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Visualize High-Dimensional Data Using t-SNE

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This example shows how to visualize the MNIST data [1], which consists of images of handwritten digits, using the tsne function. The images are 28-by-28 pixels in grayscale. Each image has an associated label from 0 through 9, which is the digit that the image represents. tsne reduces the dimension of the data from 784 original dimensions to 50 using PCA, and then to two or three using the t-SNE Barnes-Hut algorithm.

Obtain Data

Begin by obtaining image and label data from

https://yann.lecun.com/exdb/mnist/

Unzip the files. For this example, use the t10k-images data.

imageFileName = 't10k-images.idx3-ubyte';
labelFileName = 't10k-labels.idx1-ubyte';

Process the files to load them in the workspace. The code for this processing function appears at the end of this example.

[X,L] = processMNISTdata(imageFileName,labelFileName);
Read MNIST image data...
Number of images in the dataset:  10000 ...
Each image is of 28 by 28 pixels...
The image data is read to a matrix of dimensions:  10000 by  784...
End of reading image data.

Read MNIST label data...
Number of labels in the dataset:  10000 ...
The label data is read to a matrix of dimensions:  10000 by  1...
End of reading label data.

Reduce Dimension of Data to Two

Obtain two-dimensional analogues of the data clusters using t-SNE. Use PCA to reduce the initial dimensionality to 50. Use the Barnes-Hut variant of the t-SNE algorithm to save time on this relatively large data set.

rng default % for reproducibility
Y = tsne(X,'Algorithm','barneshut','NumPCAComponents',50);

Display the result, colored with the correct labels.

figure
numGroups = length(unique(L));
clr = hsv(numGroups);
gscatter(Y(:,1),Y(:,2),L,clr)

t-SNE creates clusters of points based solely on their relative similarities that correspond closely to the true labels.

Reduce Dimension of Data to Three

t-SNE can also reduce the data to three dimensions. Set the tsne 'NumDimensions' name-value pair to 3.

rng default % for fair comparison
Y3 = tsne(X,'Algorithm','barneshut','NumPCAComponents',50,'NumDimensions',3);
figure
scatter3(Y3(:,1),Y3(:,2),Y3(:,3),15,clr(L+1,:),'filled');
view(-93,14)

Here is the code of the function that reads the data into the workspace.

function [X,L] = processMNISTdata(imageFileName,labelFileName)

[fileID,errmsg] = fopen(imageFileName,'r','b');
if fileID < 0
    error(errmsg);
end
%%
% First read the magic number. This number is 2051 for image data, and
% 2049 for label data
magicNum = fread(fileID,1,'int32',0,'b');
if magicNum == 2051
    fprintf('\nRead MNIST image data...\n')
end
%%
% Then read the number of images, number of rows, and number of columns
numImages = fread(fileID,1,'int32',0,'b');
fprintf('Number of images in the dataset: %6d ...\n',numImages);
numRows = fread(fileID,1,'int32',0,'b');
numCols = fread(fileID,1,'int32',0,'b');
fprintf('Each image is of %2d by %2d pixels...\n',numRows,numCols);
%%
% Read the image data
X = fread(fileID,inf,'unsigned char');
%%
% Reshape the data to array X
X = reshape(X,numCols,numRows,numImages);
X = permute(X,[2 1 3]);
%%
% Then flatten each image data into a 1 by (numRows*numCols) vector, and 
% store all the image data into a numImages by (numRows*numCols) array.
X = reshape(X,numRows*numCols,numImages)';
fprintf(['The image data is read to a matrix of dimensions: %6d by %4d...\n',...
    'End of reading image data.\n'],size(X,1),size(X,2));
%%
% Close the file
fclose(fileID);
%%
% Similarly, read the label data.
[fileID,errmsg] = fopen(labelFileName,'r','b');
if fileID < 0
    error(errmsg);
end
magicNum = fread(fileID,1,'int32',0,'b');
if magicNum == 2049
    fprintf('\nRead MNIST label data...\n')
end
numItems = fread(fileID,1,'int32',0,'b');
fprintf('Number of labels in the dataset: %6d ...\n',numItems);

L = fread(fileID,inf,'unsigned char');
fprintf(['The label data is read to a matrix of dimensions: %6d by %2d...\n',...
    'End of reading label data.\n'],size(L,1),size(L,2));
fclose(fileID);

References

[1] Yann LeCun (Courant Institute, NYU) and Corinna Cortes (Google Labs, New York) hold the copyright of MNIST dataset, which is a derivative work from original NIST datasets. MNIST dataset is made available under the terms of the Creative Commons Attribution-Share Alike 3.0 license, https://creativecommons.org/licenses/by-sa/3.0/

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