pca.py－20170728

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Jul 18 20:20:39 2017

@author: vicky
"""


import numpy as np
x=np.array([2.5,0.5,2.2,1.9,3.1,2.3,2,1,1.5,1.1])
y=np.array([2.4,0.7,2.9,2.2,3,2.7,1.6,1.1,1.6,0.9])
mean_x=np.mean(x)
mean_y=np.mean(y)
scaled_x=x-mean_x
scaled_y=y-mean_y
data=np.matrix([[scaled_x[i],scaled_y[i]] for i in range(len(scaled_x))])

import matplotlib.pyplot as plt
plt.plot(scaled_x,scaled_y,'o')

cov=np.cov(scaled_x,scaled_y)

np.dot(np.transpose(data),data)

eig_val, eig_vec = np.linalg.eig(cov)

plt.plot(scaled_x,scaled_y,'o',)
xmin ,xmax = scaled_x.min(), scaled_x.max()
ymin, ymax = scaled_y.min(), scaled_y.max()
dx = (xmax - xmin) * 0.2
dy = (ymax - ymin) * 0.2
plt.xlim(xmin - dx, xmax + dx)
plt.ylim(ymin - dy, ymax + dy)
plt.plot([eig_vec[:,0][0],0],[eig_vec[:,0][1],0],color='red')
plt.plot([eig_vec[:,1][0],0],[eig_vec[:,1][1],0],color='red')

new_data=np.transpose(np.dot(eig_vec,np.transpose(data)))

eig_pairs = [(np.abs(eig_val[i]), eig_vec[:,i]) for i in range(len(eig_val))]
eig_pairs.sort(reverse=True)

feature=eig_pairs[0][1]

new_data_reduced=np.transpose(np.dot(feature,np.transpose(data)))

plt.plot(scaled_x,scaled_y,'o',color='red')
plt.plot([eig_vec[:,0][0],0],[eig_vec[:,0][1],0],color='red')
plt.plot([eig_vec[:,1][0],0],[eig_vec[:,1][1],0],color='blue')
plt.plot(new_data[:,0],new_data[:,1],'^',color='blue')
plt.plot(new_data_reduced[:,0],[1.2]*10,'*',color='green')

import numpy as np
def pca(X,k):#k is the components you want
  #mean of each feature
  n_samples, n_features = X.shape
  mean=np.array([np.mean(X[:,i]) for i in range(n_features)])
  #normalization
  norm_X=X-mean
  #scatter matrix
  scatter_matrix=np.dot(np.transpose(norm_X),norm_X)
  #Calculate the eigenvectors and eigenvalues
  eig_val, eig_vec = np.linalg.eig(scatter_matrix)
  eig_pairs = [(np.abs(eig_val[i]), eig_vec[:,i]) for i in range(n_features)]
  # sort eig_vec based on eig_val from highest to lowest
  eig_pairs.sort(reverse=True)
  # select the top k eig_vec
  feature=np.array([ele[1] for ele in eig_pairs[:k]])
  #get new data
  data=np.dot(norm_X,np.transpose(feature))
  return data

from sklearn.decomposition import PCA
X = np.array([[-1, 1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
pca=PCA(n_components=1)
pca.fit(X)
pca.transform(X)