PCA

Principle Component Analysis

library(stats)
# Data normalization: data 0 to 1 range e ana both axis e, maximum minimum difference diye each data ke divide kora
# Data standardization: mean (0,0), range +1 to -1

#scale = data normalization, center = data standardization
iris_PCA = prcomp(iris[ , -5],scale = TRUE,center = TRUE)
iris_PCA

Standard deviations (1, .., p=4):
[1] 1.7083611 0.9560494 0.3830886 0.1439265

Rotation (n x k) = (4 x 4):
                    PC1         PC2        PC3        PC4
sepal.length  0.5210659 -0.37741762  0.7195664  0.2612863
sepal.width  -0.2693474 -0.92329566 -0.2443818 -0.1235096
petal.length  0.5804131 -0.02449161 -0.1421264 -0.8014492
petal.width   0.5648565 -0.06694199 -0.6342727  0.5235971

Summary

summary(iris_PCA)

Importance of components:
                          PC1    PC2     PC3     PC4
Standard deviation     1.7084 0.9560 0.38309 0.14393
Proportion of Variance 0.7296 0.2285 0.03669 0.00518
Cumulative Proportion  0.7296 0.9581 0.99482 1.00000

#Proportion of Variance: pc1 72.9% variance represent kore
# dimention reduce korar jonno pc1 and pc2 nibo

