Grupo_05 10/9/2021
Integrantes del Grupo-05
BACA QUIÑONEZ, Pedro
COSIOS LEONA, Jose (17160182)
ESQUIVEL GUILLERMO, Antoni (17160183)
GARRO DOROTEO, Jamir (17160185)
RIVERA REAÑO, Ricardo (17160037)
Primero Cargamos las librerias
library(PerformanceAnalytics)
library(GGally)
library(lattice)
library(cptcity)
library(psych)
library(readxl)
library(mice)
library(VIM)
library(tidyverse)
library(dplyr)
library(factoextra)
library(NbClust)
library(ade4)
library(factoextra)
library(corrplot)
library(rgl)
library(NbClust)
library(LICORS)
library(clusterSim)
library(clValid)Leemos los datos
data <- read_xls("Mundial.xls") %>%
dplyr::select(-Paises, -Casos, -Poblacion, -Death, -vel)
head(data)## # A tibble: 6 x 9
## Tasa_Casos Tasa_Muerte t_med t_max t_min presion ha hr p_rocio
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 8.56 0.529 54.9 65.1 46.5 1011. 0.164 0.642 42.4
## 2 1.63 0.100 71.7 85.8 55.8 1012. 0.0456 0.174 24.5
## 3 0.0213 0.00609 83.0 91.2 77.4 1009. 0.224 0.749 74.3
## 4 7.15 0 77.5 83.3 71.5 1017. 0.201 0.722 67.9
## 5 2.32 0.0595 72.6 89.0 60.3 1014. 0.149 0.560 55.1
## 6 17.7 0.0701 69.0 77.4 59.9 1017. 0.173 0.656 56.4
Vemos si tiene Missin Value
mice::md.pattern(data, rotate.names = TRUE)## /\ /\
## { `---' }
## { O O }
## ==> V <== No need for mice. This data set is completely observed.
## \ \|/ /
## `-----'
## Tasa_Casos Tasa_Muerte t_med t_max t_min presion ha hr p_rocio
## 82 1 1 1 1 1 1 1 1 1 0
## 0 0 0 0 0 0 0 0 0 0
Estandarizamos con Scale
scale_data <- scale(data)Hallamos su covarianza
cor(scale_data)## Tasa_Casos Tasa_Muerte t_med t_max t_min presion
## Tasa_Casos 1.0000000 0.64132877 -0.5259046 -0.5667345 -0.46185563 0.2751922
## Tasa_Muerte 0.6413288 1.00000000 -0.3481158 -0.3821285 -0.32081515 0.1763982
## t_med -0.5259046 -0.34811584 1.0000000 0.9576501 0.94807794 -0.5456415
## t_max -0.5667345 -0.38212851 0.9576501 1.0000000 0.84664184 -0.6125344
## t_min -0.4618556 -0.32081515 0.9480779 0.8466418 1.00000000 -0.4668720
## presion 0.2751922 0.17639821 -0.5456415 -0.6125344 -0.46687199 1.0000000
## ha 0.1863853 0.01868854 -0.1015149 -0.2787273 0.13575996 0.1388064
## hr 0.1448730 0.06069128 -0.2135802 -0.3782905 0.03248243 0.2611722
## p_rocio -0.3030153 -0.22036350 0.5685375 0.4110904 0.71385556 -0.1622819
## ha hr p_rocio
## Tasa_Casos 0.18638532 0.14487304 -0.3030153
## Tasa_Muerte 0.01868854 0.06069128 -0.2203635
## t_med -0.10151487 -0.21358017 0.5685375
## t_max -0.27872734 -0.37829052 0.4110904
## t_min 0.13575996 0.03248243 0.7138556
## presion 0.13880638 0.26117219 -0.1622819
## ha 1.00000000 0.96261925 0.7001754
## hr 0.96261925 1.00000000 0.6537214
## p_rocio 0.70017543 0.65372137 1.0000000
Hallamos su covarianza
cov <- cov(scale_data)
diag(cov) %>% sum()## [1] 9
Justificamos las variables con grafica
chart.Correlation(scale_data, histogram = T, pch = 20)
ggpairs(as.data.frame(scale_data))
mtx <- cor(scale_data)
levelplot(
mtx,
col.regions =
cpt(
pal = "cb_div_RdBu_11", n = 100, rev = F
)
)
pca <-
dudi.pca(
scale_data,
scale = F, scannf = F,
nf = ncol(scale_data)
)
summary(pca)## Class: pca dudi
## Call: dudi.pca(df = scale_data, scale = F, scannf = F, nf = ncol(scale_data))
##
## Total inertia: 8.89
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 4.1128 2.6306 1.1062 0.5911 0.3325
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 46.262 29.590 12.443 6.649 3.740
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 46.26 75.85 88.29 94.94 98.68
##
## (Only 5 dimensions (out of 9) are shown)
Valores Propios
pca$eig## [1] 4.112802025 2.630602276 1.106200136 0.591128233 0.332489406 0.065572224
## [7] 0.026665685 0.019157480 0.005626437
sum(pca$eig)## [1] 8.890244
Vectores propios
pca$c1## CS1 CS2 CS3 CS4 CS5
## Tasa_Casos -0.33854656 0.07013446 -0.53680541 -0.01831205 0.74162937
## Tasa_Muerte -0.26031490 0.01302306 -0.70687051 0.24709547 -0.59959174
## t_med 0.46965761 -0.01513546 -0.19000695 0.22641514 0.11320738
## t_max 0.46246425 -0.13152891 -0.15032839 0.12483885 0.06932651
## t_min 0.44811951 0.13337881 -0.19428555 0.23504755 0.14356872
## presion -0.30323986 0.12577859 0.32815429 0.86583149 0.12470961
## ha -0.03111211 0.59908893 -0.01351074 -0.19692318 0.09592381
## hr -0.07773103 0.59595800 0.07105140 -0.10938304 -0.14182884
## p_rocio 0.28878252 0.47926921 -0.05300764 0.12690561 -0.08586208
## CS6 CS7 CS8 CS9
## Tasa_Casos -0.12861758 -0.11113701 0.10848292 -0.03599205
## Tasa_Muerte 0.02443827 0.09052681 -0.04609038 0.03029116
## t_med 0.03519777 0.07255904 -0.33302463 -0.74940055
## t_max -0.50112330 0.53155617 0.36332606 0.24526534
## t_min 0.69670919 -0.13366497 0.21270764 0.34536682
## presion -0.03679916 0.13187360 -0.01183200 0.02094329
## ha 0.10242012 0.54490725 -0.49308297 0.20351223
## hr 0.04078593 0.06397384 0.65121409 -0.41452098
## p_rocio -0.48123342 -0.59612344 -0.17493077 0.20753076
Scree Plot
fviz_eig(pca, addlabels = T)
correlaciones entre variables y Componentes
pca$co## Comp1 Comp2 Comp3 Comp4 Comp5
## Tasa_Casos -0.68657392 0.11375200 -0.56459073 -0.01407920 0.42763754
## Tasa_Muerte -0.52791978 0.02112227 -0.74345848 0.18997901 -0.34573595
## t_med 0.95246772 -0.02454841 -0.19984180 0.17407898 0.06527752
## t_max 0.93787956 -0.21332847 -0.15810946 0.09598218 0.03997498
## t_min 0.90878836 0.21632885 -0.20434187 0.18071599 0.08278444
## presion -0.61497178 0.20400194 0.34513972 0.66569337 0.07190992
## ha -0.06309551 0.97167022 -0.01421006 -0.15140412 0.05531148
## hr -0.15763888 0.96659212 0.07472906 -0.08409900 -0.08178119
## p_rocio 0.58565223 0.77733303 -0.05575134 0.09757120 -0.04950970
## Comp6 Comp7 Comp8 Comp9
## Tasa_Casos -0.032935200 -0.01814826 0.015015180 -0.002699749
## Tasa_Muerte 0.006257925 0.01478269 -0.006379395 0.002272127
## t_med 0.009013120 0.01184862 -0.046094122 -0.056212220
## t_max -0.128323013 0.08680116 0.050288159 0.018397250
## t_min 0.178406836 -0.02182700 0.029440981 0.025905820
## presion -0.009423189 0.02153447 -0.001637674 0.001570947
## ha 0.026226797 0.08898134 -0.068247885 0.015265367
## hr 0.010444082 0.01044669 0.090134900 -0.031093045
## p_rocio -0.123229798 -0.09734476 -0.024212264 0.015566795
grafica de correlacione entre variables y Componentes
levelplot(
as.matrix(pca$co),
col.regions =
cpt(
pal = "cb_div_RdBu_11", n = 100, rev = F
)
)
Contribucion de las variables a los componentes
contrib <- as.matrix(pca$co * pca$co)
head(contrib)## Comp1 Comp2 Comp3 Comp4 Comp5
