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Thursday, June 25, 2020

Principal Component Analysis (PCA) in Python

Principal Component Analysis (PCA) in Python



0_MacOS_Python_setup.txt
# Install on Terminal of MacOS

# 1. pandas
#pip3 install -U pandas

# 2. NumPy
#pip3 install -U numpy

# 3. matplotlib
#pip3 install -U matplotlib

# 4. scikit-learn (sklearn)
#pip3 install -U scikit-learn


1_MacOS_Terminal.txt
########## Run Terminal on MacOS and execute
### TO UPDATE
cd "YOUR_WORKING_DIRECTORY"

python3 pca.py wine.csv

#python3 pca.py wine4data.csv



Input data files



wine.csv
,class,Alcohol,Malic acid,Ash,Alcalinity of ash,Magnesium,Total phenols,Flavanoids,Nonflavanoid phenols,Proanthocyanins,Color intensity,Hue,OD280/OD315 of diluted wines,Proline
0,1,14.23,1.71,2.43,15.6,127,2.8,3.06,0.28,2.29,5.64,1.04,3.92,1065
1,1,13.2,1.78,2.14,11.2,100,2.65,2.76,0.26,1.28,4.38,1.05,3.4,1050
2,1,13.16,2.36,2.67,18.6,101,2.8,3.24,0.3,2.81,5.68,1.03,3.17,1185
3,1,14.37,1.95,2.5,16.8,113,3.85,3.49,0.24,2.18,7.8,0.86,3.45,1480
4,1,13.24,2.59,2.87,21.0,118,2.8,2.69,0.39,1.82,4.32,1.04,2.93,735
5,1,14.2,1.76,2.45,15.2,112,3.27,3.39,0.34,1.97,6.75,1.05,2.85,1450
6,1,14.39,1.87,2.45,14.6,96,2.5,2.52,0.3,1.98,5.25,1.02,3.58,1290
7,1,14.06,2.15,2.61,17.6,121,2.6,2.51,0.31,1.25,5.05,1.06,3.58,1295
8,1,14.83,1.64,2.17,14.0,97,2.8,2.98,0.29,1.98,5.2,1.08,2.85,1045
9,1,13.86,1.35,2.27,16.0,98,2.98,3.15,0.22,1.85,7.22,1.01,3.55,1045
10,1,14.1,2.16,2.3,18.0,105,2.95,3.32,0.22,2.38,5.75,1.25,3.17,1510
11,1,14.12,1.48,2.32,16.8,95,2.2,2.43,0.26,1.57,5.0,1.17,2.82,1280
12,1,13.75,1.73,2.41,16.0,89,2.6,2.76,0.29,1.81,5.6,1.15,2.9,1320
13,1,14.75,1.73,2.39,11.4,91,3.1,3.69,0.43,2.81,5.4,1.25,2.73,1150
14,1,14.38,1.87,2.38,12.0,102,3.3,3.64,0.29,2.96,7.5,1.2,3.0,1547
15,1,13.63,1.81,2.7,17.2,112,2.85,2.91,0.3,1.46,7.3,1.28,2.88,1310
16,1,14.3,1.92,2.72,20.0,120,2.8,3.14,0.33,1.97,6.2,1.07,2.65,1280
17,1,13.83,1.57,2.62,20.0,115,2.95,3.4,0.4,1.72,6.6,1.13,2.57,1130
18,1,14.19,1.59,2.48,16.5,108,3.3,3.93,0.32,1.86,8.7,1.23,2.82,1680
19,1,13.64,3.1,2.56,15.2,116,2.7,3.03,0.17,1.66,5.1,0.96,3.36,845
20,1,14.06,1.63,2.28,16.0,126,3.0,3.17,0.24,2.1,5.65,1.09,3.71,780
21,1,12.93,3.8,2.65,18.6,102,2.41,2.41,0.25,1.98,4.5,1.03,3.52,770
22,1,13.71,1.86,2.36,16.6,101,2.61,2.88,0.27,1.69,3.8,1.11,4.0,1035
23,1,12.85,1.6,2.52,17.8,95,2.48,2.37,0.26,1.46,3.93,1.09,3.63,1015
24,1,13.5,1.81,2.61,20.0,96,2.53,2.61,0.28,1.66,3.52,1.12,3.82,845
25,1,13.05,2.05,3.22,25.0,124,2.63,2.68,0.47,1.92,3.58,1.13,3.2,830
26,1,13.39,1.77,2.62,16.1,93,2.85,2.94,0.34,1.45,4.8,0.92,3.22,1195
27,1,13.3,1.72,2.14,17.0,94,2.4,2.19,0.27,1.35,3.95,1.02,2.77,1285
28,1,13.87,1.9,2.8,19.4,107,2.95,2.97,0.37,1.76,4.5,1.25,3.4,915
29,1,14.02,1.68,2.21,16.0,96,2.65,2.33,0.26,1.98,4.7,1.04,3.59,1035
30,1,13.73,1.5,2.7,22.5,101,3.0,3.25,0.29,2.38,5.7,1.19,2.71,1285
31,1,13.58,1.66,2.36,19.1,106,2.86,3.19,0.22,1.95,6.9,1.09,2.88,1515
32,1,13.68,1.83,2.36,17.2,104,2.42,2.69,0.42,1.97,3.84,1.23,2.87,990
33,1,13.76,1.53,2.7,19.5,132,2.95,2.74,0.5,1.35,5.4,1.25,3.0,1235
34,1,13.51,1.8,2.65,19.0,110,2.35,2.53,0.29,1.54,4.2,1.1,2.87,1095
35,1,13.48,1.81,2.41,20.5,100,2.7,2.98,0.26,1.86,5.1,1.04,3.47,920
36,1,13.28,1.64,2.84,15.5,110,2.6,2.68,0.34,1.36,4.6,1.09,2.78,880
37,1,13.05,1.65,2.55,18.0,98,2.45,2.43,0.29,1.44,4.25,1.12,2.51,1105
38,1,13.07,1.5,2.1,15.5,98,2.4,2.64,0.28,1.37,3.7,1.18,2.69,1020
39,1,14.22,3.99,2.51,13.2,128,3.0,3.04,0.2,2.08,5.1,0.89,3.53,760
40,1,13.56,1.71,2.31,16.2,117,3.15,3.29,0.34,2.34,6.13,0.95,3.38,795
41,1,13.41,3.84,2.12,18.8,90,2.45,2.68,0.27,1.48,4.28,0.91,3.0,1035
42,1,13.88,1.89,2.59,15.0,101,3.25,3.56,0.17,1.7,5.43,0.88,3.56,1095
43,1,13.24,3.98,2.29,17.5,103,2.64,2.63,0.32,1.66,4.36,0.82,3.0,680
44,1,13.05,1.77,2.1,17.0,107,3.0,3.0,0.28,2.03,5.04,0.88,3.35,885
45,1,14.21,4.04,2.44,18.9,111,2.85,2.65,0.3,1.25,5.24,0.87,3.33,1080
46,1,14.38,3.59,2.28,16.0,102,3.25,3.17,0.27,2.19,4.9,1.04,3.44,1065
47,1,13.9,1.68,2.12,16.0,101,3.1,3.39,0.21,2.14,6.1,0.91,3.33,985
48,1,14.1,2.02,2.4,18.8,103,2.75,2.92,0.32,2.38,6.2,1.07,2.75,1060
49,1,13.94,1.73,2.27,17.4,108,2.88,3.54,0.32,2.08,8.9,1.12,3.1,1260
50,1,13.05,1.73,2.04,12.4,92,2.72,3.27,0.17,2.91,7.2,1.12,2.91,1150
51,1,13.83,1.65,2.6,17.2,94,2.45,2.99,0.22,2.29,5.6,1.24,3.37,1265
52,1,13.82,1.75,2.42,14.0,111,3.88,3.74,0.32,1.87,7.05,1.01,3.26,1190
53,1,13.77,1.9,2.68,17.1,115,3.0,2.79,0.39,1.68,6.3,1.13,2.93,1375
54,1,13.74,1.67,2.25,16.4,118,2.6,2.9,0.21,1.62,5.85,0.92,3.2,1060
55,1,13.56,1.73,2.46,20.5,116,2.96,2.78,0.2,2.45,6.25,0.98,3.03,1120
56,1,14.22,1.7,2.3,16.3,118,3.2,3.0,0.26,2.03,6.38,0.94,3.31,970
57,1,13.29,1.97,2.68,16.8,102,3.0,3.23,0.31,1.66,6.0,1.07,2.84,1270
58,1,13.72,1.43,2.5,16.7,108,3.4,3.67,0.19,2.04,6.8,0.89,2.87,1285
59,2,12.37,0.94,1.36,10.6,88,1.98,0.57,0.28,0.42,1.95,1.05,1.82,520
60,2,12.33,1.1,2.28,16.0,101,2.05,1.09,0.63,0.41,3.27,1.25,1.67,680
61,2,12.64,1.36,2.02,16.8,100,2.02,1.41,0.53,0.62,5.75,0.98,1.59,450
62,2,13.67,1.25,1.92,18.0,94,2.1,1.79,0.32,0.73,3.8,1.23,2.46,630
63,2,12.37,1.13,2.16,19.0,87,3.5,3.1,0.19,1.87,4.45,1.22,2.87,420
64,2,12.17,1.45,2.53,19.0,104,1.89,1.75,0.45,1.03,2.95,1.45,2.23,355
65,2,12.37,1.21,2.56,18.1,98,2.42,2.65,0.37,2.08,4.6,1.19,2.3,678
66,2,13.11,1.01,1.7,15.0,78,2.98,3.18,0.26,2.28,5.3,1.12,3.18,502
67,2,12.37,1.17,1.92,19.6,78,2.11,2.0,0.27,1.04,4.68,1.12,3.48,510
68,2,13.34,0.94,2.36,17.0,110,2.53,1.3,0.55,0.42,3.17,1.02,1.93,750
69,2,12.21,1.19,1.75,16.8,151,1.85,1.28,0.14,2.5,2.85,1.28,3.07,718
70,2,12.29,1.61,2.21,20.4,103,1.1,1.02,0.37,1.46,3.05,0.9060000000000000,1.82,870
71,2,13.86,1.51,2.67,25.0,86,2.95,2.86,0.21,1.87,3.38,1.36,3.16,410
72,2,13.49,1.66,2.24,24.0,87,1.88,1.84,0.27,1.03,3.74,0.98,2.78,472
73,2,12.99,1.67,2.6,30.0,139,3.3,2.89,0.21,1.96,3.35,1.31,3.5,985
74,2,11.96,1.09,2.3,21.0,101,3.38,2.14,0.13,1.65,3.21,0.99,3.13,886
75,2,11.66,1.88,1.92,16.0,97,1.61,1.57,0.34,1.15,3.8,1.23,2.14,428
76,2,13.03,0.9,1.71,16.0,86,1.95,2.03,0.24,1.46,4.6,1.19,2.48,392
77,2,11.84,2.89,2.23,18.0,112,1.72,1.32,0.43,0.95,2.65,0.96,2.52,500
78,2,12.33,0.99,1.95,14.8,136,1.9,1.85,0.35,2.76,3.4,1.06,2.31,750
79,2,12.7,3.87,2.4,23.0,101,2.83,2.55,0.43,1.95,2.57,1.19,3.13,463
80,2,12.0,0.92,2.0,19.0,86,2.42,2.26,0.3,1.43,2.5,1.38,3.12,278
81,2,12.72,1.81,2.2,18.8,86,2.2,2.53,0.26,1.77,3.9,1.16,3.14,714
82,2,12.08,1.13,2.51,24.0,78,2.0,1.58,0.4,1.4,2.2,1.31,2.72,630
