Analisis de Cluster con Motor 2
Carlos Garcia
Fecha de revisión: 05-09-2024
## CURRENT_A_CALC CURRENT_B_CALC CURRENT_C_CALC CURRENT_D_CALC
## Min. :-1.39208 Min. :-1.4121 Min. :-1.41549 Min. :-1.41614
## 1st Qu.:-1.03022 1st Qu.:-0.9935 1st Qu.:-0.98864 1st Qu.:-0.98956
## Median : 0.08182 Median : 0.0667 Median : 0.06832 Median : 0.06671
## Mean : 0.00000 Mean : 0.0000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.68198 3rd Qu.: 0.6401 3rd Qu.: 0.63746 3rd Qu.: 0.63363
## Max. : 8.89878 Max. : 3.6549 Max. : 4.88563 Max. : 3.79507
## POWER_A POWER_B POWER_C POWER_D
## Min. :-1.3235 Min. :-1.40078 Min. :-1.40648 Min. :-1.40714
## 1st Qu.:-1.0313 1st Qu.:-1.01204 1st Qu.:-0.98045 1st Qu.:-0.98187
## Median : 0.1375 Median : 0.08349 Median : 0.08464 Median : 0.08132
## Mean : 0.0000 Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.7220 3rd Qu.: 0.64893 3rd Qu.: 0.65268 3rd Qu.: 0.64835
## Max. : 7.4428 Max. : 3.61747 Max. : 4.87753 Max. : 3.76702
## TEMPERATURE_A TEMPERATURE_B TEMPERATURE_C TEMPERATURE_D
## Min. :-1.5740 Min. :-1.7281 Min. :-1.6676 Min. :-1.7747
## 1st Qu.:-0.6707 1st Qu.:-0.6730 1st Qu.:-0.6711 1st Qu.:-0.6705
## Median :-0.3178 Median :-0.3175 Median :-0.3183 Median :-0.3189
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4858 3rd Qu.: 0.4642 3rd Qu.: 0.4741 3rd Qu.: 0.4718
## Max. : 3.9758 Max. : 3.5756 Max. : 3.8538 Max. : 3.5963
## VOLTAGE_A VOLTAGE_B VOLTAGE_C VOLTAGE_D
## Min. :-2.4687 Min. :-3.5467 Min. :-2.91327 Min. :-3.06058
## 1st Qu.:-0.7246 1st Qu.:-0.7247 1st Qu.:-0.71919 1st Qu.:-0.71763
## Median : 0.0474 Median : 0.0456 Median : 0.04837 Median : 0.05014
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.7071 3rd Qu.: 0.7079 3rd Qu.: 0.70732 3rd Qu.: 0.70977
## Max. : 2.2828 Max. : 2.2845 Max. : 2.28590 Max. : 2.28856Procedemos 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 1.000000000 0.7789833 0.7641235 0.7469246
## CURRENT_B_CALC 0.778983294 1.0000000 0.9540672 0.9396939
## CURRENT_C_CALC 0.764123546 0.9540672 1.0000000 0.9517695
## CURRENT_D_CALC 0.746924593 0.9396939 0.9517695 1.0000000
## POWER_A 0.990784032 0.8026559 0.7878943 0.7704020
## POWER_B 0.780047595 0.9905349 0.9561484 0.9415855
## POWER_C 0.764531712 0.9525822 0.9837139 0.9524837
## POWER_D 0.745877941 0.9402051 0.9508205 0.9819570
## TEMPERATURE_A 0.001043999 0.2486937 0.2486241 0.2493491
## TEMPERATURE_B 0.002127075 0.2517762 0.2514906 0.2522941
## TEMPERATURE_C 0.004327604 0.2537269 0.2532802 0.2543212
## TEMPERATURE_D 0.003959536 0.2534880 0.2530125 0.2541494
## VOLTAGE_A -0.376302843 -0.5870905 -0.5782704 -0.5696625
## VOLTAGE_B -0.368076675 -0.5910004 -0.5840623 -0.5764762
## VOLTAGE_C -0.361325097 -0.5859090 -0.5858401 -0.5801554
## VOLTAGE_D -0.354872030 -0.5819982 -0.5820949 -0.5832809
