python实现tsne

参考链接:

https://blog.csdn.net/zhangweiguo_717/article/details/70998959

原博客代码完整如下:

#-*- coding:utf-8 -*-
import sys
reload(sys)
sys.setdefaultencoding('utf-8')
import time
import numpy
import copy
from sklearn import *
#计算高维空间分布P
def cal_matrix_P(X,neighbors):  
    entropy=numpy.log(neighbors)  
    n1,n2=X.shape #n1,多少条数据;n2,数据的属性 
    from sklearn import *
    D=numpy.square(metrics.pairwise_distances(X))  
    D_sort=numpy.argsort(D,axis=1)  
    P=numpy.zeros((n1,n1))  
    for i in xrange(n1):  
        Di=D[i,D_sort[i,1:]]  
        P[i,D_sort[i,1:]]=cal_p(Di,entropy=entropy)  
    P=(P+numpy.transpose(P))/(2*n1)  
    P=numpy.maximum(P,1e-100)  
    return P



def cal_p(D,entropy,K=50):
    beta=1.0
    H=cal_entropy(D,beta)
    error=H-entropy
    k=0
    betamin=-numpy.inf
    betamax=numpy.inf
    while numpy.abs(error)>1e-4 and k<=K:
        if error > 0:
            betamin=copy.deepcopy(beta)
            if betamax==numpy.inf:
                beta=beta*2
            else:
                beta=(beta+betamax)/2
        else:
            betamax=copy.deepcopy(beta)
            if betamin==-numpy.inf:
                beta=beta/2
            else:
                beta=(beta+betamin)/2
        H=cal_entropy(D,beta)
        error=H-entropy
        k+=1
    P=numpy.exp(-D*beta)
    P=P/numpy.sum(P)
    return P



def cal_entropy(D,beta):  #计算熵
    # P=numpy.exp(-(numpy.sqrt(D))*beta)  
    P=numpy.exp(-D*beta)  
    sumP=sum(P)  
    sumP=numpy.maximum(sumP,1e-200)  
    H=numpy.log(sumP) + beta * numpy.sum(D * P) / sumP  
    return H



#计算低维空间分布Q
#这里修改掉几个注释就能在TSNE和Largevis之间转换。
def cal_matrix_Q(Y):  
    n1,n2=Y.shape  
    D=numpy.square(metrics.pairwise_distances(Y))  
    #Q=1/(1+numpy.exp(D))  
    #Q=1/(1+numpy.square(D))  
    #Q=1/(1+2*D)  
    #Q=1/(1+0.5*D)  
    Q=(1/(1+D))/(numpy.sum(1/(1+D))-n1)  
    Q=Q/(numpy.sum(Q)-numpy.sum(Q[range(n1),range(n1)]))  
    Q[range(n1),range(n1)]=0  
    Q=numpy.maximum(Q,1e-100)  
    return Q

#计算梯度:

def cal_gradients(P,Q,Y):  
    n1,n2=Y.shape  
    DC=numpy.zeros((n1,n2))  
    for i in xrange(n1):  
        E=(1+numpy.sum((Y[i,:]-Y)**2,axis=1))**(-1)  
        F=Y[i,:]-Y  
        G=(P[i,:]-Q[i,:])  
        E=E.reshape((-1,1))  
        G=G.reshape((-1,1))  
        G=numpy.tile(G,(1,n2))  
        E=numpy.tile(E,(1,n2))  
        DC[i,:]=numpy.sum(4*G*E*F,axis=0)  
    return DC

# 4、计算损失函数KL散度,同时这个也是损失函数
def cal_loss(P,Q):  
    C=numpy.sum(P * numpy.log(P / Q))  
    return C


def tsne(X,n=2,neighbors=30,max_iter=200):  
    import shelve
    tsne_dat=shelve.open('tsne.dat')  
    data=[]  
    n1,n2=X.shape  
    P=cal_matrix_P(X,neighbors)  
    Y=numpy.random.randn(n1,n)*1e-4  
    Q = cal_matrix_Q(Y)  
    DY = cal_gradients(P, Q, Y)  
    A=200.0  
    B=0.1  
    for i  in xrange(max_iter):  
        data.append(Y)  
        if i==0:  
            Y=Y-A*DY  
            Y1=Y  
            error1=cal_loss(P,Q)  
        elif i==1:  
            Y=Y-A*DY  
            Y2=Y  
            error2=cal_loss(P,Q)  
        else:  
            YY=Y-A*DY+B*(Y2-Y1)  
            QQ = cal_matrix_Q(YY)  
            error=cal_loss(P,QQ)  
            if error>error2:  
                A=A*0.7  
                continue  
            elif (error-error2)>(error2-error1):  
                A=A*1.2  
            Y=YY  
            error1=error2  
            error2=error  
            Q = QQ  
            DY = cal_gradients(P, Q, Y)  
            Y1=Y2  
            Y2=Y  
        if cal_loss(P,Q)<1e-3:  
            return Y  
        if numpy.fmod(i+1,10)==0:  
            print '%s iterations the error is %s, A is %s'%(str(i+1),str(round(cal_loss(P,Q),2)),str(round(A,3)))  
    tsne_dat['data']=data  
    tsne_dat.close()  
    return Y


def test_iris():  
    from sklearn import *
    from sklearn.datasets import load_iris
    data=datasets.load_iris()  

    X=data.data  #属性
    target=data.target#标签  
    t1=time.time()  
    Y=tsne(X,n=2,max_iter=300,neighbors=20)  
    t2=time.time()  
    print "Custom TSNE cost time: %s"%str(round(t2-t1,2))  
    import matplotlib.pyplot as plt
    figure1=plt.figure()  
    
    plt.subplot(1,2,1)  
    plt.plot(Y[0:50,0],Y[0:50,1],'ro',markersize=30)  
    plt.plot(Y[50:100,0],Y[50:100,1],'gx',markersize=30)  
    plt.plot(Y[100:150,0],Y[100:150,1],'b*',markersize=30)  
    plt.title('CUSTOM')  
    plt.subplot(1,2,2)  
    t1=time.time()  
    Y1=manifold.TSNE(2).fit_transform(data.data)  
    t2=time.time()  
    print "Sklearn TSNE cost time: %s"%str(round(t2-t1,2))  
    plt.plot(Y1[0:50,0],Y1[0:50,1],'ro',markersize=30)  
    plt.plot(Y1[50:100,0],Y1[50:100,1],'gx',markersize=30)  
    plt.plot(Y1[100:150,0],Y1[100:150,1],'b*',markersize=30)  
    plt.title('SKLEARN')  
    plt.show()  
if __name__ == '__main__':
    test_iris()