pca.py

import numpy as np

def normalize(X):
    """數據標準化處理
    Args:
        X 樣本
    Returns:
        XNorm 標準化後的樣本
    """
    XNorm = X.copy()
    m,n = XNorm.shape
    mean = np.mean(XNorm, axis=0)
    std = np.std(XNorm, axis=0)
    XNorm = (XNorm - mean) / std
    return XNorm

def PCA(X, k = 1):
    """PCA
    Args:
        X 樣本
        k 目的維度
    Returns:
        XNorm 標準化後的樣本
        Z 降維後的新樣本
        U U
        UReduce UReduce
        S S
        V V
    """
    m, n = X.shape
    # 數據歸一化
    XNorm = normalize(X)
    # 計算協方差矩陣
    Coef = XNorm.T * XNorm/m
    # 奇異值分解
    U, S, V = np.linalg.svd(Coef)
    # 取出前 k 個向量
    UReduce = U[:, 0:k]
    Z = XNorm * UReduce
    return XNorm, Z, U, UReduce, S, V

def recover(UReduce, Z):
    """數據恢復
    Args:
        UReduce UReduce
        Z 降維後的樣本
    """
    return Z * UReduce.T