ANÁLISIS DE COMPONENTES PRINCIPALES
Alegre Veliz Rosa Mercedes - Ñahuiña Balbuena Carlos Harold - Mendoza Chate Luis - Pariona Navareete Alexis - Manayaye Jose
9/8/2020
PCA (análisis de componentes principales)
El análisis de componentes principales (principal component analysis) o PCA es una de las técnicas de aprendizaje no supervisado, las cuales suelen aplicarse como parte del análisis exploratorio de los datos. Una de las aplicaciones de PCA es la reducción de dimensionalidad (variables), perdiendo la menor cantidad de información (varianza) posible: cuando contamos con un gran número de variables cuantitativas posiblemente correlacionadas (indicativo de existencia de información redundante), PCA permite reducirlas a un número menor de variables transformadas (componentes principales) que explican gran parte de la variabilidad en los datos.
Esta evaluación y modificación que se realizará en el conjunto de datos es parte del proceso de la metodología CRISP-DM, la cual es la construcción de nuevos datos.
- Carga de datos formato csv.
data <- read.csv("https://raw.githubusercontent.com/cnahuina/data-mineria/master/breast-cancer.csv")De manera previa se tiene una limpieza general de los datos.
Como se mostró anteriormente, la última columna no se toma en cuenta y la otra variable a no tomar en cuenta es el identificador.
data_var <- data[,3:32]Limpiar la data
- Se hace uso de una función en este caso denominada replace_outliers para eliminar los valores outliers de la data.
Capar los valores extremos, es decir, localizar todo lo que cayera fuera del bigote más arriba o más abajo de 1,5 veces de el rango intercuartilico. Y decidir capar dichas obsevaciones sustituyendolas con el percentil número 5. En el caso de los que están debajo del bigote inferior y con el percentil 95 con los que están por encima del bigote superior.
replace_outliers <- function(x, removeNA = TRUE){
qrts <- quantile(x, probs = c(0.25, 0.75), na.rm = removeNA)
caps <- quantile(x, probs = c(.05, 0.95), na.rm = removeNA)
iqr <- qrts[2]-qrts[1]
h <- 1.5*iqr
x[x<qrts[1]-h] <- caps[1]
x[x>qrts[2]+h] <- caps[2]
x
}- Hacemos uso de la función en las variables presentadas, en el boxplot realizado con anterioridad.
data_var$radius_mean <- replace_outliers(data_var$radius_mean)
data_var$texture_mean <- replace_outliers(data_var$texture_mean)
data_var$perimeter_mean <- replace_outliers(data_var$perimeter_mean)
data_var$area_mean <- replace_outliers(data_var$area_mean)
data_var$smoothness_mean <- replace_outliers(data_var$smoothness_mean )
data_var$compactness_mean <- replace_outliers(data_var$compactness_mean)
data_var$concavity_mean <- replace_outliers(data_var$concavity_mean)
data_var$concave.points_mean <- replace_outliers(data_var$concave.points_mean)
data_var$symmetry_mean <- replace_outliers(data_var$symmetry_mean)
data_var$fractal_dimension_mean <- replace_outliers(data_var$fractal_dimension_mean)
data_var$radius_se <- replace_outliers(data_var$radius_se)
data_var$texture_se <- replace_outliers(data_var$texture_se )
data_var$perimeter_se <- replace_outliers(data_var$perimeter_se)
data_var$area_se <- replace_outliers(data_var$area_se)
data_var$smoothness_se <- replace_outliers(data_var$smoothness_se)
data_var$compactness_se <- replace_outliers(data_var$compactness_se)
data_var$concavity_se <- replace_outliers(data_var$concavity_se)
data_var$concave.points_se <- replace_outliers(data_var$concave.points_se)
data_var$symmetry_se <- replace_outliers(data_var$symmetry_se)
data_var$fractal_dimension_se <- replace_outliers(data_var$fractal_dimension_s)
data_var$radius_worst <- replace_outliers(data_var$radius_worst)
data_var$texture_worst <- replace_outliers(data_var$texture_worst )
data_var$perimeter_worst <- replace_outliers(data_var$perimeter_worst)
data_var$area_worst <- replace_outliers(data_var$area_worst)
data_var$smoothness_worst <- replace_outliers(data_var$smoothness_worst)
data_var$compactness_worst <- replace_outliers(data_var$compactness_worst)
data_var$concavity_worst <- replace_outliers(data_var$concavity_worst)
data_var$concave.points_worst <- replace_outliers(data_var$concave.points_worst)
data_var$symmetry_worst <- replace_outliers(data_var$symmetry_worst)Se establece una semilla
set.seed(2018)- Hacemos uso de la siguiente librería, para poder visualizar la existencia de correlación en las variables.
library(corrplot)- Hacemos uso de la función cor(), para poder ver la correlación en las variables.