83,2,13.05,3.86,2.32,22.5,85,1.65,1.59,0.61,1.62,4.8,0.84,2.01,515
84,2,11.84,0.89,2.58,18.0,94,2.2,2.21,0.22,2.35,3.05,0.79,3.08,520
85,2,12.67,0.98,2.24,18.0,99,2.2,1.94,0.3,1.46,2.62,1.23,3.16,450
86,2,12.16,1.61,2.31,22.8,90,1.78,1.69,0.43,1.56,2.45,1.33,2.26,495
87,2,11.65,1.67,2.62,26.0,88,1.92,1.61,0.4,1.34,2.6,1.36,3.21,562
88,2,11.64,2.06,2.46,21.6,84,1.95,1.69,0.48,1.35,2.8,1.0,2.75,680
89,2,12.08,1.33,2.3,23.6,70,2.2,1.59,0.42,1.38,1.74,1.07,3.21,625
90,2,12.08,1.83,2.32,18.5,81,1.6,1.5,0.52,1.64,2.4,1.08,2.27,480
91,2,12.0,1.51,2.42,22.0,86,1.45,1.25,0.5,1.63,3.6,1.05,2.65,450
92,2,12.69,1.53,2.26,20.7,80,1.38,1.46,0.58,1.62,3.05,0.96,2.06,495
93,2,12.29,2.83,2.22,18.0,88,2.45,2.25,0.25,1.99,2.15,1.15,3.3,290
94,2,11.62,1.99,2.28,18.0,98,3.02,2.26,0.17,1.35,3.25,1.16,2.96,345
95,2,12.47,1.52,2.2,19.0,162,2.5,2.27,0.32,3.28,2.6,1.16,2.63,937
96,2,11.81,2.12,2.74,21.5,134,1.6,0.99,0.14,1.56,2.5,0.95,2.26,625
97,2,12.29,1.41,1.98,16.0,85,2.55,2.5,0.29,1.77,2.9,1.23,2.74,428
98,2,12.37,1.07,2.1,18.5,88,3.52,3.75,0.24,1.95,4.5,1.04,2.77,660
99,2,12.29,3.17,2.21,18.0,88,2.85,2.99,0.45,2.81,2.3,1.42,2.83,406
100,2,12.08,2.08,1.7,17.5,97,2.23,2.17,0.26,1.4,3.3,1.27,2.96,710
101,2,12.6,1.34,1.9,18.5,88,1.45,1.36,0.29,1.35,2.45,1.04,2.77,562
102,2,12.34,2.45,2.46,21.0,98,2.56,2.11,0.34,1.31,2.8,0.8,3.38,438
103,2,11.82,1.72,1.88,19.5,86,2.5,1.64,0.37,1.42,2.06,0.94,2.44,415
104,2,12.51,1.73,1.98,20.5,85,2.2,1.92,0.32,1.48,2.94,1.04,3.57,672
105,2,12.42,2.55,2.27,22.0,90,1.68,1.84,0.66,1.42,2.7,0.86,3.3,315
106,2,12.25,1.73,2.12,19.0,80,1.65,2.03,0.37,1.63,3.4,1.0,3.17,510
107,2,12.72,1.75,2.28,22.5,84,1.38,1.76,0.48,1.63,3.3,0.88,2.42,488
108,2,12.22,1.29,1.94,19.0,92,2.36,2.04,0.39,2.08,2.7,0.86,3.02,312
109,2,11.61,1.35,2.7,20.0,94,2.74,2.92,0.29,2.49,2.65,0.96,3.26,680
110,2,11.46,3.74,1.82,19.5,107,3.18,2.58,0.24,3.58,2.9,0.75,2.81,562
111,2,12.52,2.43,2.17,21.0,88,2.55,2.27,0.26,1.22,2.0,0.9,2.78,325
112,2,11.76,2.68,2.92,20.0,103,1.75,2.03,0.6,1.05,3.8,1.23,2.5,607
113,2,11.41,0.74,2.5,21.0,88,2.48,2.01,0.42,1.44,3.08,1.1,2.31,434
114,2,12.08,1.39,2.5,22.5,84,2.56,2.29,0.43,1.04,2.9,0.93,3.19,385
115,2,11.03,1.51,2.2,21.5,85,2.46,2.17,0.52,2.01,1.9,1.71,2.87,407
116,2,11.82,1.47,1.99,20.8,86,1.98,1.6,0.3,1.53,1.95,0.95,3.33,495
117,2,12.42,1.61,2.19,22.5,108,2.0,2.09,0.34,1.61,2.06,1.06,2.96,345
118,2,12.77,3.43,1.98,16.0,80,1.63,1.25,0.43,0.83,3.4,0.7,2.12,372
119,2,12.0,3.43,2.0,19.0,87,2.0,1.64,0.37,1.87,1.28,0.93,3.05,564
120,2,11.45,2.4,2.42,20.0,96,2.9,2.79,0.32,1.83,3.25,0.8,3.39,625
121,2,11.56,2.05,3.23,28.5,119,3.18,5.08,0.47,1.87,6.0,0.93,3.69,465
122,2,12.42,4.43,2.73,26.5,102,2.2,2.13,0.43,1.71,2.08,0.92,3.12,365
123,2,13.05,5.8,2.13,21.5,86,2.62,2.65,0.3,2.01,2.6,0.73,3.1,380
124,2,11.87,4.31,2.39,21.0,82,2.86,3.03,0.21,2.91,2.8,0.75,3.64,380
125,2,12.07,2.16,2.17,21.0,85,2.6,2.65,0.37,1.35,2.76,0.86,3.28,378
126,2,12.43,1.53,2.29,21.5,86,2.74,3.15,0.39,1.77,3.94,0.69,2.84,352
127,2,11.79,2.13,2.78,28.5,92,2.13,2.24,0.58,1.76,3.0,0.97,2.44,466
128,2,12.37,1.63,2.3,24.5,88,2.22,2.45,0.4,1.9,2.12,0.89,2.78,342
129,2,12.04,4.3,2.38,22.0,80,2.1,1.75,0.42,1.35,2.6,0.79,2.57,580
130,3,12.86,1.35,2.32,18.0,122,1.51,1.25,0.21,0.94,4.1,0.76,1.29,630