## Tasa_Casos 0.4713838 0.0129395170 0.31876269 0.0001982237 0.182873866
## Tasa_Muerte 0.2786993 0.0004461502 0.55273051 0.0360920261 0.119533350
## t_med 0.9071948 0.0006026242 0.03993675 0.0303034901 0.004261154
## t_max 0.8796181 0.0455090375 0.02499860 0.0092125787 0.001597999
## t_min 0.8258963 0.0467981694 0.04175560 0.0326582698 0.006853264
## presion 0.3781903 0.0416167927 0.11912142 0.4431476570 0.005171037
## Comp6 Comp7 Comp8 Comp9
## Tasa_Casos 1.084727e-03 0.0003293595 2.254556e-04 7.288643e-06
## Tasa_Muerte 3.916163e-05 0.0002185280 4.069669e-05 5.162563e-06
## t_med 8.123633e-05 0.0001403899 2.124668e-03 3.159814e-03
## t_max 1.646680e-02 0.0075344417 2.528899e-03 3.384588e-04
## t_min 3.182900e-02 0.0004764177 8.667714e-04 6.711115e-04
## presion 8.879650e-05 0.0004637335 2.681977e-06 2.467876e-06
Contribucion de las variables a los componentes
corrplot(contrib, is.corr = F)
Obteniendo los Score O Puntuaciones
as.tibble(scale_data)## # A tibble: 82 x 9
## Tasa_Casos Tasa_Muerte t_med t_max t_min presion ha hr
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -0.141 -0.0242 -1.91 -1.72 -1.79 -0.480 -0.298 0.0975
## 2 -0.295 -0.166 -0.403 0.0361 -0.962 -0.207 -2.65 -2.67
## 3 -0.331 -0.197 0.617 0.492 0.964 -1.11 0.882 0.729
## 4 -0.172 -0.199 0.121 -0.178 0.436 1.23 0.441 0.572
## 5 -0.280 -0.180 -0.317 0.309 -0.560 0.456 -0.606 -0.387
## 6 0.0639 -0.176 -0.645 -0.676 -0.592 1.26 -0.120 0.178
## 7 -0.252 -0.199 -0.0952 -0.237 0.214 2.63 0.269 0.480
## 8 0.411 -0.121 -0.387 -0.560 0.00973 0.977 -0.350 -0.0778
## 9 -0.331 -0.198 0.294 0.380 0.232 -0.680 -0.455 -0.451
## 10 -0.0680 -0.199 0.322 0.0215 0.718 0.658 0.324 0.338
## # ... with 72 more rows, and 1 more variable: p_rocio <dbl>
head(pca$li)## Axis1 Axis2 Axis3 Axis4 Axis5 Axis6
## 1 -2.680979752 -0.81632842 0.9867556 -1.60881537 -0.66979266 0.20109010
## 2 -0.875631494 -4.62676899 0.4532449 -0.05188124 0.02565907 0.23847409
## 3 1.657010299 1.33749760 -0.4386080 -0.69980986 -0.12898965 0.15767682
## 4 0.005306261 1.08411046 0.5620529 1.04538929 0.12382711 0.17779984
## 5 -0.321761905 -0.86272494 0.5516533 0.30104409 -0.10621358 -0.42411191
## 6 -1.338121092 0.06828199 0.8743985 0.64433378 0.09506283 -0.01317926
## Axis7 Axis8 Axis9
## 1 -0.22142002 0.06799444 0.009222714
## 2 0.07908999 -0.04273997 -0.007049377
## 3 -0.02645513 0.02761341 0.061561357
## 4 -0.02608987 0.02475638 0.007287898
## 5 0.17726287 0.18846850 0.087600063
## 6 -0.05507734 0.07234008 -0.029815667
dim(pca$li)## [1] 82 9
result <-
as.tibble(pca$li) %>%
dplyr::select(sprintf("Axis%1$s", 1:3))calculo de las distancias
distancia <- dist(scale(result), method = "euclidean")
as.matrix(distancia) %>% dim()## [1] 82 82
cluster::daisy(result, metric = "euclidean")## Dissimilarities :
## 1 2 3 4 5 6 7
## 2 4.2501027
## 3 5.0486420 6.5408067
## 4 3.3178567 5.7794493 1.9477303
## 5 2.3994532 3.8058486 3.1204384 1.9741453
## 6 1.6119644 4.7365357 3.5079490 1.7129694 1.4156004
## 7 2.6928519 5.6465584 2.8547202 0.9171800 1.9660583 1.1577151
## 8 2.0247052 4.4994622 3.0395554 1.5191037 0.9468850 0.7183538 1.3843070
## 9 3.7047322 4.3809544 2.1612702 2.0329907 1.3631039 2.5028765 2.5567344
## 10 3.6662844 5.6388045 1.4118322 0.6654672 1.9204386 2.1016799 1.5334125
## 11 4.0781291 6.4966266 1.4488122 0.9836592 2.7546638 2.5396625 1.7821209
## 12 5.1964936 5.2336443 2.0157167 3.0570006 2.8628399 3.9562348 3.7950702
## 13 4.6469468 6.3378886 0.4463756 1.5022133 2.7928988 3.0878936 2.4087532
## 14 4.3241630 6.3577943 0.9164238 1.1084705 2.6791241 2.7514988 2.0100982
## 15 6.2913241 3.6369399 5.3845167 5.8024493 4.4071179 5.8062634 6.2066687
## 16 4.6996883 5.3838597 1.3350144 2.2591468 2.4291108 3.3291029 3.0393203
## 17 3.2429690 5.5792974 1.8750342 0.3305368 1.7909896 1.6640258 1.0986870
## 18 4.9611203 5.7534637 1.0685171 2.3497724 2.7565115 3.5550612 3.1906769
## 19 6.2451157 3.1544633 5.8932574 6.1248273 4.5619126 5.9366426 6.4440160
## 20 1.8704039 3.1525415 3.9874851 2.7465478 0.9042467 1.6170680 2.5419437
## 21 0.9836373 4.9076238 4.4873993 2.6132713 2.2496710 1.0170496 1.8553502
## 22 2.9189313 3.8541929 2.7914840 2.0612590 0.6369842 1.9109105 2.3127445
## 23 4.8414432 5.8718770 0.7883740 2.0851016 2.6978623 3.3865618 2.9474827
## 24 3.5864972 5.4898176 1.4790944 0.7339976 1.7850262 2.0400768 1.5541195
## 25 3.8827192 6.0777701 1.3207553 0.6671207 2.3333071 2.3034332 1.5767669
## 26 3.3350753 5.5869973 1.7538122 0.4792347 1.8245298 1.7785888 1.2731958
## 27 2.8942552 1.5457742 5.2410400 4.2806783 2.3127057 3.1964135 4.1060085
## 28 3.4351576 4.6354263 2.0256471 1.4966289 1.1659468 2.0803035 1.9880033
## 29 5.4451584 7.4776629 1.1025365 2.1905852 3.8551271 3.8740855 3.0072873
## 30 1.2806433 3.6382322 4.7097657 3.0854172 1.7750491 1.5768288 2.5013399
## 31 2.7672786 4.9338878 2.3861482 0.8589362 1.1317529 1.2221539 1.0190640
## 32 5.0335274 7.2039792 1.1029664 1.7827112 3.5207263 3.4621437 2.5858408
## 33 5.2702446 3.7555511 3.8817382 4.3107520 3.1209460 4.5149363 4.7797330
## 34 5.4072422 6.2726994 0.8915868 2.5794708 3.2395604 3.9465607 3.4555730
## 35 0.9165762 4.8237787 5.7929885 3.9588785 3.2463658 2.2945452 3.2114842
## 36 4.0471284 6.1199672 1.1443674 0.8135749 2.4026895 2.4619978 1.7215467
## 37 1.8260535 4.9169622 3.3878075 1.5366225 1.4897943 0.2732221 0.9039885
## 38 4.6515167 4.2019480 2.7704192 3.2019607 2.3308013 3.6404534 3.7513185
## 39 4.2629707 6.5490451 1.2524580 0.9944771 2.7998162 2.6797888 1.8238730
## 40 3.6188212 4.7674858 1.8177965 1.5454596 1.3787350 2.2614463 2.1436604
## 41 5.5453578 8.8755460 8.8345751 7.4227195 7.4438254 6.3880372 6.9902133
## 42 4.3351568 4.5194745 2.1814229 2.5660259 1.9848673 3.1708890 3.1723947
## 43 5.0734698 6.8008188 0.3852067 1.8674945 3.2719187 3.5074378 2.7605086
## 44 1.3557661 3.2932668 4.3679827 2.9188898 1.3143869 1.4892298 2.5318465
## 45 3.2188648 7.2114179 7.1891105 5.3795659 5.3845755 4.1158050 4.6620305
## 46 7.4912021 9.2265214 10.0194440 9.1694617 8.7679900 8.2733921 9.0518598
## 47 3.7219243 5.5879181 1.4170336 0.7416318 1.8874923 2.1520749 1.5588624
## 48 0.6708585 4.7782786 5.2964164 3.4490928 2.8156402 1.7938648 2.6957527
## 49 2.3585435 2.5727940 4.2635427 3.2281694 1.2640097 2.2392948 3.0959459
## 50 4.7779657 5.6504194 1.0475027 2.1814512 2.5849467 3.3687734 3.0154298
## 51 0.6485911 4.5797529 4.6626174 2.8388259 2.1928861 1.1548615 2.1268932
## 52 5.0193296 7.0934402 0.9264058 1.7907746 3.4476688 3.4555969 2.6327539
## 53 5.2097839 6.7603677 0.2211267 2.0552592 3.3197868 3.6572211 2.9567130
## 54 1.0631452 4.5098709 6.0796160 