In [1]:

    

import warnings
warnings.filterwarnings('ignore')


    

In [2]:

    

%matplotlib inline


    

In [3]:

    

import numpy as np
from sklearn.decomposition import PCA


    

In [4]:

    

X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2], [4, 3], [4, -1]])
# X = np.array([[-1, 1], [-2, 2], [-3, 3], [1, 1], [2, 2], [3, 3], [4, 4]])


    

In [5]:

    

X


    

    
Out[5]:





array([[-1, -1],
       [-2, -1],
       [-3, -2],
       [ 1,  1],
       [ 2,  1],
       [ 3,  2],
       [ 4,  3],
       [ 4, -1]])

In [6]:

    

import matplotlib.pyplot as plt


    

In [7]:

    

plt.figure(figsize=(10,10))
plt.scatter(X[:, 0], X[:, 1])
# plt.savefig('original.png')


    

    
Out[7]:





<matplotlib.collections.PathCollection at 0x1a74bfce4a8>






    

In [8]:

    

from sklearn.preprocessing import StandardScaler


    

In [9]:

    

scaler = StandardScaler()


    

In [10]:

    

scaler.fit(X)


    

    
Out[10]:





StandardScaler(copy=True, with_mean=True, with_std=True)

In [15]:

    

scaler.mean_


    

    
Out[15]:





array([1.  , 0.25])

In [16]:

    

scaler.var_


    

    
Out[16]:





array([6.5   , 2.6875])

In [17]:

    

X_scaled = scaler.transform(X)


    

In [18]:

    

plt.scatter(X_scaled[:, 0], X_scaled[:, 1])


    

    
Out[18]:





<matplotlib.collections.PathCollection at 0x1a74c3e99e8>






    

In [15]:

    

import pandas as pd


    

In [16]:

    

df = pd.DataFrame(X_scaled)


    

In [17]:

    

corr_mat = df.corr()


    

In [18]:

    

corr_mat


    

    
Out[18]:







  

    

      

      
0
      
1
    
  
  

    

      
0
      
1.000000
      
0.717778
    
    

      
1
      
0.717778
      
1.000000
    
  

In [19]:

    

import seaborn as sns


    

In [20]:

    

plt.figure(figsize=(10,10))
sns.heatmap(corr_mat, annot=True)
# plt.savefig('correlation.png')


    

    
Out[20]:





<matplotlib.axes._subplots.AxesSubplot at 0x2087012cd68>






    

In [21]:

    

pca = PCA(n_components=2)
pca.fit(X)


    

    
Out[21]:





PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,
  svd_solver='auto', tol=0.0, whiten=False)

In [22]:

    

pca.explained_variance_


    

    
Out[22]:





array([9.3121762, 1.1878238])

In [23]:

    

# sum is 1, first pc has a very high variance, i.e. is very good, second could be deleted
pca.explained_variance_ratio_


    

    
Out[23]:





array([0.88687392, 0.11312608])

In [24]:

    

X_reduced = pca.transform(X)


    

In [25]:

    

plt.figure(figsize=(10,10))
plt.scatter(X_reduced[:, 0], X_reduced[:, 1])
# plt.savefig('reduced.png')


    

    
Out[25]:





<matplotlib.collections.PathCollection at 0x2086fa26518>






    

In [ ]: