Analisis de Cluster con Motor 1
Carlos Garcia
Fecha de revisión: 05-09-2024
## CURRENT_A_CALC CURRENT_B_CALC CURRENT_C_CALC CURRENT_D_CALC
## Min. :-1.3283 Min. :-1.4045 Min. :-1.4092 Min. :-1.4162
## 1st Qu.:-1.1946 1st Qu.:-1.3895 1st Qu.:-1.3942 1st Qu.:-1.3996
## Median : 0.1352 Median : 0.2756 Median : 0.2585 Median : 0.2736
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.8707 3rd Qu.: 0.8714 3rd Qu.: 0.8714 3rd Qu.: 0.8746
## Max. : 7.8616 Max. : 2.2006 Max. : 2.5605 Max. : 2.0827
## POWER_A POWER_B POWER_C POWER_D
## Min. :-1.2576 Min. :-1.3927 Min. :-1.4007 Min. :-1.4024
## 1st Qu.:-1.2576 1st Qu.:-1.3639 1st Qu.:-1.3717 1st Qu.:-1.3734
## Median : 0.1745 Median : 0.2794 Median : 0.2478 Median : 0.2795
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.8905 3rd Qu.: 0.8704 3rd Qu.: 0.8792 3rd Qu.: 0.8885
## Max. : 8.2896 Max. : 2.1821 Max. : 2.5614 Max. : 2.3965
## TEMPERATURE_A TEMPERATURE_B TEMPERATURE_C TEMPERATURE_D
## Min. :-1.50393 Min. :-1.5054 Min. :-1.509990 Min. :-1.80942
## 1st Qu.:-0.96883 1st Qu.:-0.9691 1st Qu.:-0.957430 1st Qu.:-0.96013
## Median :-0.02548 Median :-0.0331 Median :-0.001013 Median :-0.03264
## Mean : 0.00000 Mean : 0.0000 Mean : 0.000000 Mean : 0.00000
## 3rd Qu.: 0.83894 3rd Qu.: 0.8358 3rd Qu.: 0.851374 3rd Qu.: 0.83851
## Max. : 2.08745 Max. : 1.7242 Max. : 2.265829 Max. : 4.94115
## VOLTAGE_A VOLTAGE_B VOLTAGE_C VOLTAGE_D
## Min. :-1.4789 Min. :-1.5691 Min. :-1.5468 Min. :-1.5986
## 1st Qu.:-0.8315 1st Qu.:-0.8380 1st Qu.:-0.8388 1st Qu.:-0.8339
## Median :-0.1682 Median :-0.1726 Median :-0.1705 Median :-0.1681
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.7291 3rd Qu.: 0.7322 3rd Qu.: 0.7359 3rd Qu.: 0.7285
## Max. : 2.3346 Max. : 2.3320 Max. : 2.3437 Max. : 2.3503Procedemos con los Clúster
Comenzamos haciendo un estudio PCA
Uno de los temas clásicos de la estadistica multivariada es el análisis de componentes principales (ACP), creado por Lebart y Marinoe.
El objeto del ACP es de observar que tan correlacionadas están las variables, disminuyendo un conjunto p-dimensiones a uno de 2D y mirar que dimensiones del modelo concentran la mayor variabilidad. Ademas PCA tiene como objetivo reducir el número de dimensiones(componente de la varianza)
Matriz de correlaciones
## [1] "La matriz de correlaciones de las variables puras"## CURRENT_A_CALC CURRENT_B_CALC CURRENT_C_CALC CURRENT_D_CALC
## CURRENT_A_CALC 1.0000000 0.8220510 0.8110276 0.7958395
## CURRENT_B_CALC 0.8220510 1.0000000 0.9711968 0.9548349
## CURRENT_C_CALC 0.8110276 0.9711968 1.0000000 0.9643766
## CURRENT_D_CALC 0.7958395 0.9548349 0.9643766 1.0000000
## POWER_A 0.9895457 0.8370202 0.8247161 0.8095635
## POWER_B 0.8221955 0.9945253 0.9709496 0.9556018
## POWER_C 0.8043514 0.9689548 0.9863382 0.9663893
## POWER_D 0.7925888 0.9537921 0.9601419 0.9776218
## TEMPERATURE_A 0.1107448 0.2436745 0.2411100 0.2365837
## TEMPERATURE_B 0.1088123 0.2429399 