主成分分析（PCA）

# -*- coding:utf-8 _*-
import numpy as np

Data = np.array([[2.5, 2.4],
                     [0.5, 0.7],
                     [2.2, 2.9],
                     [1.9, 2.2],
                     [3.1, 3.0],
                     [2.3, 2.7],
                     [2, 1.6],
                     [1, 1.1],
                     [1.5, 1.6],
                     [1.1, 0.9],
                     ])
# x,y平均值
avg_x = np.average(Data[:, 0])
avg_y = np.average(Data[:, 1])
avg = np.array([avg_x, avg_y])
# 每组数据减去对应均值后的数值
DataAdjust = Data-avg
# print(DataAdjust)

# 样本X方差
Variance_x = np.sum(DataAdjust[:,0]*DataAdjust[:, 0])/9
# 样本Y方差
Variance_y = np.sum(DataAdjust[:,1]*DataAdjust[:, 1])/9
# 样本X Y协方差
Cov_xy = np.sum(DataAdjust[:,0]*DataAdjust[:, 1])/9

# 协方差矩阵
C = np.array([[Variance_x, Cov_xy],
             [Cov_xy, Variance_y]])


# 特征值，特征向量
eigenvalues, eigenvectors = np.linalg.eig(C)
max_values = np.array(max(eigenvalues))
max_vectors = np.array([eigenvectors[0][1],eigenvectors[1][1]])


FinalData = np.dot(DataAdjust, max_vectors.T).reshape(10, 1)
print(FinalData)