Machine Learning Basics-Principal Component Analysis PCA-16

PCA (Principal Component Analysis)

PCA-simple example

import numpy as np
import matplotlib.pyplot as plt

# 载入数据
data = np.genfromtxt("data.csv", delimiter=",")
x_data = data[:,0]
y_data = data[:,1]
plt.scatter(x_data,y_data)
plt.show()
print(x_data.shape)

# 数据中心化
def zeroMean(dataMat):
    # 按列求平均，即各个特征的平均
    meanVal = np.mean(dataMat, axis=0) 
    newData = dataMat - meanVal
    return newData, meanVal

newData,meanVal=zeroMean(data)  
# np.cov用于求协方差矩阵，参数rowvar=0说明数据一行代表一个样本
covMat = np.cov(newData, rowvar=0)

# 协方差矩阵
covMat

# np.linalg.eig求矩阵的特征值和特征向量
eigVals, eigVects = np.linalg.eig(np.mat(covMat))

# 特征值
eigVals

# 特征向量
eigVects

# 对特征值从小到大排序
eigValIndice = np.argsort(eigVals)
eigValIndice

top = 1
# 最大的top个特征值的下标
n_eigValIndice = eigValIndice[-1:-(top+1):-1]

n_eigValIndice

# 最大的n个特征值对应的特征向量
n_eigVect = eigVects[:,n_eigValIndice]
n_eigVect

# 低维特征空间的数据
lowDDataMat = newData*n_eigVect
lowDDataMat

# 利用低纬度数据来重构数据
reconMat = (lowDDataMat*n_eigVect.T) + meanVal
reconMat

# 载入数据
data = np.genfromtxt("data.csv", delimiter=",")
x_data = data[:,0]
y_data = data[:,1]
plt.scatter(x_data,y_data)

# 重构的数据
x_data = np.array(reconMat)[:,0]
y_data = np.array(reconMat)[:,1]
plt.scatter(x_data,y_data,c='r')
plt.show()

Handwritten digit recognition and dimensionality reduction visualization

from sklearn.neural_network import MLPClassifier
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,confusion_matrix
import numpy as np
import matplotlib.pyplot as plt

digits = load_digits()#载入数据
x_data = digits.data #数据
y_data = digits.target #标签

x_train,x_test,y_train,y_test = train_test_split(x_data,y_data) #分割数据1/4为测试数据，3/4为训练数据

x_data.shape

mlp = MLPClassifier(hidden_layer_sizes=(100,50) ,max_iter=500)
mlp.fit(x_train,y_train)

# 数据中心化
def zeroMean(dataMat):
    # 按列求平均，即各个特征的平均
    meanVal = np.mean(dataMat, axis=0) 
    newData = dataMat - meanVal
    return newData, meanVal

def pca(dataMat,top):
    # 数据中心化
    newData,meanVal=zeroMean(dataMat) 
    # np.cov用于求协方差矩阵，参数rowvar=0说明数据一行代表一个样本
    covMat = np.cov(newData, rowvar=0)
    # np.linalg.eig求矩阵的特征值和特征向量
    eigVals, eigVects = np.linalg.eig(np.mat(covMat))
    # 对特征值从小到大排序
    eigValIndice = np.argsort(eigVals)
    # 最大的n个特征值的下标
    n_eigValIndice = eigValIndice[-1:-(top+1):-1]
    # 最大的n个特征值对应的特征向量
    n_eigVect = eigVects[:,n_eigValIndice]
    # 低维特征空间的数据
    lowDDataMat = newData*n_eigVect
    # 利用低纬度数据来重构数据
    reconMat = (lowDDataMat*n_eigVect.T) + meanVal
    # 返回低维特征空间的数据和重构的矩阵
    return lowDDataMat,reconMat 

lowDDataMat,reconMat = pca(x_data,2)

# 重构的数据
x = np.array(lowDDataMat)[:,0]
y = np.array(lowDDataMat)[:,1]
plt.scatter(x,y,c='r')
plt.show()

predictions = mlp.predict(x_data)

# 重构的数据
x = np.array(lowDDataMat)[:,0]
y = np.array(lowDDataMat)[:,1]
plt.scatter(x,y,c=y_data)
plt.show()

lowDDataMat,reconMat = pca(x_data,3)

from mpl_toolkits.mplot3d import Axes3D  
x = np.array(lowDDataMat)[:,0]
y = np.array(lowDDataMat)[:,1]
z = np.array(lowDDataMat)[:,2]
ax = plt.figure().add_subplot(111, projection = '3d') 
ax.scatter(x, y, z, c = y_data, s = 10) #点为红色三角形 

plt.show()

Sklearn-handwritten digit dimensionality reduction prediction

from sklearn.neural_network import MLPClassifier
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,confusion_matrix
from sklearn import decomposition
import matplotlib.pyplot as plt

digits = load_digits()#载入数据
x_data = digits.data #数据
y_data = digits.target #标签

x_train,x_test,y_train,y_test = train_test_split(x_data,y_data) #分割数据1/4为测试数据，3/4为训练数据

mlp = MLPClassifier(hidden_layer_sizes=(100,50) ,max_iter=500)
mlp.fit(x_train,y_train )

predictions = mlp.predict(x_test)
print(classification_report(predictions, y_test))
print(confusion_matrix(predictions, y_test))

pca = decomposition.PCA()
pca.fit(x_data)

# 方差
pca.explained_variance_

# 方差占比
pca.explained_variance_ratio_

variance = []
for i in range(len(pca.explained_variance_ratio_)):
    variance.append(sum(pca.explained_variance_ratio_[:i+1]))

plt.plot(range(1,len(pca.explained_variance_ratio_)+1), variance)
plt.show()

pca = decomposition.PCA(whiten=True,n_components=0.8)
pca.fit(x_data)

pca.explained_variance_ratio_

x_train_pca = pca.transform(x_train)

mlp = MLPClassifier(hidden_layer_sizes=(100,50) ,max_iter=500)
mlp.fit(x_train_pca,y_train )

x_test_pca = pca.transform(x_test)
predictions = mlp.predict(x_test_pca)
print(classification_report(predictions, y_test))
print(confusion_matrix(predictions, y_test))