4.2908389 3.3671566 2.5906423 3.5722033
## 55 3.4776750 5.6651004 1.7113480 0.3409881 1.8831140 1.8771577 1.1740259
## 56 1.3782552 5.4897395 4.7550694 2.8384289 2.8118543 1.4665489 2.0286086
## 57 6.6794979 3.3786848 6.3519408 6.6106242 5.0401038 6.4110638 6.9259456
## 58 2.8146040 3.3488926 3.2818561 2.4969667 0.6766649 2.0602989 2.6162811
## 59 4.4495726 4.8157987 1.9683088 2.5602194 2.2101424 3.2667854 3.2517859
## 60 5.2727141 7.1166562 0.6823121 2.0504984 3.5612746 3.7089344 2.9242052
## 61 4.3715252 4.7114060 1.9728384 2.4417537 2.0338110 3.1519614 3.0915442
## 62 4.7304182 6.6571364 0.6441059 1.5189829 3.0402837 3.1643589 2.4111182
## 63 4.4307881 6.6090357 1.0681932 1.1586392 2.8905567 2.8470230 2.0083745
## 64 2.2720499 3.4202483 3.4701698 2.4169614 0.5800128 1.6438920 2.4069989
## 65 3.5185131 6.0259939 1.8317870 0.2693438 2.2239067 1.9259278 1.0811190
## 66 3.7346071 5.7648363 1.4023782 0.5971195 2.0288877 2.1486042 1.4803631
## 67 3.8006366 5.7681309 1.3089755 0.6970560 2.0549206 2.2236845 1.5845504
## 68 6.1799221 3.1308058 5.8055283 6.0306686 4.4722390 5.8526444 6.3472756
## 69 5.1150608 6.7018095 0.2025286 1.9853625 3.2501388 3.5716551 2.8939404
## 70 4.7038842 6.2394386 0.3649567 1.6312292 2.7667503 3.1614745 2.5341070
## 71 4.4100077 5.7669887 0.8483081 1.5160094 2.3378159 2.8921747 2.3589763
## 72 6.8337325 9.0225164 8.5061122 7.8350408 7.7926091 7.2495333 7.8370074
## 73 4.1789843 6.1760695 1.0193677 0.9424065 2.4829641 2.5922094 1.8426160
## 74 2.5450346 5.0886733 2.5348292 0.8351057 1.3316155 0.9748134 0.8730853
## 75 5.3231981 5.9910118 1.1559939 2.6542827 3.0945028 3.9090289 3.5033096
## 76 5.1436679 7.0386123 0.6900001 1.8951439 3.4480316 3.5695593 2.7604066
## 77 3.7613679 5.6264315 1.3075928 0.8045062 1.9454795 2.2088297 1.6673808
## 78 0.7033130 3.7086295 4.9533211 3.2956608 2.0500229 1.6311466 2.7064788
## 79 2.8259691 3.9039974 2.7909402 1.9524287 0.4884597 1.7732593 2.1618558
## 80 1.9466943 5.7731262 4.1006093 2.4065637 2.7533372 1.5067882 1.9460719
## 81 2.7341413 4.5864721 2.4273939 1.2064766 0.8023782 1.3315395 1.4406122
## 82 5.4161321 5.0765253 2.4725093 3.4658214 3.0684914 4.2552913 4.1636176
## 8 9 10 11 12 13 14
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9 1.8715374
## 10 1.6894393 1.5475513
## 11 2.2601081 2.4419051 0.9630843
## 12 3.3168427 1.5055231 2.4130140 3.0645864
## 13 2.6539570 1.9859162 0.9914578 1.0806285 2.1603825
## 14 2.3866537 2.1167878 0.7636651 0.5915512 2.5649001 0.5054506
## 15 5.2236374 3.7738764 5.3006017 6.1374553 3.4057888 5.4382843 5.7384606
## 16 2.7277968 1.1309728 1.6085622 2.2635187 0.8229107 1.3839683 1.7590506
## 17 1.3413550 1.7944254 0.5114671 0.9975842 2.8529756 1.4431422 1.0888859
## 18 2.9599606 1.4921039 1.6888065 2.1826095 0.9557690 1.2296855 1.6630261
## 19 5.3948321 4.1242331 5.6709074 6.5326879 3.9637269 5.9075490 6.1688988
## 20 1.3688296 2.1267481 2.7710688 3.5275555 3.5695219 3.6629108 3.5229558
## 21 1.6777075 3.4752134 3.0830634 3.4014351 4.9524022 4.0578997 3.6852328
## 22 1.2831951 0.8338838 1.8013781 2.6666003 2.3003862 2.5283534 2.5071655
## 23 2.8231553 1.5277201 1.4324444 1.8842057 1.2572416 0.9121824 1.3510103
## 24 1.5912844 1.4070604 0.1540120 1.0925743 2.3355829 1.0775246 0.8944632
## 25 1.9721402 1.9855364 0.4594277 0.5267658 2.7037900 0.8826153 0.4528363
## 26 1.3975954 1.7218251 0.4255428 0.9312277 2.7337914 1.3325306 0.9952871
## 27 2.9783127 3.1205177 4.2032575 5.0402071 4.2567311 4.9853903 4.9457084
## 28 1.5280086 0.6006052 1.1020666 2.0546112 1.9232966 1.7464941 1.7726171
## 29 3.5542085 3.1372494 1.9434275 1.3910640 3.1109956 1.1533405 1.1850557
## 30 1.8871439 3.1251438 3.3526104 4.0003841 4.6076825 4.3222776 4.0869724
## 31 0.8947127 1.5486277 1.0030070 1.7468957 2.8785745 1.9789134 1.7382926
## 32 3.1711129 2.9194690 1.6005924 0.9832725 3.0963110 0.9823233 0.8494397
## 33 3.9018200 2.2849268 3.7873793 4.6250203 1.9554855 3.9154513 4.2131190
## 34 3.3890050 2.0096018 1.9483511 2.2632054 1.2795647 1.2192727 1.7153423
## 35 2.8354972 4.5665992 4.3928058 4.7164549 6.0659336 5.3734126 5.0119302
## 36 2.1148226 1.9501487 0.4858109 0.6356267 2.5750055 0.6998179 0.3226963
## 37 0.8308922 2.5023369 1.9775429 2.4007392 3.9298613 2.9584093 2.6102810
## 38 3.0044673 1.2109945 2.6501745 3.4792755 1.0398734 2.7724881 3.0600699
## 39 2.4116873 2.4048616 0.9139921 0.4092786 2.9467851 0.8662118 0.3959705
## 40 1.6654716 0.5058727 1.0443386 1.9582698 1.7105787 1.5724468 1.6448330
## 41 6.6741656 8.3431704 7.8079517 7.5573480 9.5503441 8.5026310 8.0771459
## 42 2.5313098 0.6681995 1.9952506 2.8194407 0.9010893 2.1398337 2.4044057
## 43 3.0982004 2.4332258 1.4364554 1.2488769 2.3976467 0.4802474 0.7774635
## 44 1.5066686 2.6377424 3.0657103 3.7486019 4.1105574 4.0108473 3.8126184
## 45 4.6656294 6.5337703 5.9155816 5.8360561 7.9479539 6.7729032 6.3135361
## 46 8.2190257 9.3269679 9.2793880 9.1485973 10.1849048 9.8149842 9.5403195
## 47 1.7554738 1.4787173 0.2368566 1.1343442 2.3372404 1.0069305 0.8550273
## 48 2.3704330 4.1222995 3.8920726 4.2253127 5.6208744 4.8733754 4.5112323
## 49 1.9461238 2.2192895 3.1626915 3.9869403 3.5350410 3.9809230 3.9102787
## 50 2.7748111 1.3466909 1.5186609 2.0538649 1.0301973 1.1418154 1.5450737
## 51 1.7335723 3.4822462 3.2561925 3.6446072 4.9785674 4.2424532 3.8967316
## 52 3.1227059 2.7876425 1.5350113 0.9752081 2.9197321 0.8392304 0.7713462
## 53 3.2111229 2.3803606 1.5630281 1.4856405 2.1921674 0.5724516 0.9846577
## 54 3.0701170 4.7077671 4.6826036 5.0704832 6.2052242 5.6693000 5.3338925
## 55 1.5852157 1.7611727 0.3919920 1.0300864 2.7349918 1.2724152 0.9644903
## 56 2.1426151 3.9694167 3.3805708 3.5453701 5.4147136 4.3175321 3.9002701
## 57 5.8764541 4.6087133 6.1547685 7.0157634 4.4016999 6.3765385 6.6461499
## 58 1.5331303 1.2119879 2.2909875 3.1691211 2.5850534 3.0256770 3.0115121
## 59 2.5877024 0.9088456 1.9454543 2.6413222 0.8453543 1.9743843 2.2505037
## 60 3.3256840 2.7570730 1.6884280 1.3043570 2.6886492 0.7952579 0.9602350
## 61 2.5131372 0.6753660 1.8477624 2.6461857 0.8304897 1.9396372 2.2180572
## 62 2.7824415 2.3412894 1.1476334 0.8536118 2.5426920 0.4116922 0.4152924
## 63 2.5478612 2.3983796 0.9757513 0.5340583 2.8359625 0.7078346 0.3044629
## 64 1.1493745 1.5913393 2.3320770 3.1125206 3.0286516 3.1702525 3.0669255
## 65 1.7376954 2.1935335 0.7086425 0.7420788 3.1156358 1.3892822 0.9440432
## 66 1.7893815 1.6843709 0.1868845 0.9120538 2.5115014 0.9662670 0.7030571
## 67 1.8369387 1.6380844 0.1612275 0.9104000 