131,3,12.88,2.99,2.4,20.0,104,1.3,1.22,0.24,0.83,5.4,0.74,1.42,530
132,3,12.81,2.31,2.4,24.0,98,1.15,1.09,0.27,0.83,5.7,0.66,1.36,560
133,3,12.7,3.55,2.36,21.5,106,1.7,1.2,0.17,0.84,5.0,0.78,1.29,600
134,3,12.51,1.24,2.25,17.5,85,2.0,0.58,0.6,1.25,5.45,0.75,1.51,650
135,3,12.6,2.46,2.2,18.5,94,1.62,0.66,0.63,0.94,7.1,0.73,1.58,695
136,3,12.25,4.72,2.54,21.0,89,1.38,0.47,0.53,0.8,3.85,0.75,1.27,720
137,3,12.53,5.51,2.64,25.0,96,1.79,0.6,0.63,1.1,5.0,0.82,1.69,515
138,3,13.49,3.59,2.19,19.5,88,1.62,0.48,0.58,0.88,5.7,0.81,1.82,580
139,3,12.84,2.96,2.61,24.0,101,2.32,0.6,0.53,0.81,4.92,0.89,2.15,590
140,3,12.93,2.81,2.7,21.0,96,1.54,0.5,0.53,0.75,4.6,0.77,2.31,600
141,3,13.36,2.56,2.35,20.0,89,1.4,0.5,0.37,0.64,5.6,0.7,2.47,780
142,3,13.52,3.17,2.72,23.5,97,1.55,0.52,0.5,0.55,4.35,0.89,2.06,520
143,3,13.62,4.95,2.35,20.0,92,2.0,0.8,0.47,1.02,4.4,0.91,2.05,550
144,3,12.25,3.88,2.2,18.5,112,1.38,0.78,0.29,1.14,8.21,0.65,2.0,855
145,3,13.16,3.57,2.15,21.0,102,1.5,0.55,0.43,1.3,4.0,0.6,1.68,830
146,3,13.88,5.04,2.23,20.0,80,0.98,0.34,0.4,0.68,4.9,0.58,1.33,415
147,3,12.87,4.61,2.48,21.5,86,1.7,0.65,0.47,0.86,7.65,0.54,1.86,625
148,3,13.32,3.24,2.38,21.5,92,1.93,0.76,0.45,1.25,8.42,0.55,1.62,650
149,3,13.08,3.9,2.36,21.5,113,1.41,1.39,0.34,1.14,9.4,0.57,1.33,550
150,3,13.5,3.12,2.62,24.0,123,1.4,1.57,0.22,1.25,8.6,0.59,1.3,500
151,3,12.79,2.67,2.48,22.0,112,1.48,1.36,0.24,1.26,10.8,0.48,1.47,480
152,3,13.11,1.9,2.75,25.5,116,2.2,1.28,0.26,1.56,7.1,0.61,1.33,425
153,3,13.23,3.3,2.28,18.5,98,1.8,0.83,0.61,1.87,10.52,0.56,1.51,675
154,3,12.58,1.29,2.1,20.0,103,1.48,0.58,0.53,1.4,7.6,0.58,1.55,640
155,3,13.17,5.19,2.32,22.0,93,1.74,0.63,0.61,1.55,7.9,0.6,1.48,725
156,3,13.84,4.12,2.38,19.5,89,1.8,0.83,0.48,1.56,9.01,0.57,1.64,480
157,3,12.45,3.03,2.64,27.0,97,1.9,0.58,0.63,1.14,7.5,0.67,1.73,880
158,3,14.34,1.68,2.7,25.0,98,2.8,1.31,0.53,2.7,13.0,0.57,1.96,660
159,3,13.48,1.67,2.64,22.5,89,2.6,1.1,0.52,2.29,11.75,0.57,1.78,620
160,3,12.36,3.83,2.38,21.0,88,2.3,0.92,0.5,1.04,7.65,0.56,1.58,520
161,3,13.69,3.26,2.54,20.0,107,1.83,0.56,0.5,0.8,5.88,0.96,1.82,680
162,3,12.85,3.27,2.58,22.0,106,1.65,0.6,0.6,0.96,5.58,0.87,2.11,570
163,3,12.96,3.45,2.35,18.5,106,1.39,0.7,0.4,0.94,5.28,0.68,1.75,675
164,3,13.78,2.76,2.3,22.0,90,1.35,0.68,0.41,1.03,9.58,0.7,1.68,615
165,3,13.73,4.36,2.26,22.5,88,1.28,0.47,0.52,1.15,6.62,0.78,1.75,520
166,3,13.45,3.7,2.6,23.0,111,1.7,0.92,0.43,1.46,10.68,0.85,1.56,695
167,3,12.82,3.37,2.3,19.5,88,1.48,0.66,0.4,0.97,10.26,0.72,1.75,685
168,3,13.58,2.58,2.69,24.5,105,1.55,0.84,0.39,1.54,8.66,0.74,1.8,750
169,3,13.4,4.6,2.86,25.0,112,1.98,0.96,0.27,1.11,8.5,0.67,1.92,630
170,3,12.2,3.03,2.32,19.0,96,1.25,0.49,0.4,0.73,5.5,0.66,1.83,510
171,3,12.77,2.39,2.28,19.5,86,1.39,0.51,0.48,0.64,9.899999000000000,0.57,1.63,470
172,3,14.16,2.51,2.48,20.0,91,1.68,0.7,0.44,1.24,9.7,0.62,1.71,660
173,3,13.71,5.65,2.45,20.5,95,1.68,0.61,0.52,1.06,7.7,0.64,1.74,740
174,3,13.4,3.91,2.48,23.0,102,1.8,0.75,0.43,1.41,7.3,0.7,1.56,750
175,3,13.27,4.28,2.26,20.0,120,1.59,0.69,0.43,1.35,10.2,0.59,1.56,835
176,3,13.17,2.59,2.37,20.0,120,1.65,0.68,0.53,1.46,9.3,0.6,1.62,840
177,3,14.13,4.1,2.74,24.5,96,2.05,0.76,0.56,1.35,9.2,0.61,1.6,560