## POWER_A POWER_B POWER_C POWER_D TEMPERATURE_A
## CURRENT_A_CALC 0.99078403 0.7800476 0.7645317 0.7458779 0.001043999
## CURRENT_B_CALC 0.80265587 0.9905349 0.9525822 0.9402051 0.248693735
## CURRENT_C_CALC 0.78789430 0.9561484 0.9837139 0.9508205 0.248624052
## CURRENT_D_CALC 0.77040204 0.9415855 0.9524837 0.9819570 0.249349071
## POWER_A 1.00000000 0.8038312 0.7883025 0.7696885 0.059467677
## POWER_B 0.80383121 1.0000000 0.9560311 0.9428867 0.246743255
## POWER_C 0.78830253 0.9560311 1.0000000 0.9527504 0.248260911
## POWER_D 0.76968846 0.9428867 0.9527504 1.0000000 0.250430951
## TEMPERATURE_A 0.05946768 0.2467433 0.2482609 0.2504310 1.000000000
## TEMPERATURE_B 0.06086755 0.2498223 0.2512078 0.2534514 0.995809479
## TEMPERATURE_C 0.06301732 0.2517402 0.2529909 0.2553218 0.995604304
## TEMPERATURE_D 0.06263390 0.2513722 0.2527102 0.2551102 0.994409200
## VOLTAGE_A -0.44537718 -0.5868472 -0.5786379 -0.5716770 -0.684832572
## VOLTAGE_B -0.43706973 -0.5911453 -0.5844798 -0.5785999 -0.685025642
## VOLTAGE_C -0.43024893 -0.5861826 -0.5866980 -0.5819925 -0.685963855
## VOLTAGE_D -0.42384914 -0.5812536 -0.5832738 -0.5852847 -0.685792430
## TEMPERATURE_B TEMPERATURE_C TEMPERATURE_D VOLTAGE_A VOLTAGE_B
## CURRENT_A_CALC 0.002127075 0.004327604 0.003959536 -0.3763028 -0.3680767
## CURRENT_B_CALC 0.251776163 0.253726932 0.253488035 -0.5870905 -0.5910004
## CURRENT_C_CALC 0.251490639 0.253280172 0.253012475 -0.5782704 -0.5840623
## CURRENT_D_CALC 0.252294126 0.254321170 0.254149420 -0.5696625 -0.5764762
## POWER_A 0.060867546 0.063017324 0.062633904 -0.4453772 -0.4370697
## POWER_B 0.249822259 0.251740215 0.251372191 -0.5868472 -0.5911453
## POWER_C 0.251207796 0.252990922 0.252710228 -0.5786379 -0.5844798
## POWER_D 0.253451426 0.255321792 0.255110205 -0.5716770 -0.5785999
## TEMPERATURE_A 0.995809479 0.995604304 0.994409200 -0.6848326 -0.6850256
## TEMPERATURE_B 1.000000000 0.994793404 0.993962920 -0.6865760 -0.6868958
## TEMPERATURE_C 0.994793404 1.000000000 0.993841988 -0.6864411 -0.6866490
## TEMPERATURE_D 0.993962920 0.993841988 1.000000000 -0.6857862 -0.6860041
## VOLTAGE_A -0.686576049 -0.686441062 -0.685786177 1.0000000 0.9957354
## VOLTAGE_B -0.686895790 -0.686649034 -0.686004082 0.9957354 1.0000000
## VOLTAGE_C -0.687838670 -0.687598128 -0.686977129 0.9928488 0.9949410
## VOLTAGE_D -0.687633541 -0.687521622 -0.686874934 0.9896242 0.9920645
## VOLTAGE_C VOLTAGE_D
## CURRENT_A_CALC -0.3613251 -0.3548720
## CURRENT_B_CALC -0.5859090 -0.5819982
## CURRENT_C_CALC -0.5858401 -0.5820949
## CURRENT_D_CALC -0.5801554 -0.5832809
## POWER_A -0.4302489 -0.4238491
## POWER_B -0.5861826 -0.5812536
## POWER_C -0.5866980 -0.5832738
## POWER_D -0.5819925 -0.5852847
## TEMPERATURE_A -0.6859639 -0.6857924
## TEMPERATURE_B -0.6878387 -0.6876335
## TEMPERATURE_C -0.6875981 -0.6875216
## TEMPERATURE_D -0.6869771 -0.6868749
## VOLTAGE_A 0.9928488 0.9896242
## VOLTAGE_B 0.9949410 0.9920645
## VOLTAGE_C 1.0000000 0.9933638
## VOLTAGE_D 0.9933638 1.0000000
PCA
