137 lines
3.8 KiB
Matlab
137 lines
3.8 KiB
Matlab
%% Machine Learning Online Class - Exercise 2: Logistic Regression
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%
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the second part
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% of the exercise which covers regularization with logistic regression.
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%
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% You will need to complete the following functions in this exericse:
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%
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% sigmoid.m
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% costFunction.m
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% predict.m
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% costFunctionReg.m
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%
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% For this exercise, you will not need to change any code in this file,
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% or any other files other than those mentioned above.
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%
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%% Initialization
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clear ; close all; clc
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%% Load Data
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% The first two columns contains the X values and the third column
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% contains the label (y).
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data = load('ex2data2.txt');
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X = data(:, [1, 2]); y = data(:, 3);
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plotData(X, y);
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% Put some labels
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hold on;
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% Labels and Legend
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xlabel('Microchip Test 1')
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ylabel('Microchip Test 2')
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% Specified in plot order
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legend('y = 1', 'y = 0')
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hold off;
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%% =========== Part 1: Regularized Logistic Regression ============
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% In this part, you are given a dataset with data points that are not
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% linearly separable. However, you would still like to use logistic
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% regression to classify the data points.
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%
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% To do so, you introduce more features to use -- in particular, you add
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% polynomial features to our data matrix (similar to polynomial
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% regression).
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%
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% Add Polynomial Features
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% Note that mapFeature also adds a column of ones for us, so the intercept
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% term is handled
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X = mapFeature(X(:,1), X(:,2));
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% Initialize fitting parameters
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initial_theta = zeros(size(X, 2), 1);
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% Set regularization parameter lambda to 1
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lambda = 1;
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% Compute and display initial cost and gradient for regularized logistic
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% regression
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[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
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fprintf('Cost at initial theta (zeros): %f\n', cost);
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fprintf('Expected cost (approx): 0.693\n');
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fprintf('Gradient at initial theta (zeros) - first five values only:\n');
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fprintf(' %f \n', grad(1:5));
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fprintf('Expected gradients (approx) - first five values only:\n');
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fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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% Compute and display cost and gradient
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% with all-ones theta and lambda = 10
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test_theta = ones(size(X,2),1);
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[cost, grad] = costFunctionReg(test_theta, X, y, 10);
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fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
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fprintf('Expected cost (approx): 3.16\n');
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fprintf('Gradient at test theta - first five values only:\n');
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fprintf(' %f \n', grad(1:5));
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fprintf('Expected gradients (approx) - first five values only:\n');
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fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============= Part 2: Regularization and Accuracies =============
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% Optional Exercise:
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% In this part, you will get to try different values of lambda and
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% see how regularization affects the decision coundart
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%
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% Try the following values of lambda (0, 1, 10, 100).
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%
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% How does the decision boundary change when you vary lambda? How does
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% the training set accuracy vary?
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%
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% Initialize fitting parameters
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initial_theta = zeros(size(X, 2), 1);
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% Set regularization parameter lambda to 1 (you should vary this)
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lambda = 1;
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% Set Options
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options = optimset('GradObj', 'on', 'MaxIter', 400);
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% Optimize
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[theta, J, exit_flag] = ...
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fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
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% Plot Boundary
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plotDecisionBoundary(theta, X, y);
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hold on;
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title(sprintf('lambda = %g', lambda))
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% Labels and Legend
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xlabel('Microchip Test 1')
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ylabel('Microchip Test 2')
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legend('y = 1', 'y = 0', 'Decision boundary')
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hold off;
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% Compute accuracy on our training set
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p = predict(theta, X);
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fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
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fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
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