In [1]:

    

#import libs, load data

%matplotlib inline
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

df_load = pd.read_csv('https://nthu-datalab.github.io/ml/labs/02_EDA_PCA/gen_dataset.csv')

X_load = df_load.drop('Class label', 1)
Y_load = df_load['Class label']

df_load.head()


    

    
Out[1]:






  

    

      

      
Class label
      
a1
      
a2
      
a3
      
a4
      
a5
      
a6
      
a7
      
a8
      
a9
      
a10
      
a11
      
a12
      
a13
      
a14
      
a15
    
  
  

    

      
0
      
2.0
      
-0.016488
      
-1.310538
      
-1.552489
      
-0.785475
      
1.548429
      
0.476687
      
1.090010
      
-0.351870
      
-0.000855
      
-1.932941
      
0.499177
      
0.149137
      
-0.640413
      
-0.782951
      
-0.903561
    
    

      
1
      
0.0
      
-0.844201
      
-1.235142
      
-0.624408
      
1.502470
      
-0.079536
      
1.482053
      
1.178544
      
-1.150090
      
-1.040124
      
-1.041435
      
0.281037
      
-0.283710
      
-1.176802
      
0.718408
      
-0.392095
    
    

      
2
      
0.0
      
-0.181053
      
0.039422
      
-0.307827
      
0.162256
      
-1.283705
      
0.541288
      
0.019113
      
-0.470718
      
-1.045754
      
0.983150
      
-0.121205
      
-0.189225
      
-0.539178
      
0.825261
      
0.612889
    
    

      
3
      
2.0
      
-0.423555
      
-1.598754
      
1.597206
      
-0.239330
      
1.443564
      
2.657538
      
1.824393
      
-1.809287
      
1.058634
      
-4.058539
      
0.255908
      
-0.952422
      
-0.315551
      
1.854246
      
-2.369018
    
    

      
4
      
2.0
      
-0.499408
      
-0.814229
      
-0.178777
      
-1.757823
      
0.678134
      
3.552825
      
1.483069
      
-2.341943
      
2.155062
      
-4.380612
      
-0.239352
      
-1.730919
      
0.586125
      
3.902178
      
-2.891653
    
  

In [4]:

    

import numpy as np
from sklearn.preprocessing import StandardScaler

# Z-normalize data
sc = StandardScaler()
Z = sc.fit_transform(X_load)
# Estimate the correlation matrix
R = np.dot(Z.T, Z) / df_load.shape[0]

#calculate the eigen values, eigen vectors
eigen_vals, eigen_vecs = np.linalg.eigh(R)

# Make a list of (eigenvalue, eigenvector) tuples
eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:,i]) for i in range(len(eigen_vals))]

# Sort the (eigenvalue, eigenvector) tuples from high to low
eigen_pairs.sort(reverse=True)

#form the projection matrix
W_2D = np.hstack((eigen_pairs[0][1][:, np.newaxis],
               eigen_pairs[1][1][:, np.newaxis]))

#you should form a projection matrix which projects from raw-data dimension to 3 dimension here
W_3D = np.hstack((eigen_pairs[0][1][:, np.newaxis],
                eigen_pairs[1][1][:, np.newaxis],
                eigen_pairs[2][1][:, np.newaxis]))


    

In [8]:

    

import os
import seaborn as sns
sns.set(style='whitegrid', context='notebook')

#import Axes3D for plottin 3d scatter
from mpl_toolkits.mplot3d import Axes3D

#cacculate z_pca(2d and 3d)
Z_pca2 = Z.dot(W_2D)
Z_pca3 = Z.dot(W_3D)

#plot settings
colors = ['r', 'b', 'g']
markers = ['s', 'x', 'o']
fig = plt.figure(figsize=(12,6))

#plot 2D
plt2 = fig.add_subplot(1,2,1)
for l, c, m in zip(np.unique(Y_load), colors, markers):
    plt2.scatter(Z_pca2[Y_load==l, 0], 
                Z_pca2[Y_load==l, 1], 
                c=c, label=l, marker=m)

plt.title('Z_pca 2D')
plt.xlabel('PC 1')
plt.ylabel('PC 2')
plt.legend(loc='lower left')
plt.tight_layout()

#plot 3D
plt3 = fig.add_subplot(1,2,2, projection='3d')
#you should plot a 3D scatter using plt3.scatter here (see Axes3D.scatter in matplotlib)
for l, c, m in zip(np.unique(Y_load), colors, markers):
    plt3.scatter(Z_pca3[Y_load==l, 0], 
                 Z_pca3[Y_load==l, 1],
                 Z_pca3[Y_load==l, 2],
                c=c, label=l, marker=m)

plt3.set_xlabel('PC 1')
plt3.set_ylabel('PC 2')
plt3.set_zlabel('PC 3')    
    
plt.title('Z_pca 3D')
plt.legend(loc='lower right')
plt.tight_layout()
    
    
if not os.path.exists('./output'):
    os.makedirs('./output')
plt.savefig('./output/fig-pca-2-3-z.png', dpi=300)
plt.show()


    

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