matlabbp神经网络手写数字识别
时间: 2023-09-16 16:08:25 浏览: 114
以下是一个示例的matlabbp神经网络手写数字识别程序:
首先,需要准备数据。这里使用MNIST数据集,包含60000个手写数字训练样本和10000个测试样本。可以从网上下载并解压缩到本地路径下,例如:
train_images_path = './mnist/train-images-idx3-ubyte';
train_labels_path = './mnist/train-labels-idx1-ubyte';
test_images_path = './mnist/t10k-images-idx3-ubyte';
test_labels_path = './mnist/t10k-labels-idx1-ubyte';
然后,读取数据到matlab中:
train_images = loadMNISTImages(train_images_path)';
train_labels = loadMNISTLabels(train_labels_path);
test_images = loadMNISTImages(test_images_path)';
test_labels = loadMNISTLabels(test_labels_path);
接下来,先定义神经网络的结构。这里使用3层全连接神经网络,输入层有784个神经元(即28x28的图片展开成一维向量),隐藏层有50个神经元,输出层有10个神经元(分别表示0-9这10个数字):
input_layer_size = 784;
hidden_layer_size = 50;
output_layer_size = 10;
然后,初始化神经网络的权重和偏置:
W1 = randn(input_layer_size, hidden_layer_size) / sqrt(input_layer_size);
b1 = zeros(1, hidden_layer_size);
W2 = randn(hidden_layer_size, output_layer_size) / sqrt(hidden_layer_size);
b2 = zeros(1, output_layer_size);
接着,定义损失函数。这里使用交叉熵损失函数:
loss_fn = @(y_hat, y) -mean(sum(y .* log(y_hat), 2));
然后,定义优化器。这里使用随机梯度下降(SGD)算法:
learning_rate = 0.1;
batch_size = 32;
num_epochs = 10;
num_batches = ceil(size(train_images, 1) / batch_size);
for epoch = 1:num_epochs
shuffle_idx = randperm(size(train_images, 1));
train_images = train_images(shuffle_idx, :);
train_labels = train_labels(shuffle_idx);
for batch = 1:num_batches
start_idx = (batch - 1) * batch_size + 1;
end_idx = min(batch * batch_size, size(train_images, 1));
batch_images = train_images(start_idx:end_idx, :);
batch_labels = train_labels(start_idx:end_idx, :);
[y_hat, z] = forward_propagation(batch_images, W1, b1, W2, b2);
loss = loss_fn(y_hat, batch_labels);
[dW1, db1, dW2, db2] = backward_propagation(batch_images, batch_labels, y_hat, z, W2);
W1 = W1 - learning_rate * dW1;
b1 = b1 - learning_rate * db1;
W2 = W2 - learning_rate * dW2;
b2 = b2 - learning_rate * db2;
end
[y_hat, ~] = forward_propagation(test_images, W1, b1, W2, b2);
[~, predicted_labels] = max(y_hat, [], 2);
accuracy = sum(predicted_labels == test_labels) / length(test_labels);
fprintf('Epoch %d, loss = %f, accuracy = %f\n', epoch, loss, accuracy);
end
最后,定义前向传播和反向传播函数:
function [y_hat, z] = forward_propagation(X, W1, b1, W2, b2)
z = X * W1 + b1;
a = relu(z);
y_hat = softmax(a * W2 + b2);
end
function [dW1, db1, dW2, db2] = backward_propagation(X, y, y_hat, z, W2)
delta2 = y_hat - y;
dW2 = z' * delta2;
db2 = mean(delta2, 1);
delta1 = delta2 * W2' .* relu_gradient(z);
dW1 = X' * delta1;
db1 = mean(delta1, 1);
end
其中,relu和softmax分别是激活函数,relu_gradient是relu函数的导数。
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