9097665          0.6406853          0.9841867 
##     x.perimeter_se          x.area_se    x.smoothness_se   x.compactness_se 
##          0.9649332          0.9431259          0.4937754          0.8236441 
##     x.concavity_se   x.concave_pts_se      x.symmetry_se   x.fractal_dim_se 
##          0.7150582          0.7722296          0.5535393          0.7098410 
##     x.radius_worst    x.texture_worst  x.perimeter_worst       x.area_worst 
##          0.9717712          0.9950102          0.9697319          0.9450665 
## x.smoothness_worst   x.symmetry_worst 
##          0.9734717          0.9950160

Penghapus Cross-Loading menghasilkan overfactoring

load_mat <- as.data.frame(unclass(fa_ml_new$loadings))

cutoff <- 0.4

ratio_sq <- apply(load_mat, 1, function(x){
  
  signif_load <- abs(x[abs(x) >= cutoff])
  
  if(length(signif_load) < 2){
    return(NA)
  }
  
  signif_sq <- signif_load^2
  
  sorted_sq <- sort(signif_sq, decreasing = TRUE)
  
  return(sorted_sq[1] / sorted_sq[2])
})

hasil_ratio_new <- cbind(load_mat, Ratio_Squared = ratio_sq)

hasil_ratio_new[, sapply(hasil_ratio_new, is.numeric)] <-
  round(hasil_ratio_new[, sapply(hasil_ratio_new, is.numeric)], 3)

hasil_ratio_new
##                       ML1    ML6    ML5    ML3    ML2    ML4 Ratio_Squared
## x.radius_mean       0.992  0.054 -0.012  0.095  0.007  0.007            NA
## x.texture_mean      0.232  0.105 -0.052  0.898 -0.013  0.065            NA
## x.perimeter_mean    0.989  0.093  0.014  0.099  0.026  0.013            NA
## x.area_mean         0.982  0.056  0.001  0.089 -0.003  0.098            NA
## x.smoothness_mean   0.169  0.264  0.781 -0.078  0.189  0.089            NA
## x.concave_pts_mean  0.805  0.350  0.312  0.092  0.170  0.064            NA
## x.symmetry_mean     0.128  0.331  0.275 -0.005  0.654  0.110            NA
## x.radius_se         0.660  0.243  0.069  0.061  0.058  0.691         1.098
## x.perimeter_se      0.653  0.300  0.047  0.069  0.074  0.661         1.025
## x.area_se           0.727  0.138  0.054  0.051  0.026  0.624         1.354
## x.smoothness_se    -0.247  0.429  0.372 -0.038 -0.150  0.294            NA
## x.compactness_se    0.157  0.859  0.101  0.093  0.202  0.039            NA
## x.concavity_se      0.149  0.817  0.062  0.058  0.132  0.030            NA
## x.concave_pts_se    0.333  0.792  0.126  0.008  0.048  0.125            NA
## x.symmetry_se      -0.135  0.416 -0.117 -0.074  0.503  0.300         1.466
## x.fractal_dim_se   -0.084  0.821  0.117  0.002  0.078  0.096            NA
## x.radius_worst      0.964  0.000  0.080  0.155  0.077  0.082            NA
## x.texture_worst     0.207 -0.002  0.082  0.969  0.075 -0.015            NA
## x.perimeter_worst   0.958  0.049  0.093  0.158  0.100  0.081            NA
## x.area_worst        0.940 -0.013  0.087  0.148  0.057  0.171            NA
## x.smoothness_worst  0.116  0.069  0.944  0.110  0.222 -0.052            NA
## x.symmetry_worst    0.150  0.040  0.261  0.112  0.934 -0.135            NA

problematic cross-Loading (1.0-1.5)

filter_problematic <- subset(hasil_ratio_new,
                             Ratio_Squared >= 1 & Ratio_Squared < 1.5)

round(filter_problematic, 3)
##                   ML1   ML6    ML5    ML3   ML2   ML4 Ratio_Squared
## x.radius_se     0.660 0.243  0.069  0.061 0.058 0.691         1.098
## x.perimeter_se  0.653 0.300  0.047  0.069 0.074 0.661         1.025
## x.area_se       0.727 0.138  0.054  0.051 0.026 0.624         1.354
## x.symmetry_se  -0.135 0.416 -0.117 -0.074 0.503 0.300         1.466

potential Cross-loading (1.5-2.0)

filter_potential <- subset(hasil_ratio_new,
                           Ratio_Squared >= 1.5 & Ratio_Squared < 2)

round(filter_potential, 3)
## [1] ML1           ML6           ML5           ML3           ML2          
## [6] ML4           Ratio_Squared
## <0 rows> (or 0-length row.names)

Ignorable Cross_Loading (>2.0)

filter_ignorable <- subset(hasil_ratio_new,
                           Ratio_Squared >= 2)

round(filter_ignorable, 3)
## [1] ML1           ML6           ML5           ML3           ML2          
## [6] ML4           Ratio_Squared
## <0 rows> (or 0-length row.names)

