Python机器学习之PCA降维算法详解

import numpy as np


# 对初始数据进行零均值化处理
def zeroMean(dataMat):
    # 求列均值
    meanVal = np.mean(dataMat, axis=0)
    # 求列差值
    newData = dataMat - meanVal
    return newData, meanVal


# 对初始数据进行降维处理
def pca(dataMat, percent=0.19):
    newData, meanVal = zeroMean(dataMat)

    # 求协方差矩阵
    covMat = np.cov(newData, rowvar=0)

    # 求特征值和特征向量
    eigVals, eigVects = np.linalg.eig(np.mat(covMat))

    # 抽取前n个特征向量
    n = percentage2n(eigVals, percent)
    print("数据降低到：" + str(n) + '维')

    # 将特征值按从小到大排序
    eigValIndice = np.argsort(eigVals)
    # 取最大的n个特征值的下标
    n_eigValIndice = eigValIndice[-1:-(n + 1):-1]
    # 取最大的n个特征值的特征向量
    n_eigVect = eigVects[:, n_eigValIndice]

    # 取得降低到n维的数据
    lowDataMat = newData * n_eigVect
    reconMat = (lowDataMat * n_eigVect.T) + meanVal

    return reconMat, lowDataMat, n


# 通过方差百分比确定抽取的特征向量的个数
def percentage2n(eigVals, percentage):
    # 按降序排序
    sortArray = np.sort(eigVals)[-1::-1]
    # 求和
    arraySum = sum(sortArray)

    tempSum = 0
    num = 0
    for i in sortArray:
        tempSum += i
        num += 1
        if tempSum >= arraySum * percentage:
            return num


if __name__ == '__main__':
    # 初始化原始数据(行代表样本,列代表维度)
    data = np.random.randint(1, 20, size=(6, 8))
    print(data)

    # 对数据降维处理
    fin = pca(data, 0.9)
    mat = fin[1]
    print(mat)

import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.datasets import load_iris

# 加载数据
data = load_iris()
x = data.data
y = data.target

# 设置数据集要降低的维度
pca = PCA(n_components=2)
# 进行数据降维
reduced_x = pca.fit_transform(x)

red_x, red_y = [], []
green_x, green_y = [], []
blue_x, blue_y = [], []

# 对数据集进行分类
for i in range(len(reduced_x)):
    if y[i] == 0:
        red_x.append(reduced_x[i][0])
        red_y.append(reduced_x[i][1])
    elif y[i] == 1:
        green_x.append(reduced_x[i][0])
        green_y.append(reduced_x[i][1])
    else:
        blue_x.append(reduced_x[i][0])
        blue_y.append(reduced_x[i][1])

plt.scatter(red_x, red_y, c='r', marker='x')
plt.scatter(green_x, green_y, c='g', marker='D')
plt.scatter(blue_x, blue_y, c='b', marker='.')
plt.show()