tsne降维可视化

 

 

Python代码：准备训练样本的数据和标签：train_X4000.txt、train_y4000.txt 放于tsne.py当前目录.（具体t-SNE – Laurens van der Maaten http://lvdmaaten.github.io/tsne/，Python implementation）,

tsne.py代码：（为了使得figure显示数据的标签，代码做了简单修改）

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#!/usr/bin/env python # -*- coding: utf-8 -*-   # #  tsne.py #  # Implementation of t-SNE in Python. The implementation was tested on Python 2.5.1, and it requires a working # installation of NumPy. The implementation comes with an example on the MNIST dataset. In order to plot the # results of this example, a working installation of matplotlib is required. # The example can be run by executing: ipython tsne.py -pylab # # #  Created by Laurens van der Maaten on 20-12-08. #  Copyright (c) 2008 Tilburg University. All rights reserved.   import numpy as Math import pylab as Plot       def Hbeta(D = Math.array([]), beta = 1.0):     """Compute the perplexity and the P-row for a specific value of the precision of a Gaussian distribution."""           # Compute P-row and corresponding perplexity     P = Math.exp(-D.copy() * beta);     sumP = sum(P)+1e-6;     H = Math.log(sumP) + beta * Math.sum(D * P) / sumP;     P = P / sumP;     return H, P;             def x2p(X = Math.array([]), tol = 1e-5, perplexity = 30.0):     """Performs a binary search to get P-values in such a way that each conditional Gaussian has the same perplexity."""       # Initialize some variables     print "Computing pairwise distances..."     (n, d) = X.shape;     sum_X = Math.sum(Math.square(X), 1);     D = Math.add(Math.add(-2 * Math.dot(X, X.T), sum_X).T, sum_X);     P = Math.zeros((n, n));     beta = Math.ones((n, 1));     logU = Math.log(perplexity);           # Loop over all datapoints     for i in range(n):               # Print progress         if i % 500 == 0:             print "Computing P-values for point ", i, " of ", n, "..."               # Compute the Gaussian kernel and entropy for the current precision         betamin = -Math.inf;         betamax =  Math.inf;         Di = D[i, Math.concatenate((Math.r_[0:i], Math.r_[i+1:n]))];         (H, thisP) = Hbeta(Di, beta[i]);                       # Evaluate whether the perplexity is within tolerance         Hdiff = H - logU;         tries = 0;         while Math.abs(Hdiff) > tol and tries < 50:                               # If not, increase or decrease precision             if Hdiff > 0:                 betamin = beta[i].copy();                 if betamax == Math.inf or betamax == -Math.inf:                     beta[i] = beta[i] * 2;                 else:                     beta[i] = (beta[i] + betamax) / 2;             else:                 betamax = beta[i].copy();                 if betamin == Math.inf or betamin == -Math.inf:                     beta[i] = beta[i] / 2;                 else:                     beta[i] = (beta[i] + betamin) / 2;                           # Recompute the values             (H, thisP) = Hbeta(Di, beta[i]);             Hdiff = H - logU;             tries = tries + 1;                       # Set the final row of P         P[i, Math.concatenate((Math.r_[0:i], Math.r_[i+1:n]))] = thisP;           # Return final P-matrix         print "Mean value of sigma: ", Math.mean(Math.sqrt(1 / beta))     return P;             def pca(X = Math.array([]), no_dims = 50):     """Runs PCA on the NxD array X in order to reduce its dimensionality to no_dims dimensions."""       print "Preprocessing the data using PCA..."     (n, d) = X.shape;     X = X - Math.tile(Math.mean(X, 0), (n, 1));     (l, M) = Math.linalg.eig(Math.dot(X.T, X));     Y = Math.dot(X, M[:,0:no_dims]);     return Y;     def tsne(X = Math.array([]), no_dims = 2, initial_dims = 50, perplexity = 30.0):     """Runs t-SNE on the dataset in the NxD array X to reduce its dimensionality to no_dims dimensions.     