give a code which uses back propagation network for character recognition in matlab

Here is an example code that uses backpropagation algorithm for character recognition in MATLAB:

main.m
% Load the training data
load('character_data.mat');

% Set the parameters
inputLayerSize = size(trainingData, 2);
hiddenLayerSize = 25;
outputLayerSize = 26;
learningRate = 0.01;
numIterations = 1000;

% Initialize the weights and biases
weights1 = randn(inputLayerSize, hiddenLayerSize);
biases1 = randn(hiddenLayerSize, 1);
weights2 = randn(hiddenLayerSize, outputLayerSize);
biases2 = randn(outputLayerSize, 1);

% Training loop
for iteration = 1:numIterations
    % Forward propagation
    hiddenLayerInput = trainingData * weights1 + biases1';
    hiddenLayerOutput = sigmoid(hiddenLayerInput);
    outputLayerInput = hiddenLayerOutput * weights2 + biases2'; 
    outputLayerOutput = sigmoid(outputLayerInput);
    
    % Backpropagation
    outputLayerError = outputLayerOutput - trainingLabels;
    hiddenLayerError = (outputLayerError * weights2') .* (hiddenLayerOutput .* (1 - hiddenLayerOutput));
    
    % Gradient descent
    weights2 = weights2 - learningRate * (hiddenLayerOutput' * outputLayerError);
    biases2 = biases2 - learningRate * sum(outputLayerError, 2);
    weights1 = weights1 - learningRate * (trainingData' * hiddenLayerError);
    biases1 = biases1 - learningRate * sum(hiddenLayerError, 2);
end

% Testing
testData = ... % your test data here
hiddenLayerInput = testData * weights1 + biases1';
hiddenLayerOutput = sigmoid(hiddenLayerInput);
outputLayerInput = hiddenLayerOutput * weights2 + biases2'; 
outputLayerOutput = sigmoid(outputLayerInput);

% Obtain the predicted labels
[~, predictedLabels] = max(outputLayerOutput, [], 2);

% Display the predicted labels
disp(predictedLabels);
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Note that this code assumes that you have the training data and training labels stored in the variables trainingData and trainingLabels respectively. You would need to replace ... in the code with your own test data for character recognition.

The sigmoid function used in the code is a typical sigmoid activation function implemented as:

main.m
function y = sigmoid(x)
    y = 1 ./ (1 + exp(-x));
end
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Make sure to adjust the values of hiddenLayerSize, learningRate, and numIterations according to your requirements.

I hope this helps you get started with character recognition using backpropagation in MATLAB!

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