wine4data.csv
,class,Alcohol,Flavanoids,Color intensity,Proline
0,1,14.23,3.06,5.64,1065
1,1,13.2,2.76,4.38,1050
2,1,13.16,3.24,5.68,1185
3,1,14.37,3.49,7.8,1480
4,1,13.24,2.69,4.32,735
5,1,14.2,3.39,6.75,1450
6,1,14.39,2.52,5.25,1290
7,1,14.06,2.51,5.05,1295
8,1,14.83,2.98,5.2,1045
9,1,13.86,3.15,7.22,1045
10,1,14.1,3.32,5.75,1510
11,1,14.12,2.43,5.0,1280
12,1,13.75,2.76,5.6,1320
13,1,14.75,3.69,5.4,1150
14,1,14.38,3.64,7.5,1547
15,1,13.63,2.91,7.3,1310
16,1,14.3,3.14,6.2,1280
17,1,13.83,3.4,6.6,1130
18,1,14.19,3.93,8.7,1680
19,1,13.64,3.03,5.1,845
20,1,14.06,3.17,5.65,780
21,1,12.93,2.41,4.5,770
22,1,13.71,2.88,3.8,1035
23,1,12.85,2.37,3.93,1015
24,1,13.5,2.61,3.52,845
25,1,13.05,2.68,3.58,830
26,1,13.39,2.94,4.8,1195
27,1,13.3,2.19,3.95,1285
28,1,13.87,2.97,4.5,915
29,1,14.02,2.33,4.7,1035
30,1,13.73,3.25,5.7,1285
31,1,13.58,3.19,6.9,1515
32,1,13.68,2.69,3.84,990
33,1,13.76,2.74,5.4,1235
34,1,13.51,2.53,4.2,1095
35,1,13.48,2.98,5.1,920
36,1,13.28,2.68,4.6,880
37,1,13.05,2.43,4.25,1105
38,1,13.07,2.64,3.7,1020
39,1,14.22,3.04,5.1,760
40,1,13.56,3.29,6.13,795
41,1,13.41,2.68,4.28,1035
42,1,13.88,3.56,5.43,1095
43,1,13.24,2.63,4.36,680
44,1,13.05,3.0,5.04,885
45,1,14.21,2.65,5.24,1080
46,1,14.38,3.17,4.9,1065
47,1,13.9,3.39,6.1,985
48,1,14.1,2.92,6.2,1060
49,1,13.94,3.54,8.9,1260
50,1,13.05,3.27,7.2,1150
51,1,13.83,2.99,5.6,1265
52,1,13.82,3.74,7.05,1190
53,1,13.77,2.79,6.3,1375
54,1,13.74,2.9,5.85,1060
55,1,13.56,2.78,6.25,1120
56,1,14.22,3.0,6.38,970
57,1,13.29,3.23,6.0,1270
58,1,13.72,3.67,6.8,1285
59,2,12.37,0.57,1.95,520
60,2,12.33,1.09,3.27,680
61,2,12.64,1.41,5.75,450
62,2,13.67,1.79,3.8,630
63,2,12.37,3.1,4.45,420
64,2,12.17,1.75,2.95,355
65,2,12.37,2.65,4.6,678
66,2,13.11,3.18,5.3,502
67,2,12.37,2.0,4.68,510
68,2,13.34,1.3,3.17,750
69,2,12.21,1.28,2.85,718
70,2,12.29,1.02,3.05,870
71,2,13.86,2.86,3.38,410
72,2,13.49,1.84,3.74,472
73,2,12.99,2.89,3.35,985
74,2,11.96,2.14,3.21,886
75,2,11.66,1.57,3.8,428
76,2,13.03,2.03,4.6,392
77,2,11.84,1.32,2.65,500
78,2,12.33,1.85,3.4,750
79,2,12.7,2.55,2.57,463
80,2,12.0,2.26,2.5,278
81,2,12.72,2.53,3.9,714
82,2,12.08,1.58,2.2,630
83,2,13.05,1.59,4.8,515
84,2,11.84,2.21,3.05,520
85,2,12.67,1.94,2.62,450
86,2,12.16,1.69,2.45,495
87,2,11.65,1.61,2.6,562
88,2,11.64,1.69,2.8,680
89,2,12.08,1.59,1.74,625
90,2,12.08,1.5,2.4,480
91,2,12.0,1.25,3.6,450
92,2,12.69,1.46,3.05,495
93,2,12.29,2.25,2.15,290
94,2,11.62,2.26,3.25,345
95,2,12.47,2.27,2.6,937
96,2,11.81,0.99,2.5,625
97,2,12.29,2.5,2.9,428
98,2,12.37,3.75,4.5,660
99,2,12.29,2.99,2.3,406
100,2,12.08,2.17,3.3,710
101,2,12.6,1.36,2.45,562
102,2,12.34,2.11,2.8,438
103,2,11.82,1.64,2.06,415
104,2,12.51,1.92,2.94,672
105,2,12.42,1.84,2.7,315
106,2,12.25,2.03,3.4,510
107,2,12.72,1.76,3.3,488
108,2,12.22,2.04,2.7,312
109,2,11.61,2.92,2.65,680
110,2,11.46,2.58,2.9,562
111,2,12.52,2.27,2.0,325
112,2,11.76,2.03,3.8,607
113,2,11.41,2.01,3.08,434
114,2,12.08,2.29,2.9,385
115,2,11.03,2.17,1.9,407
116,2,11.82,1.6,1.95,495
117,2,12.42,2.09,2.06,345
118,2,12.77,1.25,3.4,372
119,2,12.0,1.64,1.28,564
120,2,11.45,2.79,3.25,625
121,2,11.56,5.08,6.0,465
122,2,12.42,2.13,2.08,365
123,2,13.05,2.65,2.6,380
124,2,11.87,3.03,2.8,380
125,2,12.07,2.65,2.76,378
126,2,12.43,3.15,3.94,352
127,2,11.79,2.24,3.0,466
128,2,12.37,2.45,2.12,342
129,2,12.04,1.75,2.6,580
130,3,12.86,1.25,4.1,630
131,3,12.88,1.22,5.4,530
132,3,12.81,1.09,5.7,560
133,3,12.7,1.2,5.0,600
134,3,12.51,0.58,5.45,650
135,3,12.6,0.66,7.1,695
136,3,12.25,0.47,3.85,720
137,3,12.53,0.6,5.0,515
138,3,13.49,0.48,5.7,580
139,3,12.84,0.6,4.92,590
140,3,12.93,0.5,4.6,600
141,3,13.36,0.5,5.6,780
142,3,13.52,0.52,4.35,520
143,3,13.62,0.8,4.4,550
144,3,12.25,0.78,8.21,855
145,3,13.16,0.55,4.0,830
146,3,13.88,0.34,4.9,415
147,3,12.87,0.65,7.65,625
148,3,13.32,0.76,8.42,650
149,3,13.08,1.39,9.4,550
150,3,13.5,1.57,8.6,500
151,3,12.79,1.36,10.8,480
152,3,13.11,1.28,7.1,425
153,3,13.23,0.83,10.52,675
154,3,12.58,0.58,7.6,640
155,3,13.17,0.63,7.9,725
156,3,13.84,0.83,9.01,480
157,3,12.45,0.58,7.5,880
158,3,14.34,1.31,13.0,660
159,3,13.48,1.1,11.75,620
160,3,12.36,0.92,7.65,520
161,3,13.69,0.56,5.88,680
162,3,12.85,0.6,5.58,570
163,3,12.96,0.7,5.28,675
164,3,13.78,0.68,9.58,615
165,3,13.73,0.47,6.62,520
166,3,13.45,0.92,10.68,695
167,3,12.82,0.66,10.26,685
168,3,13.58,0.84,8.66,750
169,3,13.4,0.96,8.5,630
170,3,12.2,0.49,5.5,510
171,3,12.77,0.51,9.899999000000000,470
172,3,14.16,0.7,9.7,660
173,3,13.71,0.61,7.7,740
174,3,13.4,0.75,7.3,750
175,3,13.27,0.69,10.2,835
176,3,13.17,0.68,9.3,840
177,3,14.13,0.76,9.2,560




