Machine Learning with MATLAB

Handwriting Recognition Using Bagged Classification Trees

This example shows how to recognize handwritten digits using an ensemble of bagged classification trees. Images of handwritten digits are first used to train a single classification tree and then an ensemble of 200 decision trees. The classification performance of each is compared to one another using a confusion matrix.

Load Training and Test Data

See the references section for information on obtaining the dataset.
clear
load('usps_all');

reduce_dim = false;
X = double(reshape(data,256,11000)');
ylabel = [1:9 0];

y = reshape(repmat(ylabel,1100,1),11000,1);

clearvars data

Visualize Six Random Handwritten Samples

figure(1)
for ii = 1:6
    subplot(2,3,ii)
    rand_num = randperm(11000,1);
    image(reshape(X(rand_num,:),16,16))
    title((y(rand_num)),'FontSize',20)
    axis off
end
colormap gray

Randomly Partition the Data into Training and Validation Sets

cv = cvpartition(y, 'holdout', .5);
Xtrain = X(cv.training,:);
Ytrain = y(cv.training,1);

Xtest = X(cv.test,:);
Ytest = y(cv.test,1);

Train and Predict Using a Single Classification Tree

mdl_ctree = ClassificationTree.fit(Xtrain,Ytrain);
ypred = predict(mdl_ctree,Xtest);
Confmat_ctree = confusionmat(Ytest,ypred);

Train and Predict Using Bagged Decision Trees

mdl = fitensemble(Xtrain,Ytrain,'bag',200,'tree','type','Classification');
ypred = predict(mdl,Xtest);
Confmat_bag = confusionmat(Ytest,ypred);

Compare Confusion Matrices

figure,
heatmap(Confmat_ctree, 0:9, 0:9, 1,'Colormap','red','ShowAllTicks',1,'UseLogColorMap',true,'Colorbar',true);
title('Confusion Matrix: Single Classification Tree')
figure,
heatmap(Confmat_bag, 0:9, 0:9, 1,'Colormap','red','ShowAllTicks',1,'UseLogColorMap',true,'Colorbar',true);
title('Confusion Matrix: Ensemble of Bagged Classification Trees')

Bagged classification trees perform much better than a single classification tree on the training set since the confusion matrix is more dominantly diagonal.

Visualization generated using Customizable Heat Maps.

Reference and License

MAT file for the images are located here: cs.nyu.edu/~roweis/data.html.