2.4213027 0.8776734 0.6478407
## 68 5.3149094 4.0324192 5.5787909 6.4475196 3.8788187 5.8171186 6.0791889
## 69 3.1174710 2.3274612 1.4874632 1.3892480 2.1902532 0.5119309 0.9047189
## 70 2.6937693 1.8667038 1.0646531 1.2734546 1.9486859 0.2168192 0.7030764
## 71 2.4008890 1.4056734 0.8938187 1.4937815 1.6906136 0.6511706 0.9547933
## 72 7.1430121 8.1783335 7.9240834 7.6444413 8.9229702 8.3335778 8.0578339
## 73 2.2368382 1.9593490 0.5726067 0.7194465 2.5032189 0.5746269 0.2681967
## 74 0.6899723 1.8585685 1.1339344 1.6443880 3.1770208 2.1158943 1.7914868
## 75 3.3230204 1.8047449 2.0030937 2.4344695 0.9435564 1.4161288 1.8923399
## 76 3.2058523 2.6895618 1.5583085 1.1813387 2.7042174 0.7053209 0.8233128
## 77 1.7680805 1.4682659 0.1406546 1.0191015 2.2783979 0.9016727 0.7431980
## 78 1.9591462 3.4047205 3.5808462 4.1402281 4.8992824 4.5632966 4.2952927
## 79 1.1736459 0.8998375 1.7357942 2.6106420 2.3944157 2.5066474 2.4628175
## 80 1.8381357 3.6115217 2.8639561 2.8095494 4.9225950 3.6979900 3.2598691
## 81 0.7788931 1.2080748 1.1370914 1.9543138 2.6292162 2.0624949 1.8957066
## 82 3.6118546 1.7567974 2.8349953 3.5201798 0.4653813 2.6211036 3.0231950
## 15 16 17 18 19 20 21
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16 4.0681380
## 17 5.5633527 2.0721477
## 18 4.3236191 0.4015724 2.1734995
## 19 0.7066463 4.5645311 5.8849022 4.8475045
## 20 4.4748826 3.2423553 2.5682588 3.5746358 4.4925655
## 21 6.5349556 4.3425377 2.6174914 4.5720687 6.5807715 2.0918878
## 22 3.9695864 1.9419528 1.8145415 2.2745571 4.1893411 1.3072343 2.8070319
## 23 4.5980724 0.5554792 1.9285321 0.3189111 5.1051129 3.5435671 4.4007585
## 24 5.1680827 1.5453163 0.5305230 1.6547513 5.5309863 2.6384302 3.0351138
## 25 5.7140434 1.8861449 0.6469677 1.8780345 6.1008284 3.1559805 3.2329012
## 26 5.4858924 1.9539541 0.1789761 2.0404278 5.8195458 2.6080810 2.7424880
## 27 3.8048131 4.2149592 4.0945753 4.5867066 3.5829001 1.6177661 3.4358131
## 28 4.3168776 1.3348017 1.2993888 1.6503196 4.6431023 2.0514774 3.0716458
## 29 6.4869325 2.4310633 2.2392883 2.1679354 6.9914119 4.7056003 4.7521648
## 30 5.5410827 4.1717083 3.0327874 4.4949736 5.4991676 1.2857100 1.4391129
## 31 5.2011770 2.1885552 0.7546803 2.4115304 5.4588489 1.9228375 2.2135804
## 32 6.4140913 2.3532003 1.8473053 2.1449918 6.8864498 4.3587979 4.3273650
## 33 1.5313492 2.5533883 4.0780037 2.8347447 2.0222907 3.4123759 5.3474726
## 34 4.6828970 0.8993314 2.4505544 0.5383502 5.2422389 4.0797715 4.9590132
## 35 7.1368419 5.5360605 3.9373012 5.7895091 7.0560498 2.7354218 1.3579810
## 36 5.6449143 1.7538304 0.8044823 1.7316621 6.0490594 3.2494246 3.4018832
## 37 5.8946913 3.2720850 1.5329168 3.4898552 6.0457779 1.7985639 1.1208975
## 38 2.6827956 1.4378547 2.9726899 1.7599746 3.1381569 2.8695025 4.5633462
## 39 6.0842822 2.1340651 1.0759030 2.0524642 6.4975522 3.6221411 3.5582863
## 40 4.2711363 1.0934976 1.3165796 1.3922304 4.6285956 2.2373372 3.2671002
## 41 10.8951272 9.0072829 7.3539541 9.0812360 10.8499874 7.0719430 5.7972159
## 42 3.3387456 0.8861017 2.3372405 1.2514550 3.7737243 2.6723290 4.1403824
## 43 5.7566423 1.6948823 1.8451178 1.4497882 6.2560315 4.1386857 4.4556685
## 44 4.9943915 3.7307974 2.7843887 4.0521948 4.9694431 0.5822614 1.6795525
## 45 9.4344943 7.3114548 5.4065657 7.4642411 9.3954685 5.0433564 3.2421439
## 46 10.7744073 9.9185338 8.9666532 9.9645000 10.6781400 8.3260899 8.0264864
## 47 5.2160836 1.5340972 0.6523845 1.6440861 5.5895860 2.7633736 3.1337837
## 48 6.8595126 5.0662755 3.4360135 5.3155106 6.8221949 2.4009737 0.8439767
## 49 3.9668948 3.3474499 3.0382863 3.7072809 3.9308645 0.6360613 2.6814443
## 50 4.3432654 0.3290108 1.9981592 0.1863680 4.8474781 3.4089556 4.3857895
## 51 6.3623779 4.4148636 2.8133039 4.6658596 6.3728879 1.8899207 0.3767082
## 52 6.2444639 2.1883970 1.8175323 1.9650306 6.7225036 4.2866634 4.3454769
## 53 5.5766688 1.5388767 2.0071892 1.2557784 6.0938738 4.1886603 4.6244075
## 54 7.0317094 5.7260388 4.2494416 5.9995079 6.9036176 2.7462395 1.7324801
## 55 5.5255858 1.9365427 0.3692942 2.0411761 5.8682147 2.7151922 2.8240727
## 56 7.1367090 4.7594574 2.8864571 4.9565876 7.1928157 2.7043258 0.6190487
## 57 1.0291794 5.0248044 6.3721390 5.3004107 0.4885965 4.9486638 7.0377546
## 58 3.7475867 2.3417880 2.2763200 2.7007037 3.8928782 1.0099327 2.8352065
## 59 3.5501952 0.7909428 2.3000272 1.0281229 4.0089021 2.8856625 4.2530182
## 60 6.0622045 2.0136155 2.0478805 1.7423750 6.5687323 4.4170845 4.6318881
## 61 3.5214010 0.6831204 2.2155080 1.0493846 3.9692056 2.7612031 4.1376420
## 62 5.8291652 1.7804226 1.5017015 1.5963755 6.2956183 3.8911878 4.0967091
## 63 6.0287493 2.0330237 1.2150053 1.9226377 6.4598573 3.7277726 3.7413435
## 64 4.2204986 2.6972144 2.1933611 3.0193181 4.3208546 0.5923332 2.3530433
## 65 5.9662341 2.3034936 0.4753242 2.3482975 6.3076637 2.9938427 2.7976218
## 66 5.4297740 1.6980478 0.5438546 1.7656686 5.8037522 2.8836146 3.1115908
## 67 5.3716481 1.6056932 0.6126384 1.6633557 5.7544949 2.9139377 3.1946300
## 68 0.6652902 4.4743526 5.7950622 4.7621830 0.1455094 4.4161392 6.5011185
## 69 5.5615637 1.5216874 1.9223624 1.2416345 6.0712961 4.1102771 4.5389591
## 70 5.2464189 1.1832168 1.5461531 1.0159223 5.7260018 3.6391291 4.1469334
## 71 4.8612192 0.8751140 1.4036651 0.8977469 5.3153784 3.2242777 3.8943748
## 72 10.0621226 8.5994691 7.6412245 8.5807922 10.0969687 7.5425428 7.1622562
## 73 5.6189084 1.6832767 0.9397054 1.6441254 6.0363116 3.3418189 3.5358878
## 74 5.5004036 2.4738278 0.7050186 2.6536952 5.7423024 1.9820114 1.9632487
## 75 4.3473855 0.6764893 2.4999786 0.3695283 4.9064699 3.9120798 4.9254770
## 76 6.0606477 1.9968415 1.9100785 1.7556170 6.5557720 4.3078497 4.4871823
## 77 5.2031395 1.4712197 0.6452644 1.5483181 5.5851529 2.8059695 3.1984493
## 78 5.7936584 4.4589955 3.2158264 4.7605367 5.7267679 1.4228308 1.2656785
## 79 4.1012490 1.9936772 1.7229193 2.3265482 4.3148165 1.2532983 2.6750102
## 80 6.9435455 4.2521877 2.3694926 4.3709168 7.0768194 2.8123565 1.4539826
## 81 4.8079260 2.0123228 0.9972522 2.2704020 5.0571002 1.6367627 2.3358995
## 82 2.9913056 1.2692876 3.2586414 1.4188566 3.5761998 3.7079720 5.2319588
## 22 23 24 25 26 27 28
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23 2.2668041
