【DeepLearning】Exercise:Softmax Regression

Exercise:Softmax Regression

习题的链接：Exercise:Softmax Regression 

softmaxCost.m

function [cost, grad] = softmaxCost(theta, numClasses, inputSize, lambda, data, labels)

% numClasses - the number of classes 
% inputSize - the size N of the input vector
% lambda - weight decay parameter
% data - the N x M input matrix, where each column data(:, i) corresponds to
%        a single test set
% labels - an M x 1 matrix containing the labels corresponding for the input data
%

% Unroll the parameters from theta
theta = reshape(theta, numClasses, inputSize);

numCases = size(data, 2);

% labels row, numCases col
groundTruth = full(sparse(labels, 1:numCases, 1));
cost = 0;

thetagrad = zeros(numClasses, inputSize);

%% ---------- YOUR CODE HERE --------------------------------------
%  Instructions: Compute the cost and gradient for softmax regression.
%                You need to compute thetagrad and cost.
%                The groundTruth matrix might come in handy.

M = theta * data;
M = bsxfun(@minus, M, max(M, [], 1));
M = exp(M);
M = bsxfun(@rdivide, M, sum(M));
diff = groundTruth - M;

cost = -(1/numCases) * sum(sum(groundTruth .* log(M))) + (lambda/2) * sum(sum(theta .* theta));
for i=1:numClasses
    thetagrad(i, :) = -(1/numCases) * (sum(data .* repmat(diff(i, :), inputSize, 1), 2))' + lambda * theta(i, :);
end
% ------------------------------------------------------------------
% Unroll the gradient matrices into a vector for minFunc
grad = [thetagrad(:)];
end

softmaxPredict.m

function [pred] = softmaxPredict(softmaxModel, data)

% softmaxModel - model trained using softmaxTrain
% data - the N x M input matrix, where each column data(:, i) corresponds to
%        a single test set
%
% Your code should produce the prediction matrix 
% pred, where pred(i) is argmax_c P(y(c) | x(i)).
 
% Unroll the parameters from theta
theta = softmaxModel.optTheta;  % this provides a numClasses x inputSize matrix
pred = zeros(1, size(data, 2));

%% ---------- YOUR CODE HERE --------------------------------------
%  Instructions: Compute pred using theta assuming that the labels start 
%                from 1.

[~, pred] = max(theta * data);

% ---------------------------------------------------------------------

end

Accuracy: 92.640%