LDA_PCA_SVD导论

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资源链接 http://download.csdn.net/detail/u012176591/8257297

相关源码：

svd.py

import numpy  import random   import matplotlib.pyplot as pyplot data = numpy.array([[1,0.6,1,0,0.4],\                    [2,1.7,2,0.2,0],\                    [1,0,1,0.1,0],\                    [3.2,4.8,5,0,0.4],\                    [1,1,1.3,2,2],\                    [0,0,0,3.2,3],\                    [0,0,0,0.9,1]])U,Sigma,VT=numpy.linalg.svd(data)print U.shape,VT.shape,Sigma.shapeprint Sigmai=2colomnclass=data.dot(VT[:i,:].T)print colomnclassrowclass = U[:,:i].T.dot(data)print rowclasspyplot.figure(1)ax1=pyplot.subplot(211)ax2=pyplot.subplot(212)pyplot.sca(ax1)pyplot.plot(colomnclass[:,0],colomnclass[:,1],'s')pyplot.sca(ax2)pyplot.plot(rowclass[0,:],rowclass[1,:],'^')pyplot.show()

PCA_sample.py

# -*- coding: cp936 -*-import numpyimport scipyimport randomimport matplotlib.pyplot as pyplotimport scipy.linalg as linalgimport scipy.stats as statsdef loaddata():    dataset=[]    locset =[]    center = numpy.array([2,2])    direct = numpy.array([-1,1])    gauss = stats.norm(0,0.6)    direct = numpy.divide(numpy.array([-1,1]),linalg.norm(numpy.array([-1,1])))    for i in range(50):        bias = random.gauss(0,2)#偏移center的长度        while numpy.abs(bias)>1.6:#限制偏移的幅度            bias = random.gauss(0,0.4)        loc =center +bias*center/linalg.norm(center)#投射到45度角上的坐标点               locset.append(loc)        gausspdf = gauss.pdf(bias)        label =random.random()-0.5        dataset.append(loc+label*gausspdf*direct)            return numpy.array(dataset),numpy.array(locset)def plot(dataset,locset):    pyplot.plot(dataset[:,0],dataset[:,1],'r^')    locset[:,0] = locset[:,0]+0.3;locset[:,1]=locset[:,1]-0.3    pyplot.plot(locset[:,0],locset[:,1],'k+')    for i in range(dataset.shape[0]):        pyplot.plot([locset[i,0],dataset[i,0]],[locset[i,1],dataset[i,1]],'y--')    pyplot.annotate('',xytext=(1.6,1.6),xy=(3.0,3.0),arrowprops=dict(facecolor='black',width =3, shrink=0.01))    pyplot.annotate('',xytext=(1.65,1.65),xy=(1.45,1.85),arrowprops=dict(facecolor='black',width =1, shrink=0.01))    pyplot.text(1.5,1.9,'Noise',color="black",ha="center")    pyplot.text(2.8,3,'Signal',color="black",ha="center")    pyplot.xlim(0.5,3.5)    pyplot.ylim(0.5,3.5)    pyplot.xlabel("x axis")    pyplot.ylabel("y axis")    #pyplot.title("PCA example")        pyplot.show()dataset,locset =loaddata()plot(dataset,locset)

本博文的TeX源码：https://code.csdn.net/snippets/610273/master/LDA_PCA_SVD%E5%AF%BC%E8%AE%BA.tex/raw

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