## 24 1.6490683 1.4183029
## 25 2.2399963 1.5849726 0.6050894
## 26 1.7874213 1.7976373 0.4378063 0.5780352
## 27 2.4699061 4.6474939 4.0589676 4.6293586 4.1174108
## 28 0.8965307 1.5689294 0.9638591 1.5605760 1.2662275 3.2644751
## 29 3.6430761 1.8896229 2.0721037 1.5948951 2.1583799 6.1004649 2.8741439
## 30 2.3795261 4.4021575 3.2574606 3.6630447 3.1395261 2.1983858 2.8535790
## 31 1.3363560 2.2294783 0.9229978 1.3325619 0.8561149 3.4311168 1.0002029
## 32 3.3544626 1.8415277 1.7389157 1.2128407 1.7781380 5.7947045 2.6016730
## 33 2.6203067 3.0938464 3.6594820 4.1954808 3.9968937 3.2786159 2.8345860
## 34 2.7889957 0.5659425 1.9532688 2.0324947 2.3214959 5.1119630 2.1015171
## 35 3.7986383 5.6482894 4.3309978 4.5619288 4.0484304 3.5845502 4.2506450
## 36 2.2787223 1.4299139 0.6328936 0.2111510 0.7338715 4.6884145 1.5423911
## 37 1.9790873 3.3049514 1.9298791 2.1590965 1.6664617 3.3722890 2.0317036
## 38 1.7706025 1.9870676 2.5280152 3.0487580 2.8842276 3.2950854 1.7667422
## 39 2.7104928 1.7383975 1.0645645 0.4767338 1.0326429 5.1006435 1.9948205
## 40 1.0014253 1.3207256 0.9055248 1.4873539 1.2436584 3.4281604 0.3014466
## 41 7.7184239 8.9223796 7.7892727 7.7517624 7.3859334 7.9271683 8.1241803
## 42 1.4203570 1.4203911 1.8765658 2.3881810 2.2427311 3.4230621 1.1961972
## 43 3.0008112 1.1593317 1.5368183 1.2259737 1.7395033 5.4605465 2.2220942
## 44 1.8244850 3.9917585 2.9486143 3.4104455 2.8519564 1.7789420 2.4756386
## 45 5.8578379 7.2667831 5.9021941 5.9042596 5.5070389 6.0347651 6.1649866
## 46 8.7885415 9.9208337 9.2214481 9.3060675 8.9238130 8.7438974 9.3710547
## 47 1.7768936 1.3927428 0.2672690 0.6087507 0.6144772 4.1604191 1.0012870
## 48 3.3799683 5.1654964 3.8335263 4.0599451 3.5523511 3.4346913 3.7774708
## 49 1.4816791 3.7269318 3.0203923 3.5811943 3.0626047 1.0573835 2.2804852
## 50 2.1138026 0.2640729 1.4782087 1.7293273 1.8656899 4.4555444 1.4780861
## 51 2.7605064 4.5164678 3.1928289 3.4462467 2.9287078 3.1346329 3.1247917
## 52 3.2467111 1.6671596 1.6637955 1.1760920 1.7299131 5.7012885 2.5045391
## 53 3.0045130 0.9910616 1.6439625 1.4181057 1.8921820 5.4560555 2.2306803
## 54 3.9108217 5.8797806 4.6087320 4.8861399 4.3541858 3.3717698 4.4367603
## 55 1.8951180 1.7824034 0.4588698 0.5654609 0.4404944 4.1932065 1.2293377
## 56 3.3473427 4.7591791 3.3565706 3.4545428 3.0179877 4.0380678 3.5314961
## 57 4.6757813 5.5635820 6.0155632 6.5838105 6.3068438 3.9631103 5.1267488
## 58 0.5268927 2.7212461 2.1414240 2.7334852 2.2696587 1.9617351 1.3245058
## 59 1.6080246 1.2214629 1.8365951 2.2826058 2.1721091 3.7200744 1.3956934
## 60 3.3021567 1.4672311 1.7998397 1.4083876 1.9455864 5.7673023 2.5405384
## 61 1.4787520 1.2114408 1.7365859 2.2240812 2.1134918 3.5873666 1.1457296
## 62 2.8173139 1.2865479 1.2644191 0.8667872 1.3995324 5.2760663 2.0662386
## 63 2.7628085 1.6059642 1.1214483 0.5785569 1.1539522 5.1789204 2.0215091
## 64 0.7591621 2.9990542 2.1893854 2.7337756 2.2013041 1.9460655 1.5768129
## 65 2.2752180 2.0659918 0.8166262 0.5246579 0.5564550 4.5316745 1.6837455
## 66 1.9441543 1.4941788 0.3249317 0.3870984 0.5050876 4.3219739 1.2136815
## 67 1.9357403 1.3906257 0.3000075 0.3878496 0.5448531 4.3366962 1.1955446
## 68 4.1042312 5.0176087 5.4394717 6.0103277 5.7319153 3.5210823 4.5455597
## 69 2.9320203 0.9705252 1.5667093 1.3368551 1.8000728 5.3913827 2.1792768
## 70 2.4623383 0.6984203 1.1250337 1.0379896 1.4284740 4.9143860 1.6811316
## 71 2.0299315 0.6292340 0.8973325 1.0883902 1.3040452 4.4485758 1.2054214
## 72 7.7559875 8.5129941 7.8883839 7.8790868 7.5817837 8.2736249 8.1934939
## 73 2.3378109 1.3359751 0.7105924 0.3576825 0.8678572 4.7573000 1.5706038
## 74 1.5554070 2.4573981 1.0776573 1.3517353 0.8091211 3.5685585 1.3733365
## 75 2.6095030 0.5782937 1.9824052 2.1563640 2.3707765 4.8696294 1.9780314
## 76 3.2144107 1.4642739 1.6769425 1.2661696 1.8175441 5.6735692 2.4388632
## 77 1.7832955 1.2933437 0.1776696 0.5224245 0.5452510 4.2080040 1.0554769
## 78 2.6061429 4.6661030 3.4857896 3.8619946 3.3101069 2.3188840 3.1642832
## 79 0.1820254 2.2982101 1.5865510 2.1750750 1.7120187 2.4878884 0.8436203
## 80 3.0863015 4.1693128 2.8493954 2.8574638 2.4418348 4.3078865 3.2376559
## 81 0.8953800 2.1386352 1.0092581 1.5342405 1.0249121 3.1074738 0.7641781
## 82 2.4981258 1.7202145 2.7487262 3.1468539 3.1457067 4.2182040 2.2309265
## 29 30 31 32 33 34 35
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23
## 24
## 25
## 26
## 27
## 28
## 29
## 30 5.2464432
## 31 2.9049393 2.3547022
## 32 0.4310366 4.8559143 2.5307257
## 33 4.9822953 4.5259671 3.7672365 4.8945758
## 34 1.9054486 4.9485809 2.7786371 1.9832039 3.2287404
## 35 6.0857260 1.8518346 3.4966415 5.6618071 6.1475659 6.2129936
## 36 1.4789387 3.7770825 1.4280781 1.1217195 4.1196376 1.8586057 4.7334403
## 37 3.7156642 1.7047847 1.1062838 3.3001444 4.5712919 3.8577242 2.4487838
## 38 3.8626028 3.9695479 2.7450112 3.7533234 1.1536957 2.2115836 5.5345369
## 39 1.2015403 4.0712936 1.7643685 0.7887151 4.5579481 2.0852441 4.8979090
## 40 2.7160549 3.1033650 1.1778986 2.4666188 2.7699362 1.8617168 4.4479540
## 41 8.7518391 6.8242403 7.3958214 8.4035590 9.9622872 9.4065012 5.2031086
## 42 3.2546768 3.7206146 2.1841243 3.1189696 1.8126670 1.7560624 5.2076378
## 43 0.7379647 4.7818804 2.4301752 0.7258220 4.2475199 1.2577645 5.7798676
## 44 4.9957474 0.7910369 2.1346327 4.6231219 3.9762316 4.5404102 2.1811981
## 45 7.1425111 4.3317802 5.2698595 6.7285485 8.3634196 7.8034961 2.5567522
## 46 10.1966956 8.6328051 9.0201796 9.9355977 10.2419252 10.3196011 7.5495069
## 47 1.9960094 3.3268997 0.9864374 1.6698732 3.6987239 1.9022930 4.4459528
## 48 5.5866232 1.5303377 2.9947120 5.1625489 5.7992099 5.7286435 0.5191593
## 49 5.0764989 1.6417529 2.3840530 4.7580089 3.0391962 4.2279321 3.1818762
## 50 2.1465999 4.3194829 2.2281537 2.0871311 2.8396740 0.6808479 5.6043516
## 51 4.9966706 1.1736305 2.3450000 4.5771170 5.2346608 5.0793377 1.1531761
## 52 0.4379922 4.8380075 2.4983567 0.2162702 4.7299764 1.8063711 5.6733486
## 53 0.9197911 4.8851401 2.5482337 0.9859669 4.0793148 1.0044882 5.9391881
## 54 6.4371571 1.8639394 3.7580499 6.0179774 6.1311588 6.4449044 0.4930552
## 55 2.0990799 3.1507880 0.8193239 1.7210056 4.0222452 2.2831037 4.1584689
## 56 4.8858441 2.0070947 2.6045617 4.4553432 5.9232486 5.3070289 1.3959865
## 57 7.4521989 5.9292055 5.9433094 7.3557281 2.4738410 5.6811341 7.4767101
## 58 4.1485150 2.1466393 1.7001922 3.8592335 2.5142018 3.2199985 3.6894141
## 59 3.0361681 3.9800226 2.2975355 2.9238462 2.0663582 1.5454302 5.3331071
## 60 0.4310625 5.0360552 2.6819653 0.5574689 4.5607265 1.5009316 5.9576586
## 61 3.0484356 3.7868437 2.1232672 2.9190165 1.9951443 1.5612943 5.2384034
## 62 0.8267930 4.4919163 2.1394344 0.5951202 4.3093191 1.5249794 5.4213158