The syntaxis of the function is Y = tsne.tsne(X, no_dims, perplexity), where X is an NxD NumPy array."""           # Check inputs     if X.dtype != "float64":         print "Error: array X should have type float64.";         return -1;     #if no_dims.__class__ != "":            # doesn't work yet!     #    print "Error: number of dimensions should be an integer.";     #    return -1;           # Initialize variables     X = pca(X, initial_dims).real;     (n, d) = X.shape;     max_iter = 1000     initial_momentum = 0.5;     final_momentum = 0.8;     eta = 500;     min_gain = 0.01;     Y = Math.random.randn(n, no_dims);     dY = Math.zeros((n, no_dims));     iY = Math.zeros((n, no_dims));     gains = Math.ones((n, no_dims));           # Compute P-values     P = x2p(X, 1e-5, perplexity);     P = P + Math.transpose(P);     P = P / (Math.sum(P));     P = P * 4;                                    # early exaggeration     P = Math.maximum(P, 1e-12);           # Run iterations     for iter in range(max_iter):                   # Compute pairwise affinities         sum_Y = Math.sum(Math.square(Y), 1);                num = 1 / (1 + Math.add(Math.add(-2 * Math.dot(Y, Y.T), sum_Y).T, sum_Y));         num[range(n), range(n)] = 0;         Q = num / Math.sum(num);         Q = Math.maximum(Q, 1e-12);                   # Compute gradient         PQ = P - Q;         for i in range(n):             dY[i,:] = Math.sum(Math.tile(PQ[:,i] * num[:,i], (no_dims, 1)).T * (Y[i,:] - Y), 0);                       # Perform the update         if iter < 20:             momentum = initial_momentum         else:             momentum = final_momentum         gains = (gains + 0.2) * ((dY > 0) != (iY > 0)) + (gains * 0.8) * ((dY > 0) == (iY > 0));         gains[gains < min_gain] = min_gain;         iY = momentum * iY - eta * (gains * dY);         Y = Y + iY;         Y = Y - Math.tile(Math.mean(Y, 0), (n, 1));                   # Compute current value of cost function         if (iter + 1) % 10 == 0:             C = Math.sum(P * Math.log(P / Q));             print "Iteration ", (iter + 1), ": error is ", C                       # Stop lying about P-values         if iter == 100:             P = P / 4;                   # Return solution     return Y;                 if __name__ == "__main__":     print "Run Y = tsne.tsne(X, no_dims, perplexity) to perform t-SNE on your dataset."     print "Running example on 2,500 MNIST digits..."     X = Math.loadtxt("train_X4000.txt"); #X = X[:100]     labels = Math.loadtxt("train_y4000.txt"); #labels = labels[:100]     Y = tsne(X, 2, 38, 20.0);     fil = open('Y.txt','w')     for i in Y:         fil.write(str(i[0])+' '+str(i[1])+'\n')     fil.close()     colors=['b', 'c', 'y', 'm', 'r']     idx_1 = [i1 for i1 in range(len(labels)) if labels[i1]==1]     flg1=Plot.scatter(Y[idx_1,0], Y[idx_1,1], 20,color=colors[0],label='1');     idx_2= [i2 for i2 in range(len(labels)) if labels[i2]==2]     flg2=Plot.scatter(Y[idx_2,0], Y[idx_2,1], 20,color=colors[1], label='2');     idx_3= [i3 for i3 in range(len(labels)) if labels[i3]==3]     flg3=Plot.scatter(Y[idx_3,0], Y[idx_3,1], 20, color=colors[2],label='3');     idx_4= [i4 for i4 in range(len(labels)) if labels[i4]==4]     flg4=Plot.scatter(Y[idx_4,0], Y[idx_4,1], 20,color=colors[3], label='4');        idx_5= [i5 for i5 in range(len(labels)) if labels[i5]==5]     flg5=Plot.scatter(Y[idx_5,0], Y[idx_5,1], 20, color=colors[4],label='5'); #    flg=Plot.scatter(Y[:,0], Y[:,1], 20,labels);     Plot.legend()     Plot.savefig('figure4000.pdf')     Plot.show()