cor(data_var)## radius_mean texture_mean perimeter_mean area_mean
## radius_mean 1.00000000 0.333768563 0.99746535 0.993332519
## texture_mean 0.33376856 1.000000000 0.34094427 0.343001580
## perimeter_mean 0.99746535 0.340944272 1.00000000 0.991450806
## area_mean 0.99333252 0.343001580 0.99145081 1.000000000
## smoothness_mean 0.16613701 -0.005972216 0.20335825 0.170815960
## compactness_mean 0.49768803 0.242677318 0.54877990 0.498715668
## concavity_mean 0.67402200 0.326599091 0.71374782 0.684270463
## concave.points_mean 0.80418961 0.304175168 0.83466039 0.810909295
## symmetry_mean 0.14495366 0.091591946 0.17923662 0.155082395
## fractal_dimension_mean -0.32220782 -0.064781678 -0.26964540 -0.303407288
## radius_se 0.67585052 0.324923667 0.68946986 0.709553294
## texture_se -0.11356719 0.422983238 -0.10458425 -0.087898037
## perimeter_se 0.67554203 0.337195035 0.69432336 0.707054681
## area_se 0.80040518 0.339638190 0.80964099 0.831377790
## smoothness_se -0.28629947 0.027542408 -0.26701928 -0.243455750
## compactness_se 0.23126066 0.226354384 0.27868133 0.241075746
## concavity_se 0.32774728 0.244162548 0.36851354 0.337608581
## concave.points_se 0.42452806 0.188294813 0.45730478 0.427872337
## symmetry_se -0.18296265 0.006935905 -0.16461220 -0.153721804
## fractal_dimension_se -0.01249584 0.115792221 0.03242500 0.008597376
## radius_worst 0.97300475 0.355625159 0.97401973 0.974071399
## texture_worst 0.30484292 0.906801131 0.31174473 0.308126243
## perimeter_worst 0.96606030 0.365727214 0.97242535 0.967257176
## area_worst 0.95786939 0.355199886 0.95920857 0.971475477
## smoothness_worst 0.13267495 0.079683802 0.16376463 0.142154866
## compactness_worst 0.45609714 0.272778738 0.50104761 0.447946862
## concavity_worst 0.56702510 0.311692282 0.60523518 0.565575668
## concave.points_worst 0.74391234 0.297646464 0.77310475 0.739347807
## symmetry_worst 0.19063984 0.107380091 0.21590882 0.187623516
## fractal_dimension_worst 0.01143701 0.118036583 0.05859202 0.014904028
## smoothness_mean compactness_mean concavity_mean
## radius_mean 0.166137006 0.49768803 0.67402200
## texture_mean -0.005972216 0.24267732 0.32659909
## perimeter_mean 0.203358251 0.54877990 0.71374782
## area_mean 0.170815960 0.49871567 0.68427046
## smoothness_mean 1.000000000 0.65887004 0.52629526
## compactness_mean 0.658870038 1.00000000 0.88993531
## concavity_mean 0.526295261 0.88993531 1.00000000
## concave.points_mean 0.561507233 0.83134376 0.92846135
## symmetry_mean 0.551348562 0.58234520 0.48253973
## fractal_dimension_mean 0.583862748 0.54855552 0.31370724
## radius_se 0.316839793 0.53103228 0.64005923
## texture_se 0.097608252 0.04073925 0.06155412
## perimeter_se 0.316829495 0.57748136 0.67321349
## area_se 0.276492223 0.53133275 0.67128381
## smoothness_se 0.344489796 0.12243847 0.06744569
## compactness_se 0.339053593 0.77817078 0.69525409
## concavity_se 0.309226306 0.72474243 0.77212387
## concave.points_se 0.419259182 0.70297190 0.71114374
## symmetry_se 0.148644407 0.13277751 0.07876289
## fractal_dimension_se 0.366883754 0.61762150 0.50050439
## radius_worst 0.227246454 0.54407142 0.70765327
## texture_worst 0.054539625 0.24573483 0.32194549
## perimeter_worst 0.249900841 0.59415210 0.74266754
## area_worst 0.227618632 0.53710142 0.70845249
## smoothness_worst 0.800757737 0.56484404 0.46989277
## compactness_worst 0.482702665 0.88200315 0.80282250
## concavity_worst 0.444025853 0.83331922 0.90731565
## concave.points_worst 0.512258451 0.82491388 0.88728707
## symmetry_worst 0.403887512 0.48875532 0.41521338
## fractal_dimension_worst 0.487057785 0.69226189 0.54298435
## concave.points_mean symmetry_mean
## radius_mean 0.804189608 0.14495366
## texture_mean 0.304175168 0.09159195
## perimeter_mean 0.834660394 0.17923662
## area_mean 0.810909295 0.15508240
## smoothness_mean 0.561507233 0.55134856
## compactness_mean 0.831343761 0.58234520
## concavity_mean 0.928461346 0.48253973
## concave.points_mean 1.000000000 0.45751099
## symmetry_mean 0.457510988 1.00000000
## fractal_dimension_mean 0.170648576 0.46304292
## radius_se 0.725692162 0.32984582
## texture_se 0.015494565 0.14414977
## perimeter_se 0.744721878 0.33320741
## area_se 0.777292123 0.27846203
## smoothness_se 0.005461134 0.20648819
## compactness_se 0.531826077 0.42018414
## concavity_se 0.585814564 0.36177637
## concave.points_se 0.678599440 0.37511588
## symmetry_se 0.022505900 0.39084369
## fractal_dimension_se 0.340670183 0.39403467
## radius_worst 0.830440842 0.19624965
## texture_worst 0.299144115 0.11112738
## perimeter_worst 0.852892438 0.22726538
## area_worst 0.826899258 0.19948912
## smoothness_worst 0.466239038 0.43013245
## compactness_worst 0.707309028 0.47375819
## concavity_worst 0.787789344 0.43645127
## concave.points_worst 0.918791350 0.42718608
## symmetry_worst 0.389031855 0.70758822
## fractal_dimension_worst 0.388921332 0.44821641
## fractal_dimension_mean radius_se texture_se
## radius_mean -0.322207815 0.675850516 -0.11356719
## texture_mean -0.064781678 0.324923667 0.42298324
## perimeter_mean -0.269645404 0.689469857 -0.10458425
## area_mean -0.303407288 0.709553294 -0.08789804
## smoothness_mean 0.583862748 0.316839793 0.09760825
## compactness_mean 0.548555519 0.531032284 0.04073925
## concavity_mean 0.313707241 0.640059233 0.06155412
## concave.points_mean 0.170648576 0.725692162 0.01549457
## symmetry_mean 0.463042921 0.329845821 0.14414977
## fractal_dimension_mean 1.000000000 0.009828685 0.16875952
## radius_se 0.009828685 1.000000000 0.24749700
## texture_se 0.168759516 0.247497000 1.00000000
## perimeter_se 0.042446603 0.968830153 0.24301857
## area_se -0.091186689 0.951676453 0.14588179
## smoothness_se 0.412528855 0.154228391 0.46039234
## compactness_se 0.539609971 0.405830493 0.23523157
## concavity_se 0.403415624 0.440636019 0.20986865
## concave.points_se 0.303575007 0.582591172 0.23888947
## symmetry_se 0.311261000 0.218366086 0.42885117
## fractal_dimension_se 0.711932490 0.295694551 0.30344083
## radius_worst -0.250903651 0.733499001 -0.11683611
## texture_worst -0.036638879 0.241637635 0.46441279
## perimeter_worst -0.200809161 0.733214853 -0.10755958
## area_worst -0.231863776 0.759618757 -0.09356314
## smoothness_worst 0.502454839 0.179201394 -0.03971119
## compactness_worst 0.450384065 0.364242740 -0.09663426
## concavity_worst 0.321575790 0.444296330 -0.06622163
## concave.points_worst 0.175884454 0.581234126 -0.10396139
## symmetry_worst 0.319493048 0.144517649 -0.13535425
## fractal_dimension_worst 0.752467599 0.090470233 -0.03159143
## perimeter_se area_se smoothness_se compactness_se
## radius_mean 0.6755420 0.80040518 -0.286299469 0.2312607
## texture_mean 0.3371950 0.33963819 0.027542408 0.2263544
## perimeter_mean 0.6943234 0.80964099 -0.267019276 0.2786813
## area_mean 0.7070547 0.83137779 -0.243455750 0.2410757
## smoothness_mean 0.3168295 0.27649222 0.344489796 0.3390536
## compactness_mean 0.5774814 0.53133275 0.122438466 0.7781708
## concavity_mean 0.6732135 0.67128381 0.067445691 0.6952541
## concave.points_mean 0.7447219 0.77729212 0.005461134 0.5318261
## symmetry_mean 0.3332074 0.27846203 0.206488195 0.4201841
## fractal_dimension_mean 0.0424466 -0.09118669 0.412528855 0.5396100
## radius_se 0.9688302 0.95167645 0.154228391 0.4058305
## texture_se 0.2430186 0.14588179 0.460392339 0.2352316
## perimeter_se 1.0000000 0.93042765 0.147009469 0.4774706
## area_se 0.9304277 1.00000000 0.025780361 0.3617208
## smoothness_se 0.1470095 0.02578036 1.000000000 0.3036438
## compactness_se 0.4774706 0.36172078 0.303643798 1.0000000
## concavity_se 0.5014484 0.41794250 0.256076935 0.8854517
## concave.points_se 0.6337872 0.54317733 0.325839005 0.7604251
## symmetry_se 0.2205236 0.08706032 0.461012120 0.3242693
## fractal_dimension_se 0.3388881 0.20959473 0.458977506 0.8281693
## radius_worst 0.7262819 0.84615382 -0.266911386 0.2464900
## texture_worst 0.2520989 0.27725866 -0.054683785 0.1669325
## perimeter_worst 0.7447576 0.84504736 -0.253416943 0.3043906
## area_worst 0.7509061 0.87098161 -0.224153975 0.2510187
## smoothness_worst 0.1737924 0.18212227 0.348520104 0.2573855
## compactness_worst 0.4228494 0.40444628 -0.056112230 0.7275143
## concavity_worst 0.4906278 0.49586555 -0.065792747 0.6670502
## concave.points_worst 0.6150970 0.65345520 -0.098728877 0.5355373
## symmetry_worst 0.1514968 0.16788087 -0.106334491 0.2586757
## fractal_dimension_worst 0.1246492 0.07286530 0.120158161 0.6158136
## concavity_se concave.points_se symmetry_se
## radius_mean 0.3277473 0.4245281 -0.182962654
## texture_mean 0.2441625 0.1882948 0.006935905
## perimeter_mean 0.3685135 0.4573048 -0.164612200
## area_mean 0.3376086 0.4278723 -0.153721804
## smoothness_mean 0.3092263 0.4192592 0.148644407
## compactness_mean 0.7247424 0.7029719 0.132777509
## concavity_mean 0.7721239 0.7111437 0.078762891
## concave.points_mean 0.5858146 0.6785994 0.022505900
## symmetry_mean 0.3617764 0.3751159 0.390843688
## fractal_dimension_mean 0.4034156 0.3035750 0.311261000
## radius_se 0.4406360 0.5825912 0.218366086
## texture_se 0.2098686 0.2388895 0.428851174
## perimeter_se 0.5014484 0.6337872 0.220523611
## area_se 0.4179425 0.5431773 0.087060324
## smoothness_se 0.2560769 0.3258390 0.461012120
## compactness_se 0.8854517 0.7604251 0.324269347
## concavity_se 1.0000000 0.7989200 0.250178804
## concave.points_se 0.7989200 1.0000000 0.272734387
## symmetry_se 0.2501788 0.2727344 1.000000000
## fractal_dimension_se 0.7027625 0.5945439 0.389641966
## radius_worst 0.3326466 0.4186309 -0.189616012
## texture_worst 0.1892518 0.1110552 -0.102164378
## perimeter_worst 0.3827335 0.4544369 -0.169198665
## area_worst 0.3352982 0.4153921 -0.164489060
## smoothness_worst 0.2469927 0.2664058 -0.067334485
## compactness_worst 0.6570193 0.5380887 -0.039477206
## concavity_worst 0.7541404 0.5875883 -0.056162772
## concave.points_worst 0.5863031 0.6633392 -0.103930996
## symmetry_worst 0.2133950 0.1425014 0.269917058
## fractal_dimension_worst 0.5038325 0.3316793 0.031368920
## fractal_dimension_se radius_worst texture_worst
## radius_mean -0.012495838 0.97300475 0.30484292
## texture_mean 0.115792221 0.35562516 0.90680113
## perimeter_mean 0.032425002 0.97401973 0.31174473
## area_mean 0.008597376 0.97407140 0.30812624
## smoothness_mean 0.366883754 0.22724645 0.05453963
## compactness_mean 0.617621503 0.54407142 0.24573483
## concavity_mean 0.500504389 0.70765327 0.32194549
## concave.points_mean 0.340670183 0.83044084 0.29914412
## symmetry_mean 0.394034668 0.19624965 0.11112738
## fractal_dimension_mean 0.711932490 -0.25090365 -0.03663888
## radius_se 0.295694551 0.73349900 0.24163764
## texture_se 0.303440832 -0.11683611 0.46441279
## perimeter_se 0.338888080 0.72628189 0.25209890
## area_se 0.209594727 0.84615382 0.27725866
## smoothness_se 0.458977506 -0.26691139 -0.05468379
## compactness_se 0.828169317 0.24649002 0.16693252
## concavity_se 0.702762493 0.33264658 0.18925175
## concave.points_se 0.594543946 