## [1] "Cálculo del PCA"## Standard deviations (1, .., p=16):
## [1] 3.17043576 2.07417441 0.92749920 0.72814577 0.32007583 0.26428610
## [7] 0.13513646 0.12690437 0.09836932 0.09053849 0.08131007 0.07965636
## [13] 0.07353887 0.07209778 0.06282289 0.06034349
##
## Rotation (n x k) = (16 x 16):
## PC1 PC2 PC3 PC4 PC5
## CURRENT_A_CALC 0.2080459 0.2875887 0.020925940 -0.62220508 0.0624483154
## CURRENT_B_CALC 0.2755064 0.2025158 0.114728542 0.14089384 -0.5141311384
## CURRENT_C_CALC 0.2749373 0.2021735 0.125092536 0.19134729 -0.0456369035
## CURRENT_D_CALC 0.2728859 0.1989636 0.132092410 0.22823376 0.4878471881
## POWER_A 0.2240433 0.2647068 -0.006515694 -0.59925073 0.0535742872
## POWER_B 0.2756593 0.2038148 0.113881423 0.14363068 -0.4916712715
## POWER_C 0.2750361 0.2022710 0.123594452 0.19150188 -0.0196392760
## POWER_D 0.2731795 0.1982606 0.129954620 0.23019635 0.4767874861
## TEMPERATURE_A 0.1944127 -0.3560600 0.279451107 -0.09059677 0.0033033421
## TEMPERATURE_B 0.1951326 -0.3552268 0.278332604 -0.08657738 0.0009647839
## TEMPERATURE_C 0.1955095 -0.3543620 0.280228749 -0.08756210 0.0017067251
## TEMPERATURE_D 0.1953417 -0.3542203 0.280501061 -0.08697940 0.0025130254
## VOLTAGE_A -0.2745629 0.1574942 0.389460011 0.01432606 0.0664816592
## VOLTAGE_B -0.2752663 0.1572311 0.386434259 -0.01751609 0.0513241511
## VOLTAGE_C -0.2750306 0.1583201 0.384250644 -0.03467828 -0.0297644222
## VOLTAGE_D -0.2743121 0.1593361 0.383011286 -0.04754164 -0.1068080131
## PC6 PC7 PC8 PC9
## CURRENT_A_CALC -0.004830751 0.0025150705 -0.0014244011 0.049460764
## CURRENT_B_CALC 0.318187354 0.0517323423 0.0369867065 0.639414929
## CURRENT_C_CALC -0.575898150 0.2155962106 0.6692671360 -0.037682186
## CURRENT_D_CALC 0.270135145 0.6729741278 -0.2142260762 -0.060167902
## POWER_A -0.005703807 -0.0050683156 0.0033919057 -0.035529726
## POWER_B 0.286461498 -0.0449269521 -0.0635100995 -0.606162149
## POWER_C -0.571642255 -0.2287417894 -0.6665726563 0.058517243
## POWER_D 0.288243117 -0.6659044517 0.2364217868 -0.006637590
## TEMPERATURE_A -0.004065998 -0.0018481096 0.0033956228 -0.009772089
## TEMPERATURE_B -0.001474769 -0.0065295949 0.0002319681 -0.011827250
## TEMPERATURE_C 0.001438966 0.0015026556 -0.0024685869 -0.001592882
## TEMPERATURE_D 0.002014381 0.0049959722 -0.0021349809 0.024267792
## VOLTAGE_A -0.015934534 -0.0060554083 -0.0132640944 0.208688018
## VOLTAGE_B -0.010818471 0.0002855455 -0.0101157751 0.146840827
## VOLTAGE_C 0.040489495 -0.0030539314 0.0095892758 0.021431635
## VOLTAGE_D -0.010720366 0.0051505083 