Hapus variabel

data_std_new2 <- data_std_new[, 
                         !colnames(data_std_new) %in% 
                         c("x.radius_se", "x.perimeter_se", "x.area_se", "x.symmetry_se" )]
fa_ml_new2 <- fa(data_std_new2,
                nfactors = 6,
                rotate   = "varimax",
                fm       = "ml")
print(fa_ml_new2$loadings, cutoff = 0.4)
## 
## Loadings:
##                    ML1    ML3    ML5    ML2    ML6    ML4   
## x.radius_mean       0.980                                   
## x.texture_mean                           0.899              
## x.perimeter_mean    0.975                                   
## x.area_mean         0.987                                   
## x.smoothness_mean                 0.877                     
## x.concave_pts_mean  0.783         0.427                     
## x.symmetry_mean                   0.541                     
## x.smoothness_se                                 0.519       
## x.compactness_se           0.912                            
## x.concavity_se             0.848                            
## x.concave_pts_se           0.757                            
## x.fractal_dim_se           0.849                            
## x.radius_worst      0.965                                   
## x.texture_worst                          0.967              
## x.perimeter_worst   0.956                                   
## x.area_worst        0.961                                   
## x.smoothness_worst                0.873                     
## x.symmetry_worst                  0.535                     
## 
##                  ML1   ML3   ML5   ML2   ML6   ML4
## SS loadings    6.603 3.298 2.518 1.893 0.479 0.123
## Proportion Var 0.367 0.183 0.140 0.105 0.027 0.007
## Cumulative Var 0.367 0.550 0.690 0.795 0.822 0.829
load_mat <- as.data.frame(unclass(fa_ml_new2$loadings))

cutoff <- 0.4

ratio_sq <- apply(load_mat, 1, function(x){
  
  signif_load <- abs(x[abs(x) >= cutoff])
  
  if(length(signif_load) < 2){
    return(NA)
  }
  
  signif_sq <- signif_load^2
  
  sorted_sq <- sort(signif_sq, decreasing = TRUE)
  
  return(sorted_sq[1] / sorted_sq[2])
})

hasil_ratio_new2 <- cbind(load_mat, Ratio_Squared = ratio_sq)

hasil_ratio_new2[, sapply(hasil_ratio_new2, is.numeric)] <-
  round(hasil_ratio_new2[, sapply(hasil_ratio_new2, is.numeric)], 3)

hasil_ratio_new2
##                       ML1   ML3    ML5    ML2    ML6    ML4 Ratio_Squared
## x.radius_mean       0.980 0.066  0.038  0.102 -0.069  0.121            NA
## x.texture_mean      0.228 0.094 -0.008  0.899  0.016  0.027            NA
## x.perimeter_mean    0.975 0.105  0.072  0.105 -0.066  0.123            NA
## x.area_mean         0.987 0.076  0.021  0.098  0.046  0.052            NA
## x.smoothness_mean   0.141 0.172  0.877 -0.090  0.246  0.106            NA
## x.concave_pts_mean  0.783 0.338  0.427  0.089  0.022  0.096         3.356
## x.symmetry_mean     0.108 0.342  0.541  0.000  0.020  0.028            NA
## x.smoothness_se    -0.221 0.357  0.211 -0.029  0.519 -0.008            NA
## x.compactness_se    0.132 0.912  0.178  0.090 -0.010  0.011            NA
## x.concavity_se      0.134 0.848  0.096  0.059  0.046 -0.006            NA
## x.concave_pts_se    0.314 0.757  0.204 -0.001  0.033  0.086            NA
## x.fractal_dim_se   -0.090 0.849  0.128 -0.002  0.139 -0.061            NA
## x.radius_worst      0.965 0.046  0.137  0.147 -0.122 -0.082            NA
## x.texture_worst     0.196 0.007  0.129  0.967 -0.061 -0.033            NA
## x.perimeter_worst   0.956 0.097  0.163  0.150 -0.136 -0.071            NA
## x.area_worst        0.961 0.046  0.112  0.140 -0.011 -0.193            NA
## x.smoothness_worst  0.090 0.051  0.873  0.102  0.120 -0.062            NA
## x.symmetry_worst    0.117 0.139  0.535  0.126 -0.250 -0.056            NA
fa_ml_new2$communality
##      x.radius_mean     x.texture_mean   x.perimeter_mean        x.area_mean 
##          0.9971544          0.8703039          0.9976373          0.9955914 
##  x.smoothness_mean x.concave_pts_mean    x.symmetry_mean    x.smoothness_se 
##          0.8983574          0.9272785          0.4228524          0.4909093 
##   x.compactness_se     x.concavity_se   x.concave_pts_se   x.fractal_dim_se 
##          0.8884527          0.7512732          0.7213539          0.7686351 
##     x.radius_worst    x.texture_worst  x.perimeter_worst       x.area_worst 
##          0.9959045          0.9950089          0.9951767          0.9957748 
## x.smoothness_worst   x.symmetry_worst 
##          0.8016212          0.4008853