Python主成分分析

【实例简介】

通过主成分分析对手写数字进行特征提取和降维

【实例截图】

第一主成分最高最低情况：

第二主成分最高最低情况：

【核心代码】

# -*- coding: utf-8 -*-
# @Time    : 4/12/2020 12:20
# @Author  : Eddie Shen
# @Email   : sheneddie@outlook.com
# @File    : HW.py
# @Software: PyCharm

import matplotlib.pyplot as plt
import numpy as np
import numpy.linalg as la

path = '你的文件位置'
data = np.loadtxt(path)

# Choose number 9.
k = 9
data_k = data[data[:, 0] == k, 1:]

# Show the 6th handwriting number.
plt.figure()
plt.imshow(data_k[5, :].reshape(16, 16), cmap="gray_r")
plt.show()

# Show the mean of data_k.
mu = np.mean(data_k, axis=0)
plt.figure()
plt.imshow(mu.reshape(16, 16), cmap="gray_r")
plt.show()

# Principal component analysis.
cov_x = np.cov(data_k, rowvar=False)
u, v = la.eig(cov_x)

# Show the first principal component.
plt.figure()
plt.imshow(v[:, 0].reshape(16, 16), cmap="gray_r")
plt.show()

# Choose handwriting numbers of the five biggest and five smallest scores.
xi1: np.ndarray = (data_k - mu) @ v[:, 0:1]
index_small = np.argsort(xi1.ravel())[0:5]  # Smallest
index_big = np.argsort(xi1.ravel())[-5:]  # Biggest
plt.figure()
for i in range(5):
    plt.subplot(2, 5, i 1)
    plt.imshow(data_k[index_small[i], :].reshape(16, 16), cmap="gray_r")
    plt.subplot(2, 5, 10 - i)
    plt.imshow(data_k[index_big[i], :].reshape(16, 16), cmap="gray_r")
plt.show()

# Show the second principal component.
plt.figure()
plt.imshow(v[:, 1].reshape(16, 16), cmap="gray_r")
plt.show()

# Choose handwriting numbers of the five biggest and five smallest scores.
xi2: np.ndarray = (data_k - mu) @ v[:, 1:2]
index_small = np.argsort(xi2.ravel())[0:5]  # Smallest
index_big = np.argsort(xi2.ravel())[-5:]  # Biggest
plt.figure()
for i in range(5):
    plt.subplot(2, 5, i 1)
    plt.imshow(data_k[index_small[i], :].reshape(16, 16), cmap="gray_r")
    plt.subplot(2, 5, 10 - i)
    plt.imshow(data_k[index_big[i], :].reshape(16, 16), cmap="gray_r")
plt.show()

# Reconstruction.
# Show the percent of each eigenvalue.
plt.figure()
u_percent = u.cumsum() / u.sum() * 100
plt.plot(u_percent)
plt.grid()
plt.xlabel("Number of eigenvalues")
plt.ylabel("Percent of contribution")
plt.show()

# Choose 50 principal components which can explain more than 90% of information.
j = 50
xi = (data_k - mu) @ v[:, 0:j]
rec_data = mu xi @ v[:, 0:j].T

# Show the difference between original picture and reconstructed picture.
m = [30, 50, 70, 90, 110]
plt.figure()
for i in range(5):
    plt.subplot(2, 5, i 1)
    plt.imshow(data_k[m[i], :].reshape(16, 16), cmap="gray_r")
    plt.subplot(2, 5, i 6)
    plt.imshow(rec_data[m[i], :].reshape(16, 16), cmap="gray_r")
plt.show()