机器学习---PCA案例

1. PCA

import numpy as np
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits

def pca(dataMat,topNfeat=9999999):
    meanVals=np.mean(dataMat,axis=0)
    # 去除平均值，实现数据中心化
    meanRemoved=dataMat-meanVals 
    covMat=np.cov(meanRemoved,rowvar=0)
    # 计算矩阵的特征值个特征向量
    eigVals,eigVects=np.linalg.eig(np.mat(covMat))
    eigValInd=np.argsort(eigVals)
    # 从大到小对N个值排序
    eigValInd=eigValInd[:-(topNfeat+1):-1]
    redEigVects=eigVects[:,eigValInd]
    # 将数据转换到新空间
    lowDDataMat=meanRemoved*redEigVects
    reconMat=(lowDDataMat*redEigVects.T)+meanVals
    return lowDDataMat,reconMat

dataMat = np.array([[1,2,3], [4,2,1], [3,2,1]])
X = load_digits().data[:, :]

lowDDataMat,reconMat = pca(X,topNfeat=2)
print(lowDDataMat)
print(reconMat)
plt.scatter(lowDDataMat[:,0].tolist(), lowDDataMat[:,1].tolist(),c =