PCA.py

import numpy as np


def PCA(data, n_component=None) -> np.ndarray:
    """
    输入：data  (n_samples, n_features)
    返回：降维后的样本矩阵 (n_samples, n_component)
    同时把 components_ 与 explained_variance_ratio_ 存为属性
    """
    # 1. 中心化
    X = data - data.mean(axis=0)

    # 2. 协方差矩阵
    C = np.cov(X, rowvar=False)          # (n_features, n_features)

    # 3. 特征分解
    eig_vals, eig_vecs = np.linalg.eigh(C)  # 特征值升序
    eig_vals = eig_vals[::-1]               # 降序
    eig_vecs = eig_vecs[:, ::-1]

    # 4. 确定主成分个数
    max_component = min(data.shape)
    if n_component is None:
        n_component_ = max_component
    else:
        n_component_ = min(n_component, data.shape[1])

    # 5. 存 components (每一列是一个主成分方向)
    components_ = eig_vecs[:, :n_component_].T   # (n_component, n_features)

    # 6. 解释方差比例
    total_var = eig_vals.sum()
    explained_variance_ratio_ = eig_vals[:n_component_] / total_var

    # 7. 投影得到降维后的数据
    return X @ components_.T, components_, explained_variance_ratio_

if __name__ == "__main__":
    data = np.random.randn(100, 8)      # 100 样本，8 特征
    embedding_pca, pca_composition, explained_variance_ratio_ = PCA(data)   # (100, 3)
    print("components:\n", pca_composition.shape)
    print("explained variance ratio:\n", explained_variance_ratio_)