iris_PCA$x

               PC1
  [1,] -2.25714118
  [2,] -2.07401302
  [3,] -2.35633511
  [4,] -2.29170679
  [5,] -2.38186270
  [6,] -2.06870061
  [7,] -2.43586845
  [8,] -2.22539189
  [9,] -2.32684533
 [10,] -2.17703491
 [11,] -2.15907699
 [12,] -2.31836413
 [13,] -2.21104370
 [14,] -2.62430902
 [15,] -2.19139921
 [16,] -2.25466121
 [17,] -2.20021676
 [18,] -2.18303613
 [19,] -1.89223284
 [20,] -2.33554476
 [21,] -1.90793125
 [22,] -2.19964383
 [23,] -2.76508142
 [24,] -1.81259716
 [25,] -2.21972701
 [26,] -1.94532930
 [27,] -2.04430277
 [28,] -2.16133650
 [29,] -2.13241965
 [30,] -2.25769799
 [31,] -2.13297647
 [32,] -1.82547925
 [33,] -2.60621687
 [34,] -2.43800983
 [35,] -2.10292986
 [36,] -2.20043723
 [37,] -2.03831765
 [38,] -2.51889339
 [39,] -2.42152026
 [40,] -2.16246625
 [41,] -2.27884081
 [42,] -1.85191836
 [43,] -2.54511203
 [44,] -1.95788857
 [45,] -2.12992356
 [46,] -2.06283361
 [47,] -2.37677076
 [48,] -2.38638171
 [49,] -2.22200263
 [50,] -2.19647504
 [51,]  1.09810244
 [52,]  0.72889556
 [53,]  1.23683580
 [54,]  0.40612251
 [55,]  1.07188379
 [56,]  0.38738955
 [57,]  0.74403715
 [58,] -0.48569562
 [59,]  0.92480346
 [60,]  0.01138804
 [61,] -0.10982834
 [62,]  0.43922201
 [63,]  0.56023148
 [64,]  0.71715934
 [65,] -0.03324333
 [66,]  0.87248429
 [67,]  0.34908221
 [68,]  0.15827980
 [69,]  1.22100316
 [70,]  0.16436725
 [71,]  0.73521959
 [72,]  0.47469691
 [73,]  1.23005729
 [74,]  0.63074514
 [75,]  0.70031506
 [76,]  0.87135454
 [77,]  1.25231375
 [78,]  1.35386953
 [79,]  0.66258066
 [80,] -0.04012419
 [81,]  0.13035846
 [82,]  0.02337438
 [83,]  0.24073180
 [84,]  1.05755171
 [85,]  0.22323093
 [86,]  0.42770626
 [87,]  1.04522645
 [88,]  1.04104379
 [89,]  0.06935597
 [90,]  0.28253073
 [91,]  0.27814596
 [92,]  0.62248441
 [93,]  0.33540673
 [94,] -0.36097409
 [95,]  0.28762268
 [96,]  0.09105561
 [97,]  0.22695654
 [98,]  0.57446378
 [99,] -0.44617230
[100,]  0.25587339
[101,]  1.83841002
[102,]  1.15401555
[103,]  2.19790361
[104,]  1.43534213
[105,]  1.86157577
[106,]  2.74268509
[107,]  0.36579225
[108,]  2.29475181
[109,]  1.99998633
[110,]  2.25223216
[111,]  1.35962064
[112,]  1.59732747
[113,]  1.87761053
[114,]  1.25590769
[115,]  1.46274487
[116,]  1.58476820
[117,]  1.46651849
[118,]  2.41822770
[119,]  3.29964148
[120,]  1.25954707
[121,]  2.03091256
[122,]  0.97471535
[123,]  2.88797650
[124,]  1.32878064
[125,]  1.69505530
[126,]  1.94780139
[127,]  1.17118007
[128,]  1.01754169
[129,]  1.78237879
[130,]  1.85742501
[131,]  2.42782030
[132,]  2.29723178
[133,]  1.85648383
[134,]  1.11042770
[135,]  1.19845835
[136,]  2.78942561
[137,]  1.57099294
[138,]  1.34179696
[139,]  0.92173701
[140,]  1.84586124
[141,]  2.00808316
[142,]  1.89543421
[143,]  1.15401555
[144,]  2.03374499
[145,]  1.99147547
[146,]  1.86425786
[147,]  1.55935649
[148,]  1.51609145
[149,]  1.36820418
[150,]  0.95744849
                PC2
  [1,] -0.478423832
  [2,]  0.671882687
  [3,]  0.340766425
  [4,]  0.595399863
  [5,] -0.644675659
  [6,] -1.484205297
  [7,] -0.047485118
  [8,] -0.222403002
  [9,]  1.111603700
 [10,]  0.467447569
 [11,] -1.040205867
 [12,] -0.132633999
 [13,]  0.726243183
 [14,]  0.958296347
 [15,] -1.853846555
 [16,] -2.677315230
