svd-from-scratch

svd-from-scratch.py

# this method works well on ALL data
# see https://towardsdatascience.com/my-notes-for-singular-value-decomposition-with-interactive-code-feat-peter-mills-7584f4f2930a
import numpy as np 
from sklearn import preprocessing
np.set_printoptions(precision=2)

X = np.array([
    [1,2,3],
    [4,10,1],    
    [5,3,2],    
    [8,1,9],    
    [5,6,9],    
])


scaler = preprocessing.StandardScaler()
X_std = scaler.fit_transform(X)

X_dot_XT = X_std.dot(X_std.T)
S,U = np.linalg.eig(X_dot_XT)
S = np.diag(np.sqrt(S))
V = X_std.T.dot(U).dot(np.linalg.inv(S))
reconstructed_X = np.dot(U,S).dot(V.T)


print('U\n',np.real(U))
print()
print('S\n',np.real(S))
print()
print('V\n',np.real(V))

print('-----------')
print('X\n', X_std)
print()
print('U * S * VT\n', np.real(reconstructed_X))