0.41863087 0.11105524
## symmetry_se 0.389641966 -0.18961601 -0.10216438
## fractal_dimension_se 1.000000000 0.01384833 0.05194817
## radius_worst 0.013848326 1.00000000 0.35667314
## texture_worst 0.051948169 0.35667314 1.00000000
## perimeter_worst 0.062806500 0.99318265 0.36610900
## area_worst 0.032873160 0.99170436 0.34927512
## smoothness_worst 0.266369531 0.23719750 0.21614797
## compactness_worst 0.510513241 0.52818510 0.34122680
## concavity_worst 0.445355860 0.62614773 0.36804438
## concave.points_worst 0.301647791 0.79606365 0.35642920
## symmetry_worst 0.164601726 0.27907335 0.23936001
## fractal_dimension_worst 0.688976054 0.10515188 0.21471829
## perimeter_worst area_worst smoothness_worst
## radius_mean 0.9660603 0.95786939 0.13267495
## texture_mean 0.3657272 0.35519989 0.07968380
## perimeter_mean 0.9724254 0.95920857 0.16376463
## area_mean 0.9672572 0.97147548 0.14215487
## smoothness_mean 0.2499008 0.22761863 0.80075774
## compactness_mean 0.5941521 0.53710142 0.56484404
## concavity_mean 0.7426675 0.70845249 0.46989277
## concave.points_mean 0.8528924 0.82689926 0.46623904
## symmetry_mean 0.2272654 0.19948912 0.43013245
## fractal_dimension_mean -0.2008092 -0.23186378 0.50245484
## radius_se 0.7332149 0.75961876 0.17920139
## texture_se -0.1075596 -0.09356314 -0.03971119
## perimeter_se 0.7447576 0.75090611 0.17379239
## area_se 0.8450474 0.87098161 0.18212227
## smoothness_se -0.2534169 -0.22415398 0.34852010
## compactness_se 0.3043906 0.25101866 0.25738553
## concavity_se 0.3827335 0.33529823 0.24699269
## concave.points_se 0.4544369 0.41539208 0.26640576
## symmetry_se -0.1691987 -0.16448906 -0.06733449
## fractal_dimension_se 0.0628065 0.03287316 0.26636953
## radius_worst 0.9931827 0.99170436 0.23719750
## texture_worst 0.3661090 0.34927512 0.21614797
## perimeter_worst 1.0000000 0.98483132 0.25729775
## area_worst 0.9848313 1.00000000 0.23899867
## smoothness_worst 0.2572978 0.23899867 1.00000000
## compactness_worst 0.5819577 0.51106468 0.56931807
## concavity_worst 0.6692728 0.61392141 0.52684856
## concave.points_worst 0.8249048 0.78045867 0.54998997
## symmetry_worst 0.3053196 0.26252759 0.50889740
## fractal_dimension_worst 0.1523208 0.10219381 0.60114001
## compactness_worst concavity_worst concave.points_worst
## radius_mean 0.45609714 0.56702510 0.74391234
## texture_mean 0.27277874 0.31169228 0.29764646
## perimeter_mean 0.50104761 0.60523518 0.77310475
## area_mean 0.44794686 0.56557567 0.73934781
## smoothness_mean 0.48270266 0.44402585 0.51225845
## compactness_mean 0.88200315 0.83331922 0.82491388
## concavity_mean 0.80282250 0.90731565 0.88728707
## concave.points_mean 0.70730903 0.78778934 0.91879135
## symmetry_mean 0.47375819 0.43645127 0.42718608
## fractal_dimension_mean 0.45038407 0.32157579 0.17588445
## radius_se 0.36424274 0.44429633 0.58123413
## texture_se -0.09663426 -0.06622163 -0.10396139
## perimeter_se 0.42284945 0.49062777 0.61509699
## area_se 0.40444628 0.49586555 0.65345520
## smoothness_se -0.05611223 -0.06579275 -0.09872888
## compactness_se 0.72751426 0.66705021 0.53553732
## concavity_se 0.65701934 0.75414044 0.58630307
## concave.points_se 0.53808866 0.58758830 0.66333925
## symmetry_se -0.03947721 -0.05616277 -0.10393100
## fractal_dimension_se 0.51051324 0.44535586 0.30164779
## radius_worst 0.52818510 0.62614773 0.79606365
## texture_worst 0.34122680 0.36804438 0.35642920
## perimeter_worst 0.58195768 0.66927284 0.82490478
## area_worst 0.51106468 0.61392141 0.78045867
## smoothness_worst 0.56931807 0.52684856 0.54998997
## compactness_worst 1.00000000 0.90790640 0.82833879
## concavity_worst 0.90790640 1.00000000 0.87940442
## concave.points_worst 0.82833879 0.87940442 1.00000000
## symmetry_worst 0.59774079 0.52963659 0.50750722
## fractal_dimension_worst 0.77184344 0.66338519 0.51111415
## symmetry_worst fractal_dimension_worst
## radius_mean 0.1906398 0.01143701
## texture_mean 0.1073801 0.11803658
## perimeter_mean 0.2159088 0.05859202
## area_mean 0.1876235 0.01490403
## smoothness_mean 0.4038875 0.48705779
## compactness_mean 0.4887553 0.69226189
## concavity_mean 0.4152134 0.54298435
## concave.points_mean 0.3890319 0.38892133
## symmetry_mean 0.7075882 0.44821641
## fractal_dimension_mean 0.3194930 0.75246760
## radius_se 0.1445176 0.09047023
## texture_se -0.1353543 -0.03159143
## perimeter_se 0.1514968 0.12464916
## area_se 0.1678809 0.07286530
## smoothness_se -0.1063345 0.12015816
## compactness_se 0.2586757 0.61581361
## concavity_se 0.2133950 0.50383249
## concave.points_se 0.1425014 0.33167926
## symmetry_se 0.2699171 0.03136892
## fractal_dimension_se 0.1646017 0.68897605
## radius_worst 0.2790733 0.10515188
## texture_worst 0.2393600 0.21471829
## perimeter_worst 0.3053196 0.15232085
## area_worst 0.2625276 0.10219381
## smoothness_worst 0.5088974 0.60114001
## compactness_worst 0.5977408 0.77184344
## concavity_worst 0.5296366 0.66338519
## concave.points_worst 0.5075072 0.51111415
## symmetry_worst 1.0000000 0.52881130
## fractal_dimension_worst 0.5288113 1.00000000- Ahora visualizamos la correlación de las variables, pero, de manera gráfica. Hacemos uso de la función corrplot()
corrplot(cor(data_var))
Pruebas de hipótesis
1ra Prueba
Formulación de hipótesis:
Ho: Matriz de correlación iguales de cero
H1: Matriz de correlación diferente de cero
library(psych)Evaluamos el p-valor y este tiene que ser < al nivel de significancia, el cual equivale a 0.05. Siendo así, se interpretaría que se rechaza a Ho.