## 63 1.0344899 4.2163182 1.8869612 0.6437779 4.5011460 1.9188511 5.0797205
## 64 4.2370552 1.7963170 1.6187010 3.9112536 3.0419404 3.5320379 3.1676195
## 65 1.9687805 3.3376484 1.1213367 1.5513628 4.4636113 2.5319436 4.1425952
## 66 1.8615104 3.4062335 1.0526794 1.5083628 3.9123576 1.9851964 4.4372279
## 67 1.8135488 3.4725087 1.1181464 1.4735466 3.8517056 1.8837475 4.5143483
## 68 6.9034911 5.4135677 5.3636484 6.7973183 1.9311421 5.1563389 6.9902259
## 69 0.9304557 4.8177838 2.4803907 0.9589319 4.0627644 1.0387988 5.8479186
## 70 1.2932937 4.3459001 2.0254555 1.1711336 3.7266086 1.0172892 5.4508028
## 71 1.7827653 3.9502398 1.7001970 1.6122551 3.3311105 1.1106134 5.1780956
## 72 8.5606988 7.9537430 7.8406295 8.3370623 9.3207364 8.8674739 7.0128894
## 73 1.3877270 3.8823418 1.5296708 1.0532989 4.0904475 1.7425826 4.8684673
## 74 2.9409707 2.3652808 0.4829161 2.5430587 4.0838517 3.0101867 3.2600338
## 75 2.2140498 4.8290485 2.7485178 2.2586061 2.8939134 0.3360106 6.1492226
## 76 0.4503384 4.8952779 2.5418022 0.4465982 4.5496163 1.5490662 5.8192463
## 77 1.9097490 3.4276483 1.0873008 1.5886075 3.6856930 1.8133032 4.5005632
## 78 5.4544630 0.6502675 2.6164887 5.0548163 4.8151180 5.2251487 1.3725896
## 79 3.6128448 2.2561788 1.1933327 3.3118863 2.7496551 2.8289207 3.6927975
## 80 4.1749409 2.7229341 2.3808848 3.7628553 5.6650968 4.6984508 2.3162689
## 81 3.0787078 2.3098243 0.4573054 2.7310935 3.3924519 2.7001536 3.5366263
## 82 3.5631183 4.7762378 3.2167912 3.5570039 1.5948974 1.7007164 6.2947836
## 36 37 38 39 40 41 42
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## 37 2.3139225
## 38 2.9681288 3.6621441
## 39 0.4573684 2.5151018 3.4046634
## 40 1.4560874 2.2211751 1.6606674 1.9120673
## 41 7.9613133 6.5409203 9.2969973 7.9222248 8.1596262
## 42 2.3084802 3.1683921 0.6612870 2.7458358 1.0399816 8.9023956
## 43 1.0588561 3.3693402 3.1251642 1.0254746 2.0412993 8.7304670 2.5189564
## 44 3.5245079 1.6903900 3.4376900 3.8572563 2.6819509 6.7358252 3.2147616
## 45 6.1070857 4.2099959 7.6186190 6.0981632 6.3012008 3.2727402 7.1856212
## 46 9.4846396 8.4952216 9.8894560 9.5453292 9.3147163 4.0906742 9.6839733
## 47 0.5723893 2.0158274 2.5634536 1.0087776 0.9750633 7.9914925 1.9150036
## 48 4.2290466 1.9361947 5.1295681 4.3947351 3.9780352 5.4487356 4.7730090
## 49 3.6481357 2.4033099 2.6963119 4.0526573 2.4545023 7.5345922 2.6479977
## 50 1.5908034 3.3043585 1.7343014 1.9334392 1.2164193 8.9222169 1.1777999
## 51 3.6091169 1.3104670 4.5158386 3.8002073 3.3264213 5.8177139 4.1378345
## 52 1.0746969 3.3061435 3.5931411 0.8096986 2.3494836 8.4112720 2.9634904
## 53 1.2429176 3.5287061 2.9760080 1.2747321 2.0303505 8.9166278 2.3948783
## 54 5.0506037 2.7637139 5.6025026 5.2457283 4.6389247 5.3464682 5.3282080
## 55 0.6432028 1.7156856 2.9031978 0.9606131 1.2629626 7.6971382 2.2633774
## 56 3.6349505 1.5064346 5.0968717 3.7189765 3.7125741 5.4594857 4.6374344
## 57 6.5294073 6.5218832 3.6052418 6.9771855 5.1125656 11.2516054 4.2469845
## 58 2.7713450 2.1575585 1.8660626 3.2029323 1.4695295 7.8120385 1.6858425
## 59 2.2107358 3.2749727 0.9944887 2.6175071 1.1473426 8.7228172 0.5481801
## 60 1.2684405 3.5671051 3.4450624 1.1160359 2.3598517 8.7369271 2.8432254
## 61 2.1368478 3.1381432 0.8431333 2.5673366 0.9525536 8.8727259 0.2100634
## 62 0.7276337 3.0252340 3.1660440 0.6548867 1.9051740 8.3579725 2.5291509
## 63 0.4922851 2.6867418 3.3477613 0.2026496 1.9172460 8.0865578 2.6932651
## 64 2.8151643 1.7982502 2.3885297 3.2090531 1.7197577 7.2249472 2.1426296
## 65 0.6905090 1.7511241 3.3383352 0.7675096 1.6955815 7.4403053 2.6898795
## 66 0.3912216 2.0033617 2.7733383 0.8021484 1.1788004 7.8727490 2.1197353
## 67 0.3586138 2.0867232 2.7082837 0.8005308 1.1350272 7.9192852 2.0516032
## 68 5.9566486 5.9573264 3.0461760 6.4059990 4.5356353 10.8333438 3.6825143
## 69 1.1729829 3.4495499 2.9530966 1.2106056 1.9717688 8.7838006 2.3623471
## 70 0.8569570 3.0418130 2.5898141 1.0748664 1.4875392 8.6229965 1.9681820
## 71 0.9240619 2.7802774 2.1844851 1.2983031 1.0312174 8.6220570 1.5501986
## 72 8.0515363 7.4368125 8.8087509 8.0514201 8.0982646 3.8543448 8.5192947
## 73 0.1479930 2.4422701 2.9374323 0.4785835 1.4735767 8.1045497 2.2806232
## 74 1.5048734 0.8830378 3.0665900 1.7652651 1.4891791 6.9402171 2.4982968
## 75 1.9931268 3.8360112 1.8905443 2.2739113 1.7344390 9.4274251 1.4733419
## 76 1.1220699 3.4203205 3.4229836 0.9572266 2.2742211 8.6686921 2.8093524
## 77 0.5007085 2.0917253 2.5431417 0.9508780 0.9685212 7.9113240 1.8853198
## 78 4.0003136 1.8270236 4.2680477 4.2713846 3.3792603 6.2250187 4.0111550
## 79 2.2182308 1.8297209 1.8893273 2.6458388 0.9965956 7.6869237 1.5173058
## 80 3.0647595 1.5893649 4.7578497 3.1011005 3.3170115 5.0682015 4.2428976
## 81 1.6152280 1.3061027 2.3994335 2.0018037 0.9313241 7.4107404 1.8699566
## 82 3.0212249 4.2424656 0.9234185 3.4019141 2.0483423 9.8485615 1.0934069
## 43 44 45 46 47 48 49
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## 44 4.4804342
## 45 7.0688858 4.5653623
## 46 10.0358646 8.2048718 6.7216849
## 47 1.4615617 3.0658009 6.0335111 9.4794316
## 48 5.2793459 1.8679007 2.8021063 7.7520530 3.9412081
## 49 4.4587331 1.0394672 5.5653890 8.5789815 3.1298829 2.9019663
## 50 1.4164626 3.8797001 7.2826836 9.8472446 1.4760651 5.1297911 3.5587359
## 51 4.6583143 1.4174758 3.3024835 7.9396183 3.2996687 0.6548710 2.4485248
## 52 0.5607540 4.5727245 6.7797123 9.8573621 1.6114271 5.1761420 4.6706552
## 53 0.2750067 4.5585067 7.2820531 10.1287074 1.5718074 5.4405715 4.4743359
## 54 6.0917765 2.1799567 2.8198346 7.5405965 4.7264473 0.9119477 3.1120658
## 55 1.6805195 2.9471168 5.6750894 9.3345279 0.4074704 3.6488158 3.1466535
## 56 4.6769300 2.2924798 2.7726789 7.9680726 3.4478235 0.9819163 3.2984732
## 57 6.7176702 5.4123563 9.8258491 10.9813788 6.0713254 7.2569768 4.3750152
## 58 3.4995522 1.5721359 5.8968996 8.8449211 2.2468495 3.3070174 1.0080288
## 59 2.3157304 3.4233523 7.1766582 9.3930868 1.9224925 4.9009320 2.9186366
## 60 0.3424921 4.7423286 7.1361676 10.0634994 1.7364075 5.4593204 4.7572625
## 61 2.3124828 3.2914995 7.1653734 9.6863610 1.7716615 4.7945056 2.7787223
## 62 0.3965351 4.2024377 6.6737113 9.7466342 1.2135547 4.9222109 4.2528797
## 63 0.8248138 3.9855701 6.2945166 9.6513049 1.0541025 4.5764404 4.1370039
## 64 3.6434943 1.1272615 5.3316642 8.3504188 2.3345426 2.7951271 0.9096382
## 65 1.7079828 3.1666407 5.4557400 9.1927509 0.8187160 3.6358994 3.4770222
## 66 1.3901097 3.1587420 5.9352430 9.4100523 0.2342579 