0.2404444 0.2362629
## TEMPERATURE_C 0.1095238 0.2430940 0.2406237 0.2365467
## TEMPERATURE_D 0.1083149 0.2398858 0.2373979 0.2334395
## VOLTAGE_A -0.4452737 -0.6098623 -0.5989877 -0.5901708
## VOLTAGE_B -0.4352930 -0.6136445 -0.6043067 -0.5961083
## VOLTAGE_C -0.4270491 -0.6084833 -0.6053073 -0.6001753
## VOLTAGE_D -0.4217828 -0.6023850 -0.6002915 -0.6013830
## POWER_A POWER_B POWER_C POWER_D TEMPERATURE_A
## CURRENT_A_CALC 0.9895457 0.8221955 0.8043514 0.7925888 0.1107448
## CURRENT_B_CALC 0.8370202 0.9945253 0.9689548 0.9537921 0.2436745
## CURRENT_C_CALC 0.8247161 0.9709496 0.9863382 0.9601419 0.2411100
## CURRENT_D_CALC 0.8095635 0.9556018 0.9663893 0.9776218 0.2365837
## POWER_A 1.0000000 0.8370713 0.8188310 0.8068310 0.1657359
## POWER_B 0.8370713 1.0000000 0.9705861 0.9560889 0.2418486
## POWER_C 0.8188310 0.9705861 1.0000000 0.9621502 0.2386556
## POWER_D 0.8068310 0.9560889 0.9621502 1.0000000 0.2383368
## TEMPERATURE_A 0.1657359 0.2418486 0.2386556 0.2383368 1.0000000
## TEMPERATURE_B 0.1635076 0.2412160 0.2379647 0.2378502 0.9970509
## TEMPERATURE_C 0.1642543 0.2413654 0.2378494 0.2381073 0.9949356
## TEMPERATURE_D 0.1626563 0.2380882 0.2348448 0.2350265 0.9903636
## VOLTAGE_A -0.5042673 -0.6094718 -0.5983360 -0.5934381 -0.7104251
## VOLTAGE_B -0.4940579 -0.6139710 -0.6044594 -0.6007391 -0.7125880
## VOLTAGE_C -0.4854711 -0.6093058 -0.6063187 -0.6045850 -0.7114198
## VOLTAGE_D -0.4803109 -0.6031667 -0.6011622 -0.6062644 -0.7097013
## TEMPERATURE_B TEMPERATURE_C TEMPERATURE_D VOLTAGE_A VOLTAGE_B
## CURRENT_A_CALC 0.1088123 0.1095238 0.1083149 -0.4452737 -0.4352930
## CURRENT_B_CALC 0.2429399 0.2430940 0.2398858 -0.6098623 -0.6136445
## CURRENT_C_CALC 0.2404444 0.2406237 0.2373979 -0.5989877 -0.6043067
## CURRENT_D_CALC 0.2362629 0.2365467 0.2334395 -0.5901708 -0.5961083
## POWER_A 0.1635076 0.1642543 0.1626563 -0.5042673 -0.4940579
## POWER_B 0.2412160 0.2413654 0.2380882 -0.6094718 -0.6139710
## POWER_C 0.2379647 0.2378494 0.2348448 -0.5983360 -0.6044594
## POWER_D 0.2378502 0.2381073 0.2350265 -0.5934381 -0.6007391
## TEMPERATURE_A 0.9970509 0.9949356 0.9903636 -0.7104251 -0.7125880
## TEMPERATURE_B 1.0000000 0.9958522 0.9915827 -0.7087805 -0.7109857
## TEMPERATURE_C 0.9958522 1.0000000 0.9893485 -0.7091808 -0.7113538
## TEMPERATURE_D 0.9915827 0.9893485 1.0000000 -0.7038988 -0.7060632
## VOLTAGE_A -0.7087805 -0.7091808 -0.7038988 1.0000000 0.9949540
## VOLTAGE_B -0.7109857 -0.7113538 -0.7060632 0.9949540 1.0000000
## VOLTAGE_C -0.7097717 -0.7102692 -0.7048281 0.9910145 0.9940312
## VOLTAGE_D -0.7080736 -0.7084693 -0.7032091 0.9874643 0.9900256
## VOLTAGE_C VOLTAGE_D
## CURRENT_A_CALC -0.4270491 -0.4217828
## CURRENT_B_CALC -0.6084833 -0.6023850
## CURRENT_C_CALC -0.6053073 -0.6002915
## CURRENT_D_CALC -0.6001753 -0.6013830
## POWER_A -0.4854711 -0.4803109
## POWER_B -0.6093058 -0.6031667
## POWER_C -0.6063187 -0.6011622
## POWER_D -0.6045850 -0.6062644
## TEMPERATURE_A -0.7114198 -0.7097013
## TEMPERATURE_B -0.7097717 -0.7080736
## TEMPERATURE_C -0.7102692 -0.7084693
## TEMPERATURE_D -0.7048281 -0.7032091
## VOLTAGE_A 0.9910145 0.9874643
## VOLTAGE_B 0.9940312 0.9900256
## VOLTAGE_C 1.0000000 0.9917098
## VOLTAGE_D 0.9917098 1.0000000
PCA
