神经网络——手写数字识别

网络模型

输入层：400个神经元；隐藏层：26个神经元；输出层：10个神经元

ex3_nn.m

%% Machine Learning Online Class - Exercise 3 | Part 2: Neural Networks

%  Instructions
%  ------------
% 
%  This file contains code that helps you get started on the
%  linear exercise. You will need to complete the following functions 
%  in this exericse:
%
%     lrCostFunction.m (logistic regression cost function)
%     oneVsAll.m
%     predictOneVsAll.m
%     predict.m
%
%  For this exercise, you will not need to change any code in this file,
%  or any other files other than those mentioned above.
%

%% Initialization
clear ; close all; clc

%% Setup the parameters you will use for this exercise
input_layer_size  = 400;  % 20x20 Input Images of Digits
hidden_layer_size = 25;   % 25 hidden units
num_labels = 10;          % 10 labels, from 1 to 10   
                          % (note that we have mapped "0" to label 10)

%% =========== Part 1: Loading and Visualizing Data =============
%  We start the exercise by first loading and visualizing the dataset. 
%  You will be working with a dataset that contains handwritten digits.
%

% Load Training Data
fprintf(Loading and Visualizing Data ...
)

load(ex3data1.mat);
m = size(X, 1);%5000

% Randomly select 100 data points to display
sel = randperm(size(X, 1));
sel = sel(1:100);

displayData(X(sel, :));

fprintf(Program paused. Press enter to continue.
);
pause;

%% ================ Part 2: Loading Pameters ================
% In this part of the exercise, we load some pre-initialized 
% neural network parameters.

fprintf(
Loading Saved Neural Network Parameters ...
)

% Load the weights into variables Theta1 and Theta2
load(ex3weights.mat);

%% ================= Part 3: Implement Predict =================
%  After training the neural network, we would like to use it to predict
%  the labels. You will now implement the "predict" function to use the
%  neural network to predict the labels of the training set. This lets
%  you compute the training set accuracy.


 
pred = predict(Theta1, Theta2, X);

fprintf(
Training Set Accuracy: %f
, mean(double(pred == y)) * 100);

fprintf(Program paused. Press enter to continue.
);
pause;

%  To give you an idea of the networks output, you can also run
%  through the examples one at the a time to see what it is predicting.

%  Randomly permute examples
rp = randperm(m);

for i = 1:m
    % Display 
    fprintf(
Displaying Example Image
);
    displayData(X(rp(i), :));

    pred = predict(Theta1, Theta2, X(rp(i),:));
    fprintf(
Neural Network Prediction: %d (digit %d)
, pred, mod(pred, 10));
    
    % Pause with quit option
    s = input(Paused - press enter to continue, q to exit:,s);
    if s == q
      break
    end
end

预测

function p = predict(Theta1, Theta2, X)
		m = size(X, 1);
		num_labels = size(Theta2, 1);
		p = zeros(size(X, 1), 1);
		X = [ones(size(X,1),1),X];%5000*201
		a2 = sigmoid(X*Theta1);
		a2 = [ones(size(a2,1),1),a2];
		a3 = sigmoid(a2*Theta2);
		[r,p] = max(a3,[],2);
end