Output files

dfclsspc.csv
,class,PC1,PC2,PC3,PC4,PC5,PC6,PC7,PC8,PC9,PC10,PC11,PC12,PC13
0,1,3.3074209742892218,-1.4394022531822968,-0.1652728297819703,-0.21502462886791013,0.6910933491309144,-0.22325036575091023,0.5947488306815286,0.06495586200824276,0.6396383626544324,1.0180839601389415,-0.4502931724404516,0.5392891438984798,-0.06605230525465954
1,1,2.203249813420225,0.3324550711941807,-2.020757060479493,-0.2905387432289206,-0.25692986617101377,-0.9245123057914416,0.05362434498856938,1.0215343244190644,-0.3079779836123777,0.15925214078798267,-0.1422560187907293,0.3871456498926666,0.0036262731908069533
2,1,2.5096606947618634,-1.0282507242941965,0.9800540552553032,0.7228631990496799,-0.25032697580580315,0.5477309633081178,0.4230121843493222,-0.34324787002566237,-1.1745212875879927,0.11304197887868297,-0.28586645250265047,0.000581931623216335,0.021655423052880457
3,1,3.746497190498001,-2.748618390858541,-0.17569622422135825,0.5663856019167641,-0.31096439791833425,0.11410911207014857,-0.38225899027920607,0.6417831052414534,0.05239661692354329,0.2387391504379256,0.7574476431290621,-0.24133877573986928,-0.3684441939604296
4,1,1.0060704895977026,-0.8673840350754072,2.0209872565518503,-0.4086131396933835,0.29761795846868305,-0.4053760832003349,0.4428253058240363,0.41552831458168393,0.32589984041222253,-0.07814604136464899,-0.5244656285832899,-0.21605469342071176,-0.07914032015451253
5,1,3.0416737256112696,-2.116430916831081,-0.6276253711399857,-0.5141870345752622,-0.6302408997615397,0.1230833540519225,0.40052392817214855,0.3937826075026363,-0.15171809772553935,-0.10170890759159312,0.4044444267393124,-0.37836536058787584,0.14474701715254223
6,1,2.4422005148251396,-1.171545342735355,-0.9743463764348986,-0.06564532699526031,-1.0248708712061014,-0.618376376956238,0.05274194975480953,-0.370887632301127,-0.4557302943391878,1.0137039217067525,-0.4411888701049246,0.14083257227219292,-0.27101368729615755
7,1,2.053643788593804,-1.6044371435937752,0.14587040015624617,-1.1892532694404772,0.0766871685043793,-1.4357561211356402,0.03228452156232402,0.23232359673626163,0.12302328241458269,0.73353084461641,0.29272910497317384,0.37859505482382616,-0.10985390195718889
8,1,2.5038113458622306,-0.9154884741383152,-1.7659873885920068,0.05611207579344695,-0.8897471068353372,-0.12881766870639613,0.12493265131002868,-0.49817261903938187,0.6048828958113518,0.17361686082084915,-0.5075012931685446,-0.6334624142350219,0.14168386288991672
9,1,2.745882382732543,-0.7872170290019044,-0.9814788553712221,0.3483987771430787,-0.46723506146572896,0.1629320385996138,-0.8718927400564324,0.1501559309777843,0.22984079886401712,0.17891540399574188,0.012443070584149108,0.5487787840836071,-0.04233543013419706
10,1,3.4699483745007793,-1.298669845233353,-0.42154608562726487,0.026766255576549346,-0.3374229485548122,-0.18238713921172017,0.2474643166009073,-1.2032168355528527,-0.5230983760329564,-0.21393410285960543,0.7304540896421186,-0.08108353968059738,0.1222571082078051
11,1,1.7498168777295426,-0.610255770402334,-1.1875284443033078,-0.8876603544925262,-0.7364950947296743,-0.5514995363688643,-0.4330446734643984,-0.9823554302145003,-0.47269705832608166,0.2196631370414422,0.041319595137458406,-0.1621036320152582,0.14236819168525308
12,1,2.107517286793351,-0.6738056143108792,-0.8626529849997499,-0.3554353694580963,-1.206525260365546,-0.21447112037911437,-0.2419147637129789,-0.46020817231746297,-0.8763413358192799,-0.09623389994997246,0.053894423602011014,-0.08949405724647415,-0.004921359024082772
13,1,3.448429214077157,-1.1274494764095218,-1.2008887892803866,0.16200107724821255,-2.0174358633910314,0.7436829854158363,1.471622149613517,-0.37931575174243415,-0.025629848511892567,-0.2439644181301538,-1.228335907770018,-0.770160959221526,0.2251860836430323
14,1,4.300652282433133,-2.090079711129265,-1.2603574351818916,0.30491306651046135,-1.0267961441431415,0.7934048131292087,0.9971580839472901,-0.4037524704055742,-0.8379787009012962,-0.36340777660023316,-0.3148579452256333,-0.14241798751992002,-0.0944575025650891
15,1,2.2987038329874876,-1.657875063256505,0.21728966750242665,-1.4365377266781327,-0.46822928494251104,-0.4210257396075808,-0.1804584505882065,0.08388008384447057,-0.40332019733664,-0.7974057420100701,0.10239527155432811,0.496395591301705,-0.06581411051361986
16,1,2.1658456828096475,-2.32075875406352,0.8293902555398711,-0.9100341775815219,-0.00011461709257406044,-0.06634216266229445,0.10917979866593315,-0.39831120973572426,0.06088354042464173,0.0194589645139306,0.0781459967699548,-0.4993884916803938,0.3371517167514269
17,1,1.8936294749078209,-1.6267799275590016,0.7926777435285638,-1.0793357115710438,-0.4374711601650541,0.3639042823579474,0.09138877248609027,0.11252284383803621,0.3809586363156592,-0.400192040489664,0.30821248171070925,-0.26308323130129213,0.5577202570204506
18,1,3.5320216723838582,-2.5112597068368268,-0.4840929395387666,-0.907762118959413,-1.1498357894573201,0.3030222314279165,-0.03337008030637092,-0.03549997731606875,-0.44032390819620665,-0.7823700003528729,0.9159245944564347,0.1646236980558128,0.5130957702205607
19,1,2.0786585582209844,-1.0581530706706517,-0.16428325513842096,0.48363314814167424,0.8800288984114187,-1.3890992216187479,-0.1021839323471412,0.5782839954550154,0.05858753222730578,-0.14962722141782256,-0.8333756983105735,0.28706483106453895,0.05854416728645179
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Python files

pca.py
#################### Principal Component Analysis (PCA) in Python
#
#
########## Run this script on Terminal of MacOS as follows:
#
#python3 pca.py (csv data file) (target: classification column name)
#
#For instance,
#python3 pca.py wine.csv
#python3 pca.py wine4data.csv
#
#
########## Reference
#https://qiita.com/maskot1977/items/082557fcda78c4cdb41f
#
#
########## Data Source
#https://raw.githubusercontent.com/maskot1977/ipython_notebook/master/toydata/wine.txt