## [1] "Cálculo del PCA"## Standard deviations (1, .., p=16):
## [1] 3.21656161 2.05478677 0.86540686 0.68606186 0.27724119 0.21146781
## [7] 0.14815141 0.11687659 0.11136743 0.09994530 0.09073070 0.08254516
## [13] 0.07272393 0.07202164 0.06409198 0.05254847
##
## Rotation (n x k) = (16 x 16):
## PC1 PC2 PC3 PC4 PC5
## CURRENT_A_CALC 0.2258778 0.2512785 0.23216854 -0.58464362 0.059607057
## CURRENT_B_CALC 0.2732133 0.2098850 0.05805774 0.16992965 -0.475893116
## CURRENT_C_CALC 0.2720717 0.2108668 0.06072129 0.21503891 -0.107931742
## CURRENT_D_CALC 0.2696061 0.2096401 0.05276784 0.24649001 0.494658794
## POWER_A 0.2384473 0.2279621 0.20430676 -0.57704747 0.042903069
## POWER_B 0.2732426 0.2106623 0.05489301 0.17125261 -0.452736265
## POWER_C 0.2716708 0.2110435 0.05232713 0.23126344 -0.063205247
## POWER_D 0.2698115 0.2076334 0.04394839 0.24677663 0.511904617
## TEMPERATURE_A 0.1937110 -0.3600033 0.28379399 0.03370842 -0.003206637
## TEMPERATURE_B 0.1933916 -0.3603495 0.28641717 0.03881262 -0.001758087
## TEMPERATURE_C 0.1934111 -0.3599137 0.28439933 0.03675802 0.001042635
## TEMPERATURE_D 0.1921215 -0.3594512 0.28956003 0.03532356 0.004270649
## VOLTAGE_A -0.2739588 0.1591088 0.36797517 0.14042998 0.096146952
## VOLTAGE_B -0.2746805 0.1595704 0.37103884 0.09990260 0.077294509
## VOLTAGE_C -0.2741766 0.1599954 0.37671659 0.07631526 -0.037010837
## VOLTAGE_D -0.2730987 0.1606961 0.38018249 0.06969407 -0.155444331
## PC6 PC7 PC8 PC9
## CURRENT_A_CALC -0.020989673 0.0053537414 0.031487894 -0.0108378966
## CURRENT_B_CALC 0.347164720 -0.0723323441 0.061919444 -0.0050313938
## CURRENT_C_CALC -0.561286485 0.0821205993 0.699955318 -0.0157259163
## CURRENT_D_CALC 0.129729852 -0.7420969191 0.015295346 0.0037156490
## POWER_A -0.008522422 0.0044236653 -0.047698274 0.0145021110
## POWER_B 0.347829401 -0.0059139865 -0.092806061 0.0030755608
## POWER_C -0.557312235 0.0809240695 -0.699171361 0.0113562382
## POWER_D 0.333059508 0.6530274268 0.026576561 0.0009792999
## TEMPERATURE_A -0.003244563 0.0078197663 -0.007600678 0.2839572042
## TEMPERATURE_B 0.001061777 0.0002416597 -0.003260826 0.2094275256
## TEMPERATURE_C 0.004882487 -0.0030269038 0.023471219 0.3689492270
## TEMPERATURE_D 0.003668267 -0.0007843244 -0.017770064 -0.8593491826
## VOLTAGE_A -0.023854489 0.0563547684 -0.038418477 0.0049367692
## VOLTAGE_B -0.019006314 -0.0044375014 0.005735991 0.0054465816
## VOLTAGE_C 0.059992801 -0.0230307913 0.042791701 -0.0078319571
## VOLTAGE_D 0.001374331 -0.0210408381 -0.017117727 0.0059086785
## PC10 PC11 PC12 PC13
## CURRENT_A_CALC -0.1337709440 0.658390311 -0.182023568 -0.009951198
## CURRENT_B_CALC -0.0606660950 -0.032246361 -0.096252760 -0.589700728
## CURRENT_C_CALC 0.0019560602 -0.038471774 0.028211020 0.057889882
## CURRENT_D_CALC 0.0719934869 0.013137005 0.021265421 0.020889030
## POWER_A 0.1004309387 -0.673568572 0.216443157 0.004161074
## POWER_B -0.1325858857 0.032044251 0.155394511 0.580461425
## POWER_C 0.0149053193 0.008822237 -0.103461970 -0.041777292
## POWER_D 0.1383896608 0.007899375 -0.034379682 -0.021970751
## TEMPERATURE_A -0.0104353581 -0.023534228 -0.011387672 -0.317064065
## TEMPERATURE_B 0.0008582287 0.011231138 -0.025179277 -0.110640680
## TEMPERATURE_C 0.0028331659 0.028246841 0.018413357 0.391599426
## TEMPERATURE_D 0.0024124503 -0.008095698 0.014738528 0.037921513
## VOLTAGE_A -0.4927786918 0.060424225 0.480875003 -0.069023925
## VOLTAGE_B -0.2878118922 -0.089306302 -0.005946856 -0.075818612
## VOLTAGE_C 0.0142053561 -0.227124170 -0.748931500 0.174246786
## VOLTAGE_D 0.7747302868 0.210267714 0.282805294 -0.027418237
## PC14 PC15 PC16
## CURRENT_A_CALC 0.011215890 0.010616943 -0.0124157256
## CURRENT_B_CALC -0.357031262 -0.059546502 0.0147719018
## CURRENT_C_CALC 0.048101371 -0.004234545 0.0006374464
## CURRENT_D_CALC 0.024926628 -0.021460830 -0.0047903765
## POWER_A -0.015689479 -0.029024796 0.0172700463
## POWER_B 0.351199454 0.103700321 -0.0149269436
## POWER_C -0.050253082 -0.006966273 -0.0010142837
## POWER_D -0.013200905 0.008933237 0.0001364599
## TEMPERATURE_A 0.497439466 0.016618222 -0.5669062806
## TEMPERATURE_B 0.221511191 0.006324191 0.8020114993
## TEMPERATURE_C -0.655240185 -0.022087320 -0.1725948571
## TEMPERATURE_D -0.062760091 0.002606804 -0.0654982052
## VOLTAGE_A -0.012915236 -0.497235692 0.0108649669
## VOLTAGE_B -0.077837958 0.801458506 0.0054773560
## VOLTAGE_C 0.084316598 -0.306112932 -0.0153452159
## VOLTAGE_D 0.007372374 0.006592898 -0.0038040565## [1] "solicito las tablas"## Principal Component Analysis Results for variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the variables"
## 2 "$cor" "Correlations between variables and dimensions"
## 3 "$cos2" "Cos2 for the variables"
## 4 "$contrib" "contributions of the variables"## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 10.346268574 64.66417859 64.66418
## Dim.2 4.222148677 26.38842923 91.05261
## Dim.3 0.748929039 4.68080649 95.73341
## Dim.4 0.470680878 2.94175549 98.67517
## Dim.5 0.076862677 0.48039173 99.15556
## Dim.6 0.044718634 0.27949146 99.43505
## Dim.7 0.021948842 0.13718026 99.57223
## Dim.8 0.013660136 0.08537585 99.65761
## Dim.9 0.012402704 0.07751690 99.73513
## Dim.10 0.009989063 0.06243165 99.79756
## Dim.11 0.008232060 0.05145038 99.84901
## Dim.12 0.006813704 0.04258565 99.89159
## Dim.13 0.005288771 0.03305482 99.92465
## Dim.14 0.005187117 0.03241948 99.95707
## Dim.15 0.004107782 0.02567364 99.98274
## Dim.16 0.002761342 0.01725839 100.00000## [1] "las gráficas"
## [1] "Cálculo de los componentes"Gráficamos clúster con k-means
