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PCA主成分分析:核心的思想
- import numpy as np
- class PCA:
- def __init__(self, n_components):
- """初始化PCA"""
- assert n_components >= 1, "n_components must be valid"
- self.n_components = n_components
- self.components_ = None
- def fit(self, X, eta=0.01, n_iters=1e4):
- """获得数据集X的前n个主成分"""
- assert self.n_components <= X.shape[1], \
- "n_components must not be greater than the feature number of X"
- def demean(X):
- return X - np.mean(X, axis=0)
- def f(w, X):
- return np.sum((X.dot(w) ** 2)) / len(X)
- def df(w, X):
- return X.T.dot(X.dot(w)) * 2. / len(X)
- def direction(w):
- return w / np.linalg.norm(w)
- def first_component(X, initial_w, eta=0.01, n_iters=1e4, epsilon=1e-8):
- w = direction(initial_w)
- cur_iter = 0
- while cur_iter < n_iters:
- gradient = df(w, X)
- last_w = w
- w = w + eta * gradient
- w = direction(w)
- if (abs(f(w, X) - f(last_w, X)) < epsilon):
- break
- cur_iter += 1
- return w
- X_pca = demean(X)
- self.components_ = np.empty(shape=(self.n_components, X.shape[1]))
- for i in range(self.n_components):
- initial_w = np.random.random(X_pca.shape[1])
- w = first_component(X_pca, initial_w, eta, n_iters)
- self.components_[i,:] = w
- X_pca = X_pca - X_pca.dot(w).reshape(-1, 1) * w
- return self
- def transform(self, X):
- """将给定的X,映射到各个主成分分量中"""
- assert X.shape[1] == self.components_.shape[1]
- return X.dot(self.components_.T)
- def inverse_transform(self, X):
- """将给定的X,反向映射回原来的特征空间"""
- assert X.shape[1] == self.components_.shape[0]
- return X.dot(self.components_)
- def __repr__(self):
- return "PCA(n_components=%d)" % self.n_components
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