 [17,] -1.478655729
 [18,] -0.487206131
 [19,] -1.400327567
 [20,] -1.124083597
 [21,] -0.407490576
 [22,] -0.921035871
 [23,] -0.456813301
 [24,] -0.085272854
 [25,] -0.136796175
 [26,]  0.623529705
 [27,] -0.241354991
 [28,] -0.525389422
 [29,] -0.312172005
 [30,]  0.336604248
 [31,]  0.502856075
 [32,] -0.422280389
 [33,] -1.787587272
 [34,] -2.143546796
 [35,]  0.458665270
 [36,]  0.205419224
 [37,] -0.659349230
 [38,] -0.590315163
 [39,]  0.901161067
 [40,] -0.267981199
 [41,] -0.440240541
 [42,]  2.329610745
 [43,]  0.477501017
 [44,] -0.470749613
 [45,] -1.138415464
 [46,]  0.708678586
 [47,] -1.116688691
 [48,]  0.384957230
 [49,] -0.994627669
 [50,] -0.009185585
 [51,] -0.860091033
 [52,] -0.592629362
 [53,] -0.614239894
 [54,]  1.748546197
 [55,]  0.207725147
 [56,]  0.591302717
 [57,] -0.770438272
 [58,]  1.846243998
 [59,] -0.032118478
 [60,]  1.030565784
 [61,]  2.645211115
 [62,]  0.063083852
 [63,]  1.758832129
 [64,]  0.185602819
 [65,]  0.437537419
 [66,] -0.507364239
 [67,]  0.195656268
 [68,]  0.789451008
 [69,]  1.616827281
 [70,]  1.298259939
 [71,] -0.395247446
 [72,]  0.415926887
 [73,]  0.930209441
 [74,]  0.414997441
 [75,]  0.063200094
 [76,] -0.249956017
 [77,]  0.076998069
 [78,] -0.330205463
 [79,]  0.225173502
 [80,]  1.055183583
 [81,]  1.557055553
 [82,]  1.567225244
 [83,]  0.774661195
 [84,]  0.631726901
 [85,]  0.286812663
 [86,] -0.842758920
 [87,] -0.520308714
 [88,]  1.378371048
 [89,]  0.218770433
 [90,]  1.324886147
 [91,]  1.116288852
 [92,] -0.024839814
 [93,]  0.985103828
 [94,]  2.012495825
 [95,]  0.852873116
 [96,]  0.180587142
 [97,]  0.383634868
 [98,]  0.154356489
 [99,]  1.538637456
[100,]  0.596852285
[101,] -0.867515056
[102,]  0.696536401
[103,] -0.560133976
[104,]  0.046830701
[105,] -0.294059697
[106,] -0.797736709
[107,]  1.556289178
[108,] -0.418663020
[109,]  0.709063226
[110,] -1.914596301
[111,] -0.690443405
[112,]  0.420292431
[113,] -0.417849815
[114,]  1.158379741
[115,]  0.440794883
[116,] -0.673986887
[117,] -0.254768327
[118,] -2.548124795
[119,] -0.017721580
[120,]  1.701046715
[121,] -0.907427443
[122,]  0.569855257
[123,] -0.412259950
[124,]  0.480202496
[125,] -1.010536476
[126,] -1.004412720
[127,]  0.315338060
[128,] -0.064131184
[129,]  0.186735633
[130,] -0.560413289
[131,] -0.258418706
[132,] -2.617554417
[133,]  0.177953334
[134,]  0.291944582
[135,]  0.808606364
[136,] -0.853942542
[137,] -1.065013214
[138,] -0.421020154
[139,] -0.017165594
[140,] -0.673870645
[141,] -0.611835930
[142,] -0.687273065
[143,]  0.696536401
[144,] -0.864624030
[145,] -1.045665670
[146,] -0.385674038
[147,]  0.893692855
[148,] -0.268170747
[149,] -1.007877934
[150,]  0.024250427
                PC3
  [1,]  0.127279624
  [2,]  0.233825517
  [3,] -0.044053900
  [4,] -0.090985297
  [5,] -0.015685647
  [6,] -0.026878250
  [7,] -0.334350297
  [8,]  0.088399352
  [9,] -0.144592465
 [10,]  0.252918268
 [11,]  0.267784001
 [12,] -0.093446191
 [13,]  0.230140246
 [14,] -0.180192423
 [15,]  0.471322025
 [16,] -0.030424684
 [17,]  0.005326251
 [18,]  0.044067686
 [19,]  0.373093377
 [20,] -0.132187626
 [21,]  0.419885937
 [22,] -0.159331502
 [23,] -0.331069982
 [24,] -0.034373442
 [25,] -0.117599566