0.0129144514 -0.380919607
## PC10 PC11 PC12 PC13
## CURRENT_A_CALC 0.111606187 0.165486814 0.643656319 0.1537874407
## CURRENT_B_CALC -0.254869801 0.028065027 0.011388294 -0.0739384186
## CURRENT_C_CALC 0.030734778 -0.004081800 -0.005514362 0.0260621640
## CURRENT_D_CALC -0.053711727 0.006644844 0.002582357 0.0031019555
## POWER_A -0.081412341 -0.172583894 -0.667324204 -0.1772554623
## POWER_B 0.383501492 -0.030409855 -0.018514577 0.0408400968
## POWER_C -0.058629503 0.001612023 -0.001992322 0.0268741661
## POWER_D -0.078211233 0.002540962 0.015121750 -0.0046444392
## TEMPERATURE_A 0.008257546 0.242763026 -0.013240976 0.0006338729
## TEMPERATURE_B 0.003135236 0.281263440 -0.065774079 -0.1696636082
## TEMPERATURE_C 0.014626420 0.313355113 -0.130162741 0.1559067874
## TEMPERATURE_D -0.018255794 -0.836727167 0.213026315 0.0109620618
## VOLTAGE_A 0.514916735 0.001692057 0.024882403 -0.4062305358
## VOLTAGE_B 0.226474787 -0.028213161 -0.079166502 -0.0405266459
## VOLTAGE_C -0.093062714 -0.035917832 -0.179639685 0.7748398578
## VOLTAGE_D -0.655579228 0.051097106 0.183471428 -0.3407444400
## PC14 PC15 PC16
## CURRENT_A_CALC 0.007864722 0.0397270967 -0.025076359
## CURRENT_B_CALC -0.013184149 -0.0059232589 0.006958446
## CURRENT_C_CALC 0.004879483 0.0039309070 -0.001277919
## CURRENT_D_CALC 0.005616160 -0.0008252887 0.007421416
## POWER_A -0.010392381 -0.0381941611 0.040837393
## POWER_B 0.007923641 -0.0014745978 -0.038904209
## POWER_C 0.005812853 -0.0011251044 0.008065073
## POWER_D -0.005681198 -0.0002265034 0.001621328
## TEMPERATURE_A 0.081981641 -0.8262611366 0.019497797
## TEMPERATURE_B 0.658696317 0.4509425391 -0.033554284
## TEMPERATURE_C -0.709272593 0.3273691344 0.009985591
## TEMPERATURE_D -0.031024880 0.0503664488 0.007014350
## VOLTAGE_A -0.075514355 0.0050542888 0.512812832
## VOLTAGE_B -0.026381626 -0.0280611143 -0.814845255
## VOLTAGE_C 0.198505256 0.0180011013 0.255008880
## VOLTAGE_D -0.095065217 0.0026969891 0.048814503## [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 10.051662928 62.82289330 62.82289
## Dim.2 4.302199484 26.88874678 89.71164
## Dim.3 0.860254759 5.37659225 95.08823
## Dim.4 0.530196256 3.31372660 98.40196
## Dim.5 0.102448538 0.64030336 99.04226
## Dim.6 0.069847141 0.43654463 99.47881
## Dim.7 0.018261862 0.11413664 99.59294
## Dim.8 0.016104719 0.10065449 99.69360
## Dim.9 0.009676522 0.06047827 99.75408
## Dim.10 0.008197219 0.05123262 99.80531
## Dim.11 0.006611328 0.04132080 99.84663
## Dim.12 0.006345136 0.03965710 99.88629
## Dim.13 0.005407965 0.03379978 99.92009
## Dim.14 0.005198090 0.03248806 99.95257
## Dim.15 0.003946716 0.02466697 99.97724
## Dim.16 0.003641336 0.02275835 100.00000## [1] "las gráficas"
## [1] "Cálculo de los componentes"Gráficamos clúster con k-means