########## import
import numpy as np
import pandas as pd
from pandas import plotting
import matplotlib.pyplot as plt
import sklearn
from sklearn.decomposition import PCA
#from sklearn.preprocessing import StandardScaler
import matplotlib.ticker as ticker
import sys


########## arguments
dfname = str(sys.argv[1])    # e.g., wine.csv
#tgname = str(sys.argv[2])    # e.g., target (classification name columns)


########## load data
#df = pd.read_csv("wine.txt", sep="\t", index_col=0)
df = pd.read_csv(dfname, sep=",", index_col=0)

#print(df.head())
'''
   class  Alcohol  Malic acid   Ash  ...  Color intensity   Hue  OD280/OD315 of diluted wines  Proline
0      1    14.23        1.71  2.43  ...             5.64  1.04                          3.92     1065
1      1    13.20        1.78  2.14  ...             4.38  1.05                          3.40     1050
2      1    13.16        2.36  2.67  ...             5.68  1.03                          3.17     1185
3      1    14.37        1.95  2.50  ...             7.80  0.86                          3.45     1480
4      1    13.24        2.59  2.87  ...             4.32  1.04                          2.93      735
'''


########## show data
#print(df.iloc[:, 1:].head())
'''
   Alcohol  Malic acid   Ash  ...   Hue  OD280/OD315 of diluted wines  Proline
0    14.23        1.71  2.43  ...  1.04                          3.92     1065
1    13.20        1.78  2.14  ...  1.05                          3.40     1050
2    13.16        2.36  2.67  ...  1.03                          3.17     1185
3    14.37        1.95  2.50  ...  0.86                          3.45     1480
4    13.24        2.59  2.87  ...  1.04                          2.93      735

[5 rows x 13 columns]
'''
#
#print(df.iloc[:, 0:].head())
'''
   class  Alcohol  Malic acid   Ash  ...  Color intensity   Hue  OD280/OD315 of diluted wines  Proline
0      1    14.23        1.71  2.43  ...             5.64  1.04                          3.92     1065
1      1    13.20        1.78  2.14  ...             4.38  1.05                          3.40     1050
2      1    13.16        2.36  2.67  ...             5.68  1.03                          3.17     1185
3      1    14.37        1.95  2.50  ...             7.80  0.86                          3.45     1480
4      1    13.24        2.59  2.87  ...             4.32  1.04                          2.93      735

[5 rows x 14 columns]
'''
#class is a column for classifications (1, 2, and 3)
plotting.scatter_matrix(df.iloc[:, 1:], figsize=(8, 8), c=list(df.iloc[:, 0]), alpha=0.5)
plt.savefig("Figure_1_scatter_matrix_raw_data.png")
plt.show()


########## Standardization (every column excluding class has mean = 0 & standard deviation = 1)
dfs = df.iloc[:, 1:].apply(lambda x: (x-x.mean())/x.std(), axis=0)
#dfs = StandardScaler().fit_transform(df)

#dfs.head()
#print(dfs.head())
'''
    Alcohol  Malic acid       Ash  ...       Hue  OD280/OD315 of diluted wines   Proline
0  1.514341   -0.560668  0.231400  ...  0.361158                      1.842721  1.010159
1  0.245597   -0.498009 -0.825667  ...  0.404908                      1.110317  0.962526
2  0.196325    0.021172  1.106214  ...  0.317409                      0.786369  1.391224
3  1.686791   -0.345835  0.486554  ... -0.426341                      1.180741  2.328007
4  0.294868    0.227053  1.835226  ...  0.361158                      0.448336 -0.037767

[5 rows x 13 columns]
'''


########## PCA
pca = PCA()
pca.fit(dfs)
feature = pca.transform(dfs)


########## PC score
#print(pd.DataFrame(feature, columns=["PC{}".format(x + 1) for x in range(len(dfs.columns))]).head())
'''
        PC1       PC2       PC3       PC4       PC5  ...       PC9      PC10      PC11      PC12      PC13
0  3.307421 -1.439402 -0.165273 -0.215025  0.691093  ...  0.639638  1.018084 -0.450293  0.539289 -0.066052
1  2.203250  0.332455 -2.020757 -0.290539 -0.256930  ... -0.307978  0.159252 -0.142256  0.387146  0.003626
2  2.509661 -1.028251  0.980054  0.722863 -0.250327  ... -1.174521  0.113042 -0.285866  0.000582  0.021655
3  3.746497 -2.748618 -0.175696  0.566386 -0.310964  ...  0.052397  0.238739  0.757448 -0.241339 -0.368444
4  1.006070 -0.867384  2.020987 -0.408613  0.297618  ...  0.325900 -0.078146 -0.524466 -0.216055 -0.079140

[5 rows x 13 columns]
'''

dfcls = df.iloc[:, 0]
dfspc = pd.DataFrame(feature, columns=["PC{}".format(x + 1) for x in range(len(dfs.columns))])
dfclsspc = pd.concat([dfcls, dfspc], axis=1)
#print(dfclsspc.head())
'''
   class       PC1       PC2       PC3       PC4       PC5  ...       PC8       PC9      PC10      PC11      PC12      PC13
0      1  3.307421 -1.439402 -0.165273 -0.215025  0.691093  ...  0.064956  0.639638  1.018084 -0.450293  0.539289 -0.066052
1      1  2.203250  0.332455 -2.020757 -0.290539 -0.256930  ...  1.021534 -0.307978  0.159252 -0.142256  0.387146  0.003626
2      1  2.509661 -1.028251  0.980054  0.722863 -0.250327  ... -0.343248 -1.174521  0.113042 -0.285866  0.000582  0.021655
3      1  3.746497 -2.748618 -0.175696  0.566386 -0.310964  ...  0.641783  0.052397  0.238739  0.757448 -0.241339 -0.368444
4      1  1.006070 -0.867384  2.020987 -0.408613  0.297618  ...  0.415528  0.325900 -0.078146 -0.524466 -0.216055 -0.079140

