import numpy as np
# 将二维数据降成1维
num = [(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)]
num_array = np.array(num)
n1_avg, n2_avg = np.mean(num_array[:, 0]), np.mean(num_array[:, 1])
# 1.样本中心化
# new_num_array = np.array(list(zip(num_array[:, 0] - n1_avg, num_array[:, 1] - n2_avg)))
new_num_array = np.c_[num_array[:, 0] - n1_avg, num_array[:, 1] - n2_avg]
# 2.计算协方差矩阵
num_cov = np.cov(new_num_array[:, 0], new_num_array[:, 1])
# 3.特征值分解
# a 特征值, b 特征向量
a, b = np.linalg.eig(num_cov)
# k=1, 取a最大值的索引对应b的特征向量
w = b[:, np.argmax(a)]
# 4.输出pca降维结果
z1_num = new_num_array.dot(w.T)
print(z1_num) # 使用sklearn中的PCA
from sklearn.decomposition import PCA
pca = PCA(n_components=1)
z2_num = pca.fit_transform(num_array)
print(z2_num)