cortest(data_var)## Tests of correlation matrices
## Call:cortest(R1 = data_var)
## Chi Square value 135780.1 with df = 435 with probability < 0Se tiene: 0 < 0.05. Entonces, se cumple, por lo tanto se rechazo Ho. Es decir, que existe correlaciones significativas entre las variables estudiadas.
2da Prueba
bartlett.test(data_var)##
## Bartlett test of homogeneity of variances
##
## data: data_var
## Bartlett's K-squared = 208467, df = 29, p-value < 2.2e-16Se tiene: 2.2e-16 < 0.05. Entonces, se cumple, por lo tanto se rechaza Ho Esto quiere decir que la matriz de correlaciones es distinta a la de la matriz de identidad (Se prueba este supuesto)
3ra Prueba
Ahora realizamos la prueba de KMO - Kaiser Meyer Olkin, el cual nos permite evaluar si se justifica el uso de PCA.
Se tiene la siguiente regla, si el valor del KMO es mayor o igual que 0.5. Entonces, se cumple la justificación del uso de PCA
KMO(data_var)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_var)
## Overall MSA = 0.86
## MSA for each item =
## radius_mean texture_mean perimeter_mean
## 0.86 0.64 0.90
## area_mean smoothness_mean compactness_mean
## 0.90 0.84 0.94
## concavity_mean concave.points_mean symmetry_mean
## 0.92 0.93 0.79
## fractal_dimension_mean radius_se texture_se
## 0.92 0.85 0.47
## perimeter_se area_se smoothness_se
## 0.88 0.96 0.67
## compactness_se concavity_se concave.points_se
## 0.88 0.87 0.89
## symmetry_se fractal_dimension_se radius_worst
## 0.53 0.88 0.84
## texture_worst perimeter_worst area_worst
## 0.59 0.89 0.89
## smoothness_worst compactness_worst concavity_worst
## 0.77 0.88 0.88
## concave.points_worst symmetry_worst fractal_dimension_worst
## 0.91 0.67 0.88Overall MSA = 0.86 >= 0.5, se cumple. Por lo tanto de justifica el PCA.
Se cumplen las pruebas preliminares, entonces procedemos a la realización de PCA.
Realización de PCA
pca <- prcomp(data_var, center = TRUE,
scale = TRUE)
pca ## Standard deviations (1, .., p=30):
## [1] 3.74289107 2.36190685 1.65704734 1.38111718 1.26553770 1.07313219
## [7] 0.77981962 0.66078938 0.59281321 0.55604237 0.52872856 0.46723675
## [13] 0.41305156 0.37990028 0.31908018 0.25289457 0.23058952 0.22085332
## [19] 0.20425114 0.19441575 0.18353131 0.15455616 0.14462946 0.14217843
## [25] 0.13052403 0.10603961 0.09475057 0.05156586 0.03530385 0.02006342
##
## Rotation (n x k) = (30 x 30):
## PC1 PC2 PC3 PC4
## radius_mean -0.211842390 0.24156980 0.01072350 -0.04435498
## texture_mean -0.106172696 0.05375799 -0.18459065 0.57523302
## perimeter_mean -0.220520774 0.22184069 0.01374533 -0.04440885
## area_mean -0.214529913 0.23647961 -0.01217047 -0.04862866
## smoothness_mean -0.138992303 -0.19425890 0.10984386 -0.09482556
## compactness_mean -0.233821115 -0.15380581 0.07969792 -0.03228401
## concavity_mean -0.251644921 -0.05498377 0.02591704 -0.01645214
## concave.points_mean -0.254248452 0.02945602 0.02565609 -0.06712488
## symmetry_mean -0.132429040 -0.18916892 0.04423381 -0.02496103
## fractal_dimension_mean -0.059013428 -0.36934177 0.05920899 -0.02197684
## radius_se -0.205196940 0.08470080 -0.26157604 -0.12560526
## texture_se -0.018978657 -0.11000488 -0.44479529 0.29092769
## perimeter_se -0.212271896 0.06902213 -0.25685510 -0.12042615
## area_se -0.216614574 0.14155617 -0.19051139 -0.10523364
## smoothness_se -0.007855442 -0.23828173 -0.30741440 -0.08028699
## compactness_se -0.175721522 -0.22513817 -0.12109833 -0.03566960
## concavity_se -0.185279711 -0.16881507 -0.12444795 -0.04301721
## concave.points_se -0.191849047 -0.11540670 -0.19085816 -0.16070441
## symmetry_se -0.016653169 -0.18946053 -0.32124048 -0.12428698
## fractal_dimension_se -0.120436643 -0.29454926 -0.15242588 -0.05946485
## radius_worst -0.224320568 0.22042649 0.03629719 -0.01529300
## texture_worst -0.105091373 0.04216131 -0.08395817 0.64499571
## perimeter_worst -0.232231589 0.19914909 0.03927971 -0.01078620
## area_worst -0.224110112 0.21546095 0.01270754 -0.02482157
## smoothness_worst -0.128250716 -0.17625369 0.23672761 0.07008853
## compactness_worst -0.215649212 -0.12943042 0.21340747 0.09776673
## concavity_worst -0.230450442 -0.07627579 0.16711366 0.08440241
## concave.points_worst -0.247709007 0.01138582 0.15090704 0.01215740
## symmetry_worst -0.121917736 -0.12103730 0.26522136 0.11364176
## fractal_dimension_worst -0.130806798 -0.27433054 0.22698695 0.12195635
## PC5 PC6 PC7 PC8
## radius_mean 0.012621691 -0.0077002735 0.079433410 -0.014103993
## texture_mean 0.017240201 0.0045068893 -0.002459530 0.107648733
## perimeter_mean 0.017666144 -0.0079779012 0.071913673 -0.027454038
## area_mean -0.004838251 -0.0008891651 0.043367400 0.031458698
## smoothness_mean -0.375512697 0.3125307663 0.093812543 -0.347861496
## compactness_mean 