PCA模型原生python实现

#使用梯度上升法

import numpy as np
import matplotlib.pyplot as plt


X = np.empty((100,2))  ##返回一个100X2的数组                      ##size为样本个数
X[:,0] = np.random.uniform(0.,100.,size =100)#随机生成100个实数在（0-100）范围内个数
X[:,1] = 0.75*X[:,0] + 3.+ np.random.normal(0,10., size =100)#正态分布
# print(X)
# print(X[:,0])
# print(X[:,1])
plt.scatter(X[:,0],X[:,1])
plt.show()


##去中心化
#demean
def demean(X):
    return X-np.mean(X, axis= 0)

X_demean = demean(X)

plt.scatter(X_demean[:,0],X_demean[:,1])
plt.show()

#梯度上升法

def f(w,X):
    return np.sum((X.dot(w)**2))/len(X)

#dot函数：运算时直接进行乘积
# 二维数组（矩阵）之间的运算，则得到的是矩阵积（mastrix product）
def df_math(w,X):
    return X.T.dot(X.dot(w))*2./len(X)
def df_debug(w,X, epsilon = 0.0001):
    res = np.empty(len(w))
    for i in range(len(w)):
        w_1 = w.copy()
        w_1[i] += epsilon
        w_2 = w.copy()
        w_2[i] -= epsilon
        res[i] = (f(w_1,X) - f(w_2,X)) / (2 * epsilon)
    return res
def direction(w):
    return w/ np.linalg.norm(w)
#np.linalg.norm：求范数，默认情况下，是求整体的矩阵元素平方和，再开根号
def gradient_ascent(df,X,initial_w,eta,n_iters = 1e4,epsilon = 1e-8):
    w = direction(initial_w)
    cur_iter = 0
    while cur_iter