3.9312091 3.2814025
## 67 1.3137654 3.2053242 6.0145624 9.4122664 0.2293451 4.0104151 3.2993346
## 68 6.1672668 4.8941141 9.3406298 10.7155613 5.4931164 6.7504239 3.8547447
## 69 0.2631142 4.4786738 7.1766978 9.9821806 1.5154945 5.3521831 4.4047587
## 70 0.5688590 4.0123257 6.9066137 9.8628936 1.0590214 4.9531917 3.9263346
## 71 1.0765248 3.6177350 6.7990310 9.8633228 0.8030853 4.6817260 3.4757354
## 72 8.4870356 7.4871923 6.1969660 2.0625434 8.1434899 7.0901914 7.8788200
## 73 0.9355333 3.6293537 6.2527566 9.6064629 0.6171515 4.3629906 3.7233594
## 74 2.5383665 2.1245968 4.8864988 8.6166756 1.2111719 2.7621137 2.5179909
## 75 1.5360536 4.3959150 7.8215329 10.2683866 1.9461477 5.6729224 4.0184329
## 76 0.3066931 4.6212036 7.0118140 10.0558348 1.5997491 5.3181022 4.6576254
## 77 1.3621451 3.1228434 6.0427381 9.3309407 0.2363967 4.0016935 3.1748927
## 78 5.0154816 0.8432559 3.8564439 8.0143995 3.5960515 1.1238650 1.8283120
## 79 2.9837136 1.7422457 5.7610949 8.8431597 1.7024492 3.2638681 1.4757086
## 80 4.0108757 2.6105425 3.1211461 7.2260660 3.0138509 1.9631154 3.4389124
## 81 2.5340351 1.9493891 5.4011611 8.8391285 1.1346632 3.0579314 2.0550028
## 82 2.8545304 4.2660950 8.2555557 10.3689767 2.7501174 5.8647444 3.5937920
## 50 51 52 53 54 55 56
## 2
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## 51 4.4802087
## 52 1.9110385 4.5823399
## 53 1.2512034 4.8116113 0.8152714
## 54 5.8164906 1.4557131 6.0187830 6.2363908
## 55 1.8726800 3.0202288 1.7025794 1.8386181 4.4651893
## 56 4.7711363 0.9100370 4.4966652 4.8707928 1.8637582 3.0975144
## 57 5.3067551 6.8217730 7.1906709 6.5499110 7.3073342 6.3523687 7.6515446
## 58 2.5516477 2.7243159 3.7565756 3.4959872 3.7393803 2.3453990 3.4188238
## 59 0.9652524 4.2687044 2.7460313 2.1794260 5.4748217 2.2747023 4.7190421
## 60 1.7221158 4.8510816 0.3970660 0.5082289 6.2859510 1.9070471 4.8163900
## 61 0.9693420 4.1536266 2.7610486 2.1863027 5.3773626 2.1338220 4.6164453
## 62 1.5193853 4.3093810 0.4474978 0.6396968 5.7441099 1.3697400 4.3012965
## 63 1.8159423 3.9760340 0.6393558 1.0779207 5.4210869 1.0787561 3.9134647
## 64 2.8554191 2.2254369 3.8206689 3.6766137 3.2309151 2.3427187 2.9364053
## 65 2.1889207 3.0391126 1.5711886 1.9174780 4.4887806 0.4778226 2.9816455
## 66 1.6029521 3.2993315 1.4636555 1.5360370 4.7372263 0.3124829 3.3888611
## 67 1.5012599 3.3766556 1.4146850 1.4496318 4.8098763 0.4166026 3.4778960
## 68 4.7613202 6.2962177 6.6355218 6.0060530 6.8419868 5.7721166 7.1136371
## 69 1.2241080 4.7252343 0.7707158 0.1468326 6.1457027 1.7762587 4.7844267
## 70 0.9345719 4.3156559 1.0159884 0.5539910 5.7319325 1.3736120 4.4315896
## 71 0.7595754 4.0325357 1.4862215 1.0464229 5.4303680 1.1973645 4.2347154
## 72 8.4748341 7.1550133 8.2629895 8.5864649 7.1234810 8.0046790 7.0757228
## 73 1.5118638 3.7404137 0.9986748 1.1149125 5.1822288 0.7484318 3.7729436
## 74 2.4686681 2.1287921 2.5173373 2.6839062 3.5554889 0.9513428 2.3038615
## 75 0.5509798 5.0218721 2.0803631 1.2996700 6.3581847 2.3436701 5.3059910
## 76 1.7197542 4.7102010 0.3058309 0.5457399 6.1501511 1.7551597 4.6693250
## 77 1.3782855 3.3625544 1.5080429 1.4694664 4.7822114 0.5173825 3.5072715
## 78 4.5815159 0.9042014 5.0317339 5.1278756 1.3577302 3.3982667 1.8003467
## 79 2.1608548 2.6373251 3.2144126 3.0002727 3.8152847 1.7955938 3.2143656
## 80 4.1930849 1.6914263 3.7764774 4.2057123 2.7295673 2.6855550 1.3396752
## 81 2.0860677 2.4049526 2.6648988 2.6131791 3.7534745 1.1042265 2.7889719
## 82 1.4945553 5.2309492 3.3816359 2.6433853 6.4026645 3.1427118 5.7211325
## 57 58 59 60 61 62 63
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## 58 4.3722195
## 59 4.4782918 1.9564460
## 60 7.0288594 3.8077949 2.6123277
## 61 4.4406128 1.7960838 0.4581755 2.6354795
## 62 6.7661007 3.3248254 2.3323814 0.5478484 2.3292879
## 63 6.9367358 3.2601463 2.5508667 0.9204449 2.5073531 0.4631077
## 64 4.7946000 0.5945268 2.3129791 3.9255945 2.2202905 3.4138700 3.2959730
## 65 6.7934122 2.7287965 2.6429943 1.8583853 2.5503314 1.3413875 0.9486179
## 66 6.2864017 2.4211269 2.0889018 1.6336558 1.9700672 1.0956021 0.8736333
## 67 6.2366472 2.4208181 2.0041930 1.5664370 1.8961855 1.0291894 0.8498736
## 68 0.5838162 3.8061835 3.9324165 6.4822213 3.8790428 6.2074602 6.3684701
## 69 6.5301307 3.4305954 2.1259834 0.5014879 2.1532291 0.5636340 1.0182482
## 70 6.1923308 2.9534224 1.7990075 0.9029794 1.7646875 0.6083862 0.9228358
## 71 5.7852578 2.4963723 1.4948006 1.4155596 1.3606396 1.0520632 1.2073620
## 72 10.4511745 7.9246640 8.1613281 8.4663712 8.4836065 8.2132701 8.1426528
## 73 6.5144319 2.8290965 2.1838891 1.1619202 2.1032767 0.6309015 0.4553174
## 74 6.2286974 1.9256798 2.5288338 2.7488635 2.4293444 2.2020408 1.9154985
## 75 5.3451652 3.0141202 1.2772399 1.8007026 1.2892261 1.7595442 2.1239058
## 76 7.0188679 3.7171177 2.6052904 0.1836250 2.6041223 0.4273883 0.7597984
## 77 6.0679140 2.2779390 1.8273496 1.6303946 1.7313555 1.0995636 0.9840861
## 78 6.1543264 2.4030571 4.2013091 5.2497715 4.0721631 4.7022456 4.4251964
## 79 4.7999994 0.5597943 1.7245610 3.2845590 1.5658337 2.7882270 2.7071361
## 80 7.5506910 3.3126968 4.1696165 4.1029362 4.1869272 3.6213362 3.2855547
## 81 5.5433075 1.2985966 1.9803882 2.8056562 1.8332883 2.2719448 2.0980369
## 82 4.0000119 2.7035499 1.1381820 3.1431569 1.1082514 3.0060345 3.2942778
## 64 65 66 67 68 69 70
## 2
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## 65 2.6497226
## 66 2.4650882 0.6155633
## 67 2.4790998 0.7009355 0.1094101
## 68 4.2446398 6.2149008 5.7090802 5.6607378
## 69 3.5946834 1.8448892 1.4714880 1.3822291 5.9854216
## 70 3.1321379 1.5446034 1.0631444 0.9661480 5.6358045 0.5061251
## 71 2.7251739 1.5181228 0.9218990 0.8298774 5.2199363 1.0210476 0.5258911
## 72 7.4512717 7.8097219 8.0444930 8.0391624 10.1200484 8.4401935 8.3959492
## 73 2.8998679 0.8235563 0.4775402 0.4293407 5.9429007 1.0541889 0.7366803
## 74 1.7042321 1.0572905 1.1937796 1.2615116 5.6548249 2.5971191 2.1916543
## 75 3.3603785 2.6383496 2.0607986 1.9597118 4.8208039 1.3185008 1.2015844
## 76 3.8286411 1.7026280 1.4900264 1.4291916 6.4669286 0.5394033 0.8441983
## 77 2.3492192 0.8387072 0.2702474 0.1902534 5.4931565 1.3950756 0.9540544
## 78 1.9326120 3.5288637 3.6503953 3.7135257 5.6543617 5.0452385 4.5961029
## 79 0.7439297 2.1774183 1.8683707 1.8692024 4.2265906 2.9303084 2.4517144
## 80 2.8080196 2.4729725 2.9066941 2.9720012 7.0109375 4.0933755 3.8212040
## 81 1.2397795 1.4427028 1.2475042 1.2777599 4.9666916 2.5371097 2.0687211
## 82 3.1898740 3.5407762 2.9356978 2.8498822 3.4916528 2.6469551 2.4093773
## 71 72 73 74 75 76 77
## 2
## 3
## 4
## 5
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## 64