0.050237462 0.0143289251 -0.015468919 -0.183458110
## concavity_mean 0.084074139 0.0170240079 0.125549209 -0.076933613
## concave.points_mean -0.056253928 0.0655331940 0.098246162 -0.162274740
## symmetry_mean -0.344374831 -0.3751681099 0.076561915 -0.259506211
## fractal_dimension_mean -0.028021197 0.0850444261 -0.342944589 -0.178397703
## radius_se -0.152306542 0.0101571265 -0.322929761 0.039664577
## texture_se -0.123590471 0.0527695973 0.065739779 -0.404002707
## perimeter_se -0.095568737 -0.0025709810 -0.289315651 0.020474232
## area_se -0.117761562 0.0160423627 -0.271030538 0.061132580
## smoothness_se -0.206475087 0.3397086831 0.216784018 0.539206501
## compactness_se 0.320217297 -0.0914691290 0.029362950 0.056277724
## concavity_se 0.340403756 -0.0472863344 0.264300393 0.052199510
## concave.points_se 0.165606961 0.0648265560 0.361198922 -0.130738811
## symmetry_se -0.217711838 -0.4667945645 0.134357881 0.208029686
## fractal_dimension_se 0.227110586 0.0023166122 -0.296683067 0.079636362
## radius_worst -0.039934261 0.0061643082 -0.042880731 0.066268276
## texture_worst -0.039982498 0.0308715599 0.007010371 -0.005643547
## perimeter_worst -0.019399266 -0.0063213346 -0.040163773 0.058876704
## area_worst -0.054303762 0.0180556827 -0.085736371 0.103996784
## smoothness_worst -0.336483456 0.3899813297 0.102668483 0.268384665
## compactness_worst 0.148847539 -0.0582655672 -0.047910331 0.084319447
## concavity_worst 0.166567755 -0.0323000863 0.131785749 0.080112131
## concave.points_worst 0.017005506 0.0444740319 0.164168651 -0.026615184
## symmetry_worst -0.305943001 -0.4877783518 0.063820137 0.224889304
## fractal_dimension_worst 0.116660254 0.0189583967 -0.369605560 0.111994232
## PC9 PC10 PC11 PC12
## radius_mean 0.24656798 -0.160171159 0.0178511810 0.063204307
## texture_mean -0.02499843 -0.119226764 -0.5337833257 -0.097344751
## perimeter_mean 0.24476425 -0.150566075 -0.0006470287 0.042268733
## area_mean 0.24033068 -0.160806570 0.0384012691 0.006041808
## smoothness_mean 0.14804225 0.133388356 -0.2121949051 -0.044580408
## compactness_mean 0.08700211 -0.005356641 -0.2040394486 -0.036623449
## concavity_mean 0.05519674 0.048051260 0.0228757134 -0.416643340
## concave.points_mean 0.11212399 0.010314805 -0.1041993158 -0.090665152
## symmetry_mean -0.31335612 -0.621986742 0.0242319064 -0.112156186
## fractal_dimension_mean 0.16976445 0.046032881 -0.1685082204 -0.107691310
## radius_se -0.28851085 0.148295393 -0.0140983366 -0.060479248
## texture_se 0.15660351 0.092670577 0.6079333722 0.094199661
## perimeter_se -0.30653640 0.178423952 -0.0620504248 -0.019536235
## area_se -0.18291532 0.072800966 0.0484992637 -0.032740051
## smoothness_se 0.01722871 -0.310790523 0.0659324205 -0.076853816
## compactness_se -0.01351116 -0.074756009 -0.0150999064 0.108962750
## concavity_se -0.16449663 0.054115901 0.1093949464 -0.337488382
## concave.points_se -0.25915721 0.070191954 -0.1943597837 0.566267954
## symmetry_se 0.43368161 0.366373264 -0.1826072893 -0.043135600
## fractal_dimension_se 0.25040965 -0.307105997 0.0416455171 0.186788678
## radius_worst 0.10010291 -0.046271347 0.0702802343 0.060049733
## texture_worst -0.04322910 0.052582076 -0.0188181530 0.077609586
## perimeter_worst 0.09018193 -0.031602620 0.0559307629 0.055187060
## area_worst 0.09434445 -0.053207728 0.0903113081 -0.002538133
## smoothness_worst -0.05330843 0.102985638 0.1233912204 0.069108475
## compactness_worst -0.05358964 0.116662183 0.0636626516 0.097411450
## concavity_worst -0.10980806 0.170592019 0.2094152209 -0.354778008
## concave.points_worst -0.08750940 0.142814548 -0.0016261104 0.242483996
## symmetry_worst -0.06715095 0.113339495 0.1315672575 0.192715257
## fractal_dimension_worst 0.09623668 -0.028114838 0.1544485516 0.153508932
## PC13 PC14 PC15 PC16
## radius_mean -0.044724072 -0.061567582 0.085331746 -0.091914923
## texture_mean 0.013384449 -0.071890969 -0.043169466 -0.145041576
## perimeter_mean -0.053622625 -0.026276006 0.086858346 -0.067591922
## area_mean -0.007104358 -0.049118820 0.125634334 -0.057760431
## smoothness_mean -0.259488247 -0.375774047 -0.191841562 -0.018265680
## compactness_mean -0.246096028 0.316545572 -0.014833499 0.074540583
## concavity_mean 0.259835478 0.124319684 -0.184463333 0.227298156
## concave.points_mean 0.269476626 0.217970846 -0.203695390 0.372630819
## symmetry_mean 0.008818221 0.021882132 -0.040915584 -0.236171375
## fractal_dimension_mean 0.185710818 0.158208666 0.708645461 -0.003107437
## radius_se 0.007288476 -0.026998203 -0.090593168 -0.026380859
## texture_se -0.047188376 0.113274797 0.024164060 -0.047905488
## perimeter_se -0.073582318 0.056390292 -0.068886850 -0.009168764
## area_se -0.005138938 -0.087589758 0.067367052 