20、PCA求解前n个主成分的方向向量 - 东方耀AI技术分享

def direction(w):
# 将w变成单位向量方向向量
# np.linalg.norm(w) 求向量的模
return w / np.linalg.norm(w)
def gradient_ascent_first_pca(df, X, initial_w, learn_rate, n_iters, epsilon = 1e-8):
w = direction(initial_w)
for step in range(n_iters):
last_w = w
w = w + learn_rate * df(w, X)
# 注意：pca求解时需要变为单位向量
w = direction(w)
if(abs(f(last_w, X) - f(w, X)) < epsilon):
break
return step, w

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def gradient_ascent_first_pca_n(n, X, learn_rate, n_iters, epsilon = 1e-8):
assert 0 < n <= X.shape[1], 'n>0且n不能大于样本特征数'
X_pca = X
X_pca = demean(X_pca)
result = []
for i in range(n):
# 这里的w代表方向向量不能为0向量的
initial_w = np.random.random(size=X_pca.shape[1])
step, w = gradient_ascent_first_pca(df_math, X_pca, initial_w, learn_rate=0.001, n_iters=10000)
print(step, w)
result.append(w)
X_pca = X_pca - X_pca.dot(w).reshape(-1, 1) * w
return result

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