 [26,]  0.304620475
 [27,] -0.086075649
 [28,]  0.206125707
 [29,]  0.270244895
 [30,] -0.068207276
 [31,]  0.074757996
 [32,]  0.269564311
 [33,] -0.047070727
 [34,]  0.082392024
 [35,]  0.169706329
 [36,]  0.224688852
 [37,]  0.482919584
 [38,] -0.019370918
 [39,] -0.192609402
 [40,]  0.175296561
 [41,] -0.034778398
 [42,]  0.203552303
 [43,] -0.304745527
 [44,] -0.308567588
 [45,] -0.247604064
 [46,]  0.063716370
 [47,] -0.057026813
 [48,] -0.139002234
 [49,]  0.180886792
 [50,]  0.152518539
 [51,]  0.682300393
 [52,]  0.093807452
 [53,]  0.552157058
 [54,]  0.023024633
 [55,]  0.396925784
 [56,] -0.123776885
 [57,] -0.148472007
 [58,] -0.248432992
 [59,]  0.594178807
 [60,] -0.537100055
 [61,]  0.046634215
 [62,] -0.204389093
 [63,]  0.763214554
 [64,]  0.068429700
 [65,] -0.194282030
 [66,]  0.501830204
 [67,] -0.489234095
 [68,]  0.301028700
 [69,]  0.480693656
 [70,]  0.172260719
 [71,] -0.614467782
 [72,]  0.264067576
 [73,]  0.367182178
 [74,]  0.290921638
 [75,]  0.444537765
 [76,]  0.471001057
 [77,]  0.724727099
 [78,]  0.259955701
 [79,] -0.085577197
 [80,]  0.318506304
 [81,]  0.149482697
 [82,]  0.240745761
 [83,]  0.150707074
 [84,] -0.104959762
 [85,] -0.663028512
 [86,] -0.449129446
 [87,]  0.394464890
 [88,]  0.685997804
 [89,] -0.290605718
 [90,] -0.089111491
 [91,] -0.094172116
 [92,]  0.020412763
 [93,]  0.198724011
 [94,] -0.105467721
 [95,] -0.130452657
 [96,] -0.128547696
 [97,] -0.155691572
 [98,]  0.270743347
 [99,] -0.189765199
[100,] -0.091572385
[101,] -1.002044077
[102,] -0.528389994
[103,]  0.202236658
[104,] -0.163083761
[105,] -0.394307408
[106,]  0.580364827
[107,] -0.983598122
[108,]  0.649530452
[109,]  0.392675073
[110,] -0.396224508
[111,] -0.283661780
[112,] -0.023108991
[113,] -0.026250468
[114,] -0.578311891
[115,] -1.000517746
[116,] -0.636297054
[117,] -0.037306280
[118,]  0.127454475
[119,]  0.700957033
[120,]  0.266643612
[121,] -0.234015510
[122,] -0.825362161
[123,]  0.854558973
[124,]  0.005410239
[125,] -0.297454114
[126,]  0.418582432
[127,] -0.129503907
[128,] -0.336588365
[129,] -0.269754304
[130,]  0.713244682
[131,]  0.725386035
[132,]  0.491826144
[133,] -0.352966242
[134,]  0.182875741
[135,]  0.164173760
[136,]  0.541093785
[137,] -0.942695700
[138,] -0.180271551
[139,] -0.415434449
[140,]  0.012629804
[141,] -0.426902678
[142,] -0.129640697
[143,] -0.528389994
[144,] -0.337014969
[145,] -0.630301866
[146,] -0.255418178
[147,]  0.026283300
[148,] -0.179576781
[149,] -0.930278721
[150,] -0.526485033
                PC4
  [1,]  0.024087508
  [2,]  0.102662845
  [3,]  0.028282305
  [4,] -0.065735340
  [5,] -0.035802870
  [6,]  0.006586116
  [7,] -0.036652767
  [8,] -0.024529919
  [9,] -0.026769540
 [10,] -0.039766068
 [11,]  0.016675503
 [12,] -0.133037725
 [13,]  0.002416941
 [14,] -0.019151375
 [15,]  0.194081578
 [16,]  0.050365010
 [17,]  0.188186988
 [18,]  0.092779618
 [19,]  0.060891973
 [20,] -0.037630354
 [21,]  0.010884821
 [22,]  0.059398340
 [23,]  0.019582826
 [24,]  0.150636353
 [25,] -0.269238379
 [26,]  0.043416203
 [27,]  0.067454082
 [28,]  0.010241084
 [29,]  0.083977887
 [30,] -0.107918349
 [31,] -0.048027970
 [32,]  0.239069476
 [33,] -0.228470534
 [34,] -0.048053409
 [35,]  0.028926042
