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- %% Machine Learning Online Class
- % Exercise 1: Linear regression with multiple variables
- %
- % Instructions
- % ------------
- %
- % This file contains code that helps you get started on the
- % linear regression exercise.
- %
- % You will need to complete the following functions in this
- % exericse:
- %
- % warmUpExercise.m
- % plotData.m
- % gradientDescent.m
- % computeCost.m
- % gradientDescentMulti.m
- % computeCostMulti.m
- % featureNormalize.m
- % normalEqn.m
- %