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  • PCA

    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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  • 原文地址:https://www.cnblogs.com/heguoxiu/p/10135568.html
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