Vectorize

machine-learning-ex1/gradientDescent.m

@@ -16,9 +16,9 @@
     % Hint: While debugging, it can be useful to print out the values
     %       of the cost function (computeCost) and gradient here.
     %
-    temp0 = theta(1) - alpha*sum(X*theta-y)/m;
-    temp1 = theta(2) - alpha*sum((X*theta-y).*X(:,2))/m;
-    theta = [temp0;temp1];
+
+
+theta=theta-alpha*X'*(X*theta-y)/m;
 
     % ============================================================
 

machine-learning-ex2/costFunction.m

@@ -19,19 +19,13 @@
 %
 % Note: grad should have the same dimensions as theta
 %
-% for i=1:m
-    % hx = sigmoid(X(i,:)*theta);
-    % J = J + (-y(i)*log(hx)-(1-y(i))*log(1-hx));
-% end
-% J = J/m;
+
 
 %Vectorization
 hx = sigmoid(X*theta);
 J = sum(-y.*log(hx)-(1-y).*log(1-hx))/m;
 
-for j=1:size(theta)
-	grad(j) = sum((hx-y).*X(:,j))/m;
-end
+grad=X'*(hx-y)/m;
 
 
 % =============================================================

machine-learning-ex2/costFunctionReg.m

@@ -7,7 +7,6 @@
 % Initialize some useful values
 m = length(y); % number of training examples
 n = length(theta);
-
 % You need to return the following variables correctly 
 J = 0;
 grad = zeros(size(theta));
@@ -17,17 +16,12 @@
 %               You should set J to the cost.
 %               Compute the partial derivatives and set grad to the partial
 %               derivatives of the cost w.r.t. each parameter in theta
-
-%Vectorization
 hx = sigmoid(X*theta);
 J = sum(-y.*log(hx)-(1-y).*log(1-hx))/m + lambda*sum(theta(2:n).^2)/(2*m);
 
+grad=X'*(hx-y)/m + lambda*theta/m;
 grad(1) = sum((hx-y).*X(:,1))/m;
 
-for j=2:n
-    grad(j) = sum((hx-y).*X(:,j))/m + lambda*theta(j)/m;
-end
-
 % =============================================================
 
 end

machine-learning-ex3/displayData.m

@@ -0,0 +1,59 @@
+function [h, display_array] = displayData(X, example_width)
+%DISPLAYDATA Display 2D data in a nice grid
+%   [h, display_array] = DISPLAYDATA(X, example_width) displays 2D data
+%   stored in X in a nice grid. It returns the figure handle h and the 
+%   displayed array if requested.
+
+% Set example_width automatically if not passed in
+if ~exist('example_width', 'var') || isempty(example_width) 
+	example_width = round(sqrt(size(X, 2)));
+end
+
+% Gray Image
+colormap(gray);
+
+% Compute rows, cols
+[m n] = size(X);
+example_height = (n / example_width);
+
+% Compute number of items to display
+display_rows = floor(sqrt(m));
+display_cols = ceil(m / display_rows);
+
+% Between images padding
+pad = 1;
+
+% Setup blank display
+display_array = - ones(pad + display_rows * (example_height + pad), ...
+                       pad + display_cols * (example_width + pad));
+
+% Copy each example into a patch on the display array
+curr_ex = 1;
+for j = 1:display_rows
+	for i = 1:display_cols
+		if curr_ex > m, 
+			break; 
+		end
+		% Copy the patch
+
+		% Get the max value of the patch
+		max_val = max(abs(X(curr_ex, :)));
+		display_array(pad + (j - 1) * (example_height + pad) + (1:example_height), ...
+		              pad + (i - 1) * (example_width + pad) + (1:example_width)) = ...
+						reshape(X(curr_ex, :), example_height, example_width) / max_val;
+		curr_ex = curr_ex + 1;
+	end
+	if curr_ex > m, 
+		break; 
+	end
+end
+
+% Display Image
+h = imagesc(display_array, [-1 1]);
+
+% Do not show axis
+axis image off
+
+drawnow;
+
+end

machine-learning-ex3/ex3.m

@@ -0,0 +1,69 @@
+%% Machine Learning Online Class - Exercise 3 | Part 1: One-vs-all
+
+%  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 part of the exercise
+input_layer_size  = 400;  % 20x20 Input Images of Digits
+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 ...\n')
+
+load('ex3data1.mat'); % training data stored in arrays X, y
+m = size(X, 1);
+
+% Randomly select 100 data points to display
+rand_indices = randperm(m);
+sel = X(rand_indices(1:100), :);
+
+displayData(sel);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ============ Part 2: Vectorize Logistic Regression ============
+%  In this part of the exercise, you will reuse your logistic regression
+%  code from the last exercise. You task here is to make sure that your
+%  regularized logistic regression implementation is vectorized. After
+%  that, you will implement one-vs-all classification for the handwritten
+%  digit dataset.
+%
+
+fprintf('\nTraining One-vs-All Logistic Regression...\n')
+
+lambda = 0.1;
+[all_theta] = oneVsAll(X, y, num_labels, lambda);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================ Part 3: Predict for One-Vs-All ================
+%  After ...
+pred = predictOneVsAll(all_theta, X);
+
+fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);
+

machine-learning-ex3/ex3_nn.m

@@ -0,0 +1,88 @@
+%% 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 ...\n')
+
+load('ex3data1.mat');
+m = size(X, 1);
+
+% 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.\n');
+pause;
+
+%% ================ Part 2: Loading Pameters ================
+% In this part of the exercise, we load some pre-initialized 
+% neural network parameters.
+
+fprintf('\nLoading Saved Neural Network Parameters ...\n')
+
+% 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('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%  To give you an idea of the network's 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('\nDisplaying Example Image\n');
+    displayData(X(rp(i), :));
+
+    pred = predict(Theta1, Theta2, X(rp(i),:));
+    fprintf('\nNeural Network Prediction: %d (digit %d)\n', pred, mod(pred, 10));
+
+    % Pause
+    fprintf('Program paused. Press enter to continue.\n');
+    pause;
+end
+