from scipy.linalg import svd

import numpy as np

class PCA():

def __init__(self, solver='svd'):

self.solver = solver

self.means = None

self.components = None

self.S = None # squared singular value sorted in non-decreasing order

def train(self, X):

# mean centering

X = X.copy()

self.means = np.mean(X, axis=0)

X -= self.means

# solver

if self.solver=="svd":

_,S,V = svd(X) # X=U*S*V, V: Unitary matrix having right singular vectors as rows.

elif self.solver=="eig":

S,V = np.linalg.eig(np.cov(X.T)) # V: the column of V is the eigenvector

V = V.T

sort_idx = np.argsort(S)[::-1]

V = V[sort_idx]

S = S[sort_idx]

else:

raise Exception("Solver Not Exist")

# save

self.S = S**2

self.components = V

def predict(self, X, n_components=2):

# mean centering

X = X.copy()

X -= self.means

# predict

V = self.components[:n_components].T

assert X.shape[1]==V.shape[0]

print ("Explained variance ratio: %f" % (np.sum(self.S[:n_components])/np.sum(self.S)) )

return X.dot(V)