Python3《機器學習實戰》代碼筆記（十三）--- PCA算法

參考資料:

機器學習實戰

'''
@version: 0.0.1
@Author: tqrs
@dev: python3 vscode
@Date: 2019-11-12 12:40:12
@LastEditTime: 2019-11-12 21:04:40
@FilePath: \\機器學習實戰\\13-PCA\\PCA.py
@Descripttion: 在低維下,數據更容易進行處理,相關特徵可能在數據中更明確地顯示出來。PCA降維是把數據從原來的座標系轉換到了新的座標系,新座標系的選擇是由數據本身決定的。
'''
import numpy as np
import matplotlib.pyplot as plt


def loadDataSet(fileName=r'13-PCA\testSet.txt'):
    with open(fileName) as fr:
        stringArr = [line.strip().split() for line in fr.readlines()]
        datArr = [list(map(float, line)) for line in stringArr]
    return np.mat(datArr)


def pca(dataMat, topNfeat=9999999):
    """
    [summary]:
        去除平均值
        計算協方差矩陣
        計算協方差矩陣的特徵值和特徵向量
        將特徵值從大到小排序
        保留最上面的N個特徵向量
        將數據轉換到上述N個特徵向量構建的新空間中
    Arguments:
        dataMat  -- 數據集
    
    Keyword Arguments:
        topNfeat {int} -- 選取的特徵數 (default: {9999999})
    
    Returns:
        [type] -- [description]
    """
    meanVals = np.mean(dataMat, axis=0)
    # 去除平均值
    meanRemoved = dataMat - meanVals
    # 計算協方差矩陣及其特徵值
    covMat = np.cov(meanRemoved, rowvar=0)  # 0-column nonzero-row
    eigVals, eigVects = np.linalg.eig(np.mat(covMat))
    # 對特徵值進行排序,argsort返回索引
    eigValInd = np.argsort(eigVals)
    eigValInd = eigValInd[-1:-(topNfeat + 1):-1]
    redEigVects = eigVects[:, eigValInd]
    lowDDataMat = meanRemoved * redEigVects
    reconMat = (lowDDataMat * redEigVects.T) + meanVals
    return lowDDataMat, reconMat


def test_pca():
    dataMat = loadDataSet(r'13-PCA\testSet.txt')
    lowDMat, reconMat = pca(dataMat, 1)
    print('lowDMat shape:', lowDMat.shape)

    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(dataMat[:, 0].flatten().A[0],
               dataMat[:, 1].flatten().A[0],
               marker='^',
               s=90)
    ax.scatter(reconMat[:, 0].flatten().A[0],
               reconMat[:, 1].flatten().A[0],
               marker='o',
               s=50,
               c='red')
    plt.show()


def replaceNanWithMean():
    datMat = loadDataSet(r'13-PCA\secom.data')
    numFeat = np.shape(datMat)[1]
    for i in range(numFeat):
        # 計算所有非NaN的平均值 np.isnan返回結果數組,元素爲np.nan的位置對應爲True
        meanVal = np.mean(datMat[np.nonzero(~np.isnan(datMat[:, i].A))[0], i])
        datMat[np.nonzero(np.isnan(datMat[:, i]))[0], i] = meanVal
    return datMat


if __name__ == '__main__':
    # test_pca()
    dataMat = replaceNanWithMean()
    meanVals = np.mean(dataMat, axis=0)
    meanRemoved = dataMat - meanVals
    # 計算協方差矩陣 rowvar=False表示每列作爲觀測量
    covMat = np.cov(meanRemoved, rowvar=False)
    eigVals, eigVects = np.linalg.eig(np.mat(covMat))
    print(eigVals)