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)

#!/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()