[5 rows x 14 columns]
'''

dfclsspc.to_csv('dfclsspc.csv', header=True, index=True)


########## PCA plot (PC1 and PC2)
plt.figure(figsize=(6, 6))
#plt.scatter(feature[:, 0], feature[:, 1], alpha=0.8, c=list(df.iloc[:, 0]))
plt.scatter(dfclsspc.iloc[:, 1], dfclsspc.iloc[:, 2], alpha=0.8, c=list(dfclsspc.iloc[:, 0]))
plt.grid()
plt.xlabel("PC1")
plt.ylabel("PC2")
#plt.legend()
#plt.legend(list(dfclsspc.iloc[:, 0]))
#print(dfclsspc.iloc[:, 0])
#

### comment out if you want to delete numbers for each data point
for x, y, name in zip(dfclsspc.iloc[:, 1], dfclsspc.iloc[:, 2], dfclsspc.iloc[:, 0]):
    plt.text(x, y, name)

plt.savefig("Figure_2_PCA_plot_PC1_and_PC2.png")
plt.show()



########## show all PCs
plotting.scatter_matrix(pd.DataFrame(feature,
                        columns=["PC{}".format(x + 1) for x in range(len(dfs.columns))]),
                        figsize=(8, 8), c=list(df.iloc[:, 0]), alpha=0.5)
plt.savefig("Figure_3_PCA_plot_all_PCs.png")
plt.show()


########## Cumulative contributions
# calculate cumulative contribution
#pd.DataFrame(pca.explained_variance_ratio_, index=["PC{}".format(x + 1) for x in range(len(dfs.columns))])
#print(pd.DataFrame(pca.explained_variance_ratio_, index=["PC{}".format(x + 1) for x in range(len(dfs.columns))]))
'''
             0
PC1   0.361988
PC2   0.192075
PC3   0.111236
PC4   0.070690
PC5   0.065633
PC6   0.049358
PC7   0.042387
PC8   0.026807
PC9   0.022222
PC10  0.019300
PC11  0.017368
PC12  0.012982
PC13  0.007952
'''


##### show cumulative contribution
plt.gca().get_xaxis().set_major_locator(ticker.MaxNLocator(integer=True))
plt.plot([0] + list( np.cumsum(pca.explained_variance_ratio_)), "-o")
plt.xlabel("Number of principal components")
plt.ylabel("Cumulative contribution rate")
plt.grid()
plt.savefig("Figure_4_PCA_plot_cum_contb.png")
plt.show()


########## PCA eigenvalues
#pd.DataFrame(pca.explained_variance_, index=["PC{}".format(x + 1) for x in range(len(dfs.columns))])
#print(pd.DataFrame(pca.explained_variance_, index=["PC{}".format(x + 1) for x in range(len(dfs.columns))]))
'''
             0
PC1   4.705850
PC2   2.496974
PC3   1.446072
PC4   0.918974
PC5   0.853228
PC6   0.641657
PC7   0.551028
PC8   0.348497
PC9   0.288880
PC10  0.250902
PC11  0.225789
PC12  0.168770
PC13  0.103378
'''


########## PCA eigenvectors
#pd.DataFrame(pca.components_, columns=df.columns[1:], index=["PC{}".format(x + 1) for x in range(len(dfs.columns))])
#print(pd.DataFrame(pca.components_, columns=df.columns[1:], index=["PC{}".format(x + 1) for x in range(len(dfs.columns))]))
'''
       Alcohol  Malic acid       Ash  Alcalinity of ash  ...  Color intensity       Hue  OD280/OD315 of diluted wines   Proline
PC1   0.144329   -0.245188 -0.002051          -0.239320  ...        -0.088617  0.296715                      0.376167  0.286752
PC2  -0.483652   -0.224931 -0.316069           0.010591  ...        -0.529996  0.279235                      0.164496 -0.364903
PC3  -0.207383    0.089013  0.626224           0.612080  ...        -0.137306  0.085222                      0.166005 -0.126746
PC4  -0.017856    0.536890 -0.214176           0.060859  ...         0.065926 -0.427771                      0.184121 -0.232071
PC5  -0.265664    0.035214 -0.143025           0.066103  ...        -0.076437 -0.173615                     -0.101161 -0.157869
PC6  -0.213539   -0.536814 -0.154475           0.100825  ...         0.418644 -0.105983                     -0.265851 -0.119726
PC7  -0.056396    0.420524 -0.149171          -0.286969  ...        -0.227712  0.232076                     -0.044764  0.076805
PC8  -0.396139   -0.065827  0.170260          -0.427970  ...         0.033797 -0.436624                      0.078108 -0.120023
PC9   0.508619   -0.075283 -0.307694           0.200449  ...         0.056218  0.085828                      0.137227 -0.575786
PC10  0.211605   -0.309080 -0.027125           0.052799  ...        -0.290775 -0.522399                      0.523706  0.162116
PC11 -0.225917    0.076486 -0.498691           0.479314  ...         0.031839 -0.048212                      0.046423  0.539270
PC12 -0.266286    0.121696 -0.049622          -0.055743  ...         0.604222  0.259214                      0.600959 -0.079402
PC13  0.014970    0.025964 -0.141218           0.091683  ...        -0.011993 -0.089889                     -0.156718  0.014447

[13 rows x 13 columns]
'''


########## PCA PC1 & PC2 and observations

plt.figure(figsize=(6, 6))
for x, y, name in zip(pca.components_[0], pca.components_[1], df.columns[1:]):
    plt.text(x, y, name)
plt.scatter(pca.components_[0], pca.components_[1], alpha=0.8)
plt.grid()
plt.xlabel("PC1")
plt.ylabel("PC2")
plt.savefig("Figure_5_PCA_plot_PC1_PC2_and_observations.png")
plt.show()




Figures
Figure_1_scatter_matrix_raw_data.png


Figure_2_PCA_plot_PC1_and_PC2.png


Figure_3_PCA_plot_all_PCs.png


Figure_4_PCA_plot_cum_contb.png


Figure_5_PCA_plot_PC1_PC2_and_observations.png


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