 [36,]  0.168343905
 [37,]  0.195702902
 [38,] -0.136048774
 [39,] -0.009705907
 [40,]  0.007023875
 [41,]  0.106626042
 [42,]  0.288896090
 [43,] -0.066379077
 [44,]  0.176501717
 [45,] -0.150539117
 [46,]  0.139801160
 [47,] -0.151722682
 [48,] -0.048671707
 [49,] -0.014878291
 [50,]  0.049206884
 [51,]  0.034717469
 [52,]  0.004887251
 [53,]  0.009391933
 [54,]  0.065549239
 [55,]  0.104387166
 [56,] -0.240027187
 [57,] -0.077111455
 [58,] -0.040384912
 [59,] -0.029779844
 [60,] -0.028366154
 [61,]  0.013714785
 [62,]  0.039992104
 [63,]  0.045578465
 [64,] -0.164256922
 [65,]  0.108684396
 [66,]  0.104593326
 [67,] -0.190869932
 [68,] -0.204612265
 [69,]  0.225145511
 [70,] -0.051554138
 [71,] -0.083006045
 [72,]  0.113189079
 [73,] -0.009911322
 [74,] -0.273304557
 [75,]  0.043313222
 [76,]  0.101376117
 [77,]  0.039556002
 [78,]  0.066604931
 [79,] -0.036318171
 [80,]  0.064571834
 [81,] -0.009371129
 [82,] -0.032663020
 [83,]  0.023572390
 [84,] -0.183354200
 [85,] -0.253977520
 [86,] -0.109308985
 [87,]  0.037084781
 [88,]  0.136378719
 [89,] -0.146653279
 [90,]  0.008876070
 [91,] -0.269753497
 [92,] -0.147193289
 [93,]  0.006508757
 [94,]  0.019505467
 [95,] -0.107043742
 [96,] -0.229191812
 [97,] -0.132163118
 [98,] -0.019794366
 [99,]  0.199278855
[100,] -0.058426315
[101,] -0.049085303
[102,] -0.040385459
[103,]  0.058986583
[104,] -0.234982858
[105,] -0.016243853
[106,] -0.101045973
[107,] -0.132679346
[108,] -0.237246445
[109,] -0.086221779
[110,]  0.104488870
[111,]  0.107500284
[112,]  0.058136869
[113,]  0.145926073
[114,]  0.098826244
[115,]  0.274738504
[116,]  0.191222383
[117,] -0.154811637
[118,] -0.272892966
[119,]  0.045037725
[120,] -0.064963167
[121,]  0.167390481
[122,]  0.027662914
[123,] -0.126911337
[124,]  0.139491837
[125,] -0.061437911
[126,] -0.217609339
[127,]  0.125001677
[128,] -0.008625505
[129,]  0.030983849
[130,] -0.207519953
[131,] -0.017863520
[132,] -0.210968943
[133,]  0.099675959
[134,] -0.185721512
[135,] -0.487849130
[136,]  0.294893130
[137,]  0.035486875
[138,] -0.214702016
[139,]  0.005220919
[140,]  0.194543500
[141,]  0.246711805
[142,]  0.468128374
[143,] -0.040385459
[144,]  0.045036251
[145,]  0.213330527
[146,]  0.387957152
[147,]  0.219456899
[148,]  0.118773236
[149,]  0.026041407
[150,] -0.162533529

##To extract data in a data frame

PCA_1_2 =as.data.frame(iris_PCA$x[ , 1:2])
head(PCA_1_2)

#head: start 6 ta data, print: 150 data show korbe

column bind

PCA_1_2 =as.data.frame(iris_PCA$x[ , 1:2])
head(PCA_1_2)

#head: start 6 ta data, print: 150 data show korbe

PCA_1_2_class = cbind(PCA_1_2,variety = iris$variety)
PCA_1_2_class

PCA plot

ggplot(PCA_1_2_class, aes(PC1, PC2, color= variety))+
  geom_point()+
  theme_minimal()

library(factoextra)

Warning: package ‘factoextra’ was built under R version 4.3.3Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

fviz_eig(iris_PCA, addlabels = TRUE)

To show contribution of variance

fviz_pca_var(iris_PCA, col.var = "contrib")

Visualization plot

library("corrplot")
var = get_pca_var(iris_PCA)
corrplot(var$cos2)

Cluster plot

fviz_pca_ind(iris_PCA,
             geom.ind = "point",
             col.ind = iris$variety,
             addEllipses = TRUE)