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## 68
## 69
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## 71
## 72 8.4820547
## 73 0.8360458 8.1649883
## 74 1.9561839 7.4149966 1.6344339
## 75 1.1593805 8.8635651 1.8891177 3.0027942
## 76 1.3347115 8.4756420 1.0137086 2.6139932 1.8366104
## 77 0.7612323 7.9722319 0.5566502 1.2433129 1.8632911 1.5077090
## 78 4.2390426 7.3890949 4.1187449 2.5147098 5.1109287 5.1172275 3.6620220
## 79 2.0134181 7.8100293 2.2813993 1.4333228 2.6629172 3.1879771 1.7280940
## 80 3.7367336 6.0875322 3.2127285 1.9232561 4.7249335 3.9877464 2.9839469
## 81 1.7005459 7.6955334 1.7061106 0.7042534 2.6222275 2.6859316 1.1794756
## 82 2.1321163 9.1617652 2.9519052 3.5311345 1.3684821 3.1609543 2.7037147
## 78 79 80 81
## 2
## 3
## 4
## 5
## 6
## 7
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## 13
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## 51
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## 65
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## 71
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## 73
## 74
## 75
## 76
## 77
## 78
## 79 2.5069682
## 80 2.4424475 2.9993504
## 81 2.5441839 0.7672633 2.5017609
## 82 5.0786945 2.6040714 5.2711284 2.9395879
##
## Metric : euclidean
## Number of objects : 82
metodo jerarquico, mediante enlace ward
hmodel <- hclust(distancia, method = "ward.D")
plot(hmodel)
proceso de agrupamiento indicando distancias
hmodel$height## [1] 0.07283456 0.08729939 0.08750183 0.09408251 0.10084704 0.10973102
## [7] 0.11964042 0.12298880 0.13025627 0.13232768 0.14698775 0.15647953
## [13] 0.15849870 0.15852137 0.16283886 0.17162465 0.17485674 0.18038708
## [19] 0.19279120 0.20482494 0.20646684 0.21764272 0.23024622 0.24994001
## [25] 0.26328315 0.26859092 0.27617748 0.27701729 0.28120102 0.29764565
## [31] 0.30199265 0.31152139 0.31708349 0.34545612 0.34723172 0.37857881
## [37] 0.38335902 0.40909605 0.43190607 0.43756582 0.45573125 0.48053717
## [43] 0.48703272 0.50983404 0.52704738 0.53964347 0.54619781 0.54847464
## [49] 0.55840571 0.56046467 0.57656835 0.60277533 0.60706448 0.61180006
## [55] 0.70069513 0.75445230 0.89493660 0.89875440 0.95619280 0.99647087
## [61] 1.14469548 1.27500411 1.38349794 1.46132791 1.49314497 1.55518272
## [67] 1.61832985 1.72829716 2.30150853 2.36221370 2.52899105 3.53194222
## [73] 4.27869266 4.37941575 5.90680720 6.72524479 10.83530063 12.51152853
## [79] 20.68092109 23.72272456 30.18644861
plot(hmodel$height, type = "p")
lines(hmodel$height)
(hmodel$height)[18]## [1] 0.1803871
k clusters
plot(hmodel)
output <- cutree(hmodel, k = 3)
length(output)## [1] 82
table(output)## output
## 1 2 3
## 31 31 20
dplyr::bind_cols(scale(result), cluster = output)## # A tibble: 82 x 4
## Axis1 Axis2 Axis3 cluster
## <dbl> <dbl> <dbl> <int>
## 1 -1.31 -0.500 0.932 1
## 2 -0.429 -2.84 0.428 1
## 3 0.812 0.820 -0.414 2
## 4 0.00260 0.664 0.531 2
## 5 -0.158 -0.529 0.521 1
## 6 -0.656 0.0418 0.826 1
## 7 -0.331 0.595 1.10 1
## 8 -0.434 -0.0787 0.333 1
## 9 0.421 -0.393 -0.0880 1
## 10 0.240 0.513 0.168 2
## # ... with 72 more rows
k clusters
dist2 <- as.matrix(distancia)
heatmap(dist2)
boxplote, caracterizacion de clusters
data2 <- dplyr::mutate(as.data.frame(scale(result)), cluster = output)
boxplot(
data2$Axis1 ~ data2$cluster,
col = c("blue", "red", "green")
)
boxplot(
data2$Axis2 ~ data2$cluster,
col = c("blue", "red", "green")
)
gráficas
set.seed(2021)
factoextra::fviz_nbclust(
result, kmeans, method = "silhouette",
k.max = 20
)
set.seed(2021)
factoextra::fviz_nbclust(
result, kmeans, method = "wss",
k.max = 20
)
nb <-
NbClust::NbClust(
as.matrix(result), diss = NULL, distance = "euclidean",
min.nc = 2, max.nc = 20, method = "kmeans", index = "all"
)
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
##
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 4 proposed 2 as the best number of clusters
## * 3 proposed 3 as the best number of clusters
## * 6 proposed 4 as the best number of clusters
## * 1 proposed 12 as the best number of clusters
## * 2 proposed 13 as the best number of clusters
## * 1 proposed 14 as the best number of clusters
## * 1 proposed 15 as the best number of clusters
## * 3 proposed 18 as the best number of clusters
## * 1 proposed 19 as the best number of clusters
## * 1 proposed 20 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 4
##
##
## *******************************************************************
factoextra::fviz_nbclust(nb)## Among all indices:
## ===================
## * 2 proposed 0 as the best number of clusters
## * 1 proposed 1 as the best number of clusters
## * 4 proposed 2 as the best number of clusters
## * 3 proposed 3 as the best number of clusters
## * 6 proposed 4 as the best number of clusters
## * 1 proposed 12 as the best number of clusters
## * 2 proposed 13 as the best number of clusters
## * 1 proposed 14 as the best number of clusters
## * 1 proposed 15 as the best number of clusters
## * 3 proposed 18 as the best number of clusters
## * 1 proposed 19 as the best number of clusters
## * 1 proposed 20 as the best number of clusters
##
## Conclusion
## =========================
## * According to the majority rule, the best number of clusters is 4 .
k-means
set.seed(2021)
model <-
kmeans(
x = result, centers = 4, iter.max = 200,
nstart = 200, algorithm = "Hartigan-Wong",
trace = F
)Suma de cuadrados Interclaster
model$withinss## [1] 79.55653 12.89757 11.94789 61.10863
model$tot.withinss## [1] 165.5106
valores de silueta
sil <- cluster::silhouette(model$cluster, dist(result))
class(sil)## [1] "silhouette"
head(sil)## cluster neighbor sil_width
## [1,] 4 1 0.5851559
## [2,] 2 4 0.2067561
## [3,] 1 4 0.6761359
## [4,] 1 4 0.4470406
## [5,] 4 1 0.1184692
## [6,] 4 1 0.3728762
factoextra::fviz_silhouette(sil) +
coord_flip() +
theme_bw()## cluster size ave.sil.width
## 1 1 51 0.53
## 2 2 6 0.58
## 3 3 3 0.53
## 4 4 22 0.36
k-means++
set.seed(2021)
model_02 <-
LICORS::kmeanspp(
data = result, k = 4,
start = "random", iter.max = 100,
nstart = 100, algorithm = "Hartigan-Wong",
trace = 0
)**Validacion **
Indice_Davis_Boulding
grupo <- model_02$cluster
index <- clusterSim::index.DB(result, grupo, centrotypes = "centroids")
index$DB## [1] 0.72429
Indice de Dum
clValid::dunn(Data = result, clusters = grupo, distance = NULL)## [1] 0.08094097