0.112924471
## smoothness_se 0.034398230 0.320937940 0.043525876 0.047027511
## compactness_se -0.500694839 0.044702585 -0.008819538 0.216123272
## concavity_se -0.031719288 -0.436959659 0.277248843 0.003980901
## concave.points_se 0.256686025 -0.055445568 0.141935965 -0.160954703
## symmetry_se 0.033160130 0.005299244 -0.106885527 -0.267017167
## fractal_dimension_se 0.114132741 -0.350239752 -0.285406092 0.244066399
## radius_worst -0.020859720 -0.046545894 0.086010550 -0.070679210
## texture_worst 0.030995052 -0.049200225 0.050343311 0.187372900
## perimeter_worst -0.063606473 0.005055075 0.097329911 -0.075995873
## area_worst 0.009206383 -0.026952457 0.131466257 -0.046266432
## smoothness_worst -0.099674624 -0.198978693 0.049230107 -0.062449845
## compactness_worst -0.413559136 0.336590481 -0.085377601 -0.183832013
## concavity_worst 0.109402347 -0.023313884 -0.087447530 -0.279781713
## concave.points_worst 0.268814041 0.193567113 -0.109700525 0.023902749
## symmetry_worst 0.019081856 -0.120554840 0.167453763 0.445251195
## fractal_dimension_worst 0.283889991 -0.034204156 -0.216950820 -0.355058173
## PC17 PC18 PC19 PC20
## radius_mean -0.036317037 -0.073046571 -0.14719975 -0.025966924
## texture_mean 0.045078101 -0.018724074 0.07584813 0.112601706
## perimeter_mean -0.038056759 -0.065159481 -0.17671295 -0.024507108
## area_mean -0.054077010 -0.014973000 -0.01888668 -0.054607489
## smoothness_mean 0.125372795 -0.379676318 0.19629795 -0.106135993
## compactness_mean -0.290255517 -0.020394665 -0.38810323 0.442877405
## concavity_mean -0.104555877 0.006130133 -0.03122774 0.035482231
## concave.points_mean -0.083424196 0.109205497 0.05534815 -0.197148159
## symmetry_mean -0.002635704 0.181200910 0.04957807 -0.073579725
## fractal_dimension_mean 0.175025758 0.065402214 0.08112002 -0.075059702
## radius_se -0.094324607 -0.034729859 -0.05607451 0.124574338
## texture_se 0.006475273 -0.013192017 -0.01917205 0.083137356
## perimeter_se 0.270821513 -0.037086179 -0.45642838 -0.388103451
## area_se -0.280988257 0.026292567 0.49322016 0.326135775
## smoothness_se 0.059907602 -0.330547963 0.03708732 -0.022054102
## compactness_se -0.158734155 0.160729846 0.27533620 -0.416953776
## concavity_se -0.166068595 -0.073869570 -0.12662217 -0.059570641
## concave.points_se -0.033393027 -0.086802239 -0.02186898 0.146791707
## symmetry_se -0.057994658 0.201350403 0.04029129 -0.041838650
## fractal_dimension_se 0.375244858 0.167160129 -0.08090806 0.265870669
## radius_worst 0.045757151 -0.020844228 0.05342835 0.005487339
## texture_worst -0.046909442 0.024870593 -0.05250541 -0.155607106
## perimeter_worst 0.164897476 -0.002299707 -0.05710063 -0.075900865
## area_worst 0.039966213 0.056444976 0.23364859 -0.010488508
## smoothness_worst -0.155635802 0.587474256 -0.20425526 0.049098768
## compactness_worst 0.216210169 -0.073245702 0.11882451 0.169647488
## concavity_worst 0.361658244 -0.043980365 0.08749700 0.148933599
## concave.points_worst 0.186084157 0.177397759 0.21162043 -0.140699496
## symmetry_worst 0.041612402 -0.322876090 -0.09572376 0.096536806
## fractal_dimension_worst -0.457908858 -0.289468007 -0.02974475 -0.246153443
## PC21 PC22 PC23 PC24
## radius_mean -0.232015941 0.099234357 0.206506014 0.0913006921
## texture_mean -0.284524593 -0.019403207 -0.229411153 -0.3365259248
## perimeter_mean -0.244988543 0.140085057 0.165617812 0.1183261331
## area_mean -0.183405270 0.035385858 0.051439950 0.0910575245
## smoothness_mean 0.079526386 -0.002545800 0.025738916 0.0251316054
## compactness_mean 0.332764999 0.065908922 -0.046229380 -0.1007000360
## concavity_mean -0.089894898 -0.428459422 -0.106141486 0.2066123970
## concave.points_mean -0.147707419 0.178016680 -0.071052527 -0.1001787112
## symmetry_mean 0.077083650 0.026455615 0.024192439 0.0692685204
## fractal_dimension_mean -0.088022536 -0.022002799 0.086437947 0.0226388952
## radius_se -0.080301020 -0.206021064 0.623298983 -0.2988369658
## texture_se -0.140434341 -0.009808999 -0.139671790 -0.2052001320
## perimeter_se -0.041551446 0.094570893 -0.318970528 0.1497332592
## area_se -0.076640133 0.322066797 -0.221191499 0.3169313274
## smoothness_se 0.085029127 0.065643445 0.051879018 0.0143609381
## compactness_se -0.122307718 -0.242069196 0.066535874 -0.0556231341
## concavity_se 0.166900111 0.332324281 -0.020686477 -0.2031028188
## concave.points_se -0.061225767 -0.264501382 -0.077232166 0.1922970102
## symmetry_se 0.120412203 0.044180958 0.035205436 0.0998814495
## fractal_dimension_se 0.056376352 0.046725545 0.022905565 0.0366193128
## radius_worst 0.247949664 -0.226063345 0.010715246 -0.1764486670
## texture_worst 0.377565475 0.028506437 0.322672725 0.4740689751
## perimeter_worst 0.246207286 -0.010251102 -0.252960270 -0.0612705262
## area_worst 0.352751552 -0.326813902 -0.213419409 -0.1517004201
## smoothness_worst -0.175163961 -0.064803545 -0.068625222 -0.0005696221
## compactness_worst -0.135983004 0.132063233 0.009555864 0.1403253603
## concavity_worst -0.099152855 -0.093128597 0.105293786 0.1313027052
## concave.points_worst 0.166095151 0.388528098 0.175422451 -0.3199084880
## symmetry_worst -0.173143223 -0.070909375 -0.070307314 -0.1310276037
## fractal_dimension_worst -0.003652793 0.017871237 -0.090297491 -0.0332870912
## PC25 PC26 PC27 PC28
## radius_mean 0.057921543 0.020469033 0.134382630 -0.279788963
## texture_mean 0.040645831 -0.014857017 0.037688679 -0.012279581
## perimeter_mean 0.031642586 0.053626687 0.181547516 -0.114934061
## area_mean 0.183110740 -0.285829689 -0.468772162 0.408755352
## smoothness_mean 0.037126772 -0.043056208 0.003427039 0.020500125
## compactness_mean 0.265320923 0.126881693 -0.120890534 -0.012278703
## concavity_mean 0.052455964 -0.402054720 0.361107423 0.038552143
## concave.points_mean -0.463556000 0.348785956 -0.293772627 -0.028380783
## symmetry_mean -0.043488106 -0.017757923 0.016690257 -0.004753927
## fractal_dimension_mean -0.007413677 0.005002139 0.046812241 -0.012669344
## radius_se -0.141360855 -0.024575936 -0.010240670 0.192418400
## texture_se 0.026171521 -0.008671482 0.013516189 -0.008572355
## perimeter_se 0.142592889 -0.072761674 -0.072984773 -0.176731019
## area_se 0.126110528 0.085739405 0.114008680 -0.044238407
## smoothness_se 0.025831170 0.029307890 0.015806801 -0.008497734
## compactness_se 0.233635165 0.178417463 0.037393341 0.022459213
## concavity_se -0.220437738 -0.149763123 -0.009544599 -0.027397394
## concave.points_se -0.095372021 0.050834866 -0.054486239 0.029773747
## symmetry_se -0.045064047 -0.001649603 0.010293989 -0.009327825
## fractal_dimension_se -0.024467360 -0.040300491 -0.011520204 -0.007228536
## radius_worst -0.158017838 0.181407105 0.254862466 -0.437858240
## texture_worst -0.058684936 0.019410386 -0.057764188 0.016000899
## perimeter_worst -0.146035070 0.256807841 0.385693693 0.659628823
## area_worst -0.026874706 -0.218137976 -0.422170071 -0.192344355
## smoothness_worst -0.032266875 0.003431287 0.013720311 -0.005738992
## compactness_worst -0.481580485 -0.326511659 -0.012533702 -0.029168224
## concavity_worst 0.268413983 0.465306806 -0.214129944 -0.010415461
## concave.points_worst 0.368311248 -0.263684363 0.168622076 -0.018861110
## symmetry_worst 0.074007503 0.014196148 -0.022864661 0.003272490
## fractal_dimension_worst 0.005676307 0.029220190 -0.005097350 0.012142839
## PC29 PC30
## radius_mean -0.0273038224 -0.7288048295
## texture_mean 0.0008313481 -0.0009068040
## perimeter_mean -0.4788483268 0.5964157597
## area_mean 0.4612104085 0.1372911682
## smoothness_mean -0.0028006234 0.0050942919
## compactness_mean 0.0167379047 -0.0147489225
## concavity_mean 0.0173247793 -0.0116804376
## concave.points_mean 0.0078183793 -0.0232073046
## symmetry_mean 0.0075963138 0.0033172523
## fractal_dimension_mean 0.0122407466 -0.0099607853
## radius_se -0.0702795575 -0.0217254860
## texture_se -0.0005125859 0.0026002717
## perimeter_se 0.0457789559 0.0139637116
## area_se 0.0267314831 -0.0027774688
## smoothness_se -0.0028538511 -0.0003150268
## compactness_se -0.0102948571 -0.0037929134
## concavity_se 0.0037361205 0.0006432705
## concave.points_se -0.0047960184 0.0034437940
## symmetry_se 0.0045938779 0.0012387126
## fractal_dimension_se 0.0034592228 0.0049532491
## radius_worst 0.5722381807 0.2544036736
## texture_worst -0.0028622058 -0.0018180606
## perimeter_worst -0.0977843021 -0.1386929974
## area_worst -0.4580475947 -0.0915326236
## smoothness_worst -0.0016690032 -0.0028329368
## compactness_worst 0.0314242337 -0.0019703336
## concavity_worst -0.0143448097 0.0031170729
## concave.points_worst -0.0048698113 0.0120322512
## symmetry_worst -0.0159307871 -0.0037460451
## fractal_dimension_worst -0.0120277777 -0.0003723341- Con el siguiente gráfico se evalúa la cantidad de variables que tomaremos en cuenta, generando así un nuevo conjunto de datos más óptimo.
scree(data_var)
De acuerdo al gráfico, interpretamos que con solo usar 6 variables podremos obtener un nuevo conjunto de datos, con variables reducidas.
Selección de variables
Conjunto de datos más óptimo.
data_comp <- pca$x
comp_data <- data_comp[,1:6]Agregamos el target.
new_data <- cbind(comp_data, data$diagnosis)Formato de la data final
write.csv(new_data, file = "dataCancerFinal2.csv")
getwd()## [1] "D:/VII CICLO/MINERIA DE DATOS/FINAL/R-MARKDOWN"Visualización de datos
Se visualiza el conjunto de datos, con las variables resumidas: https://raw.githubusercontent.com/cnahuina/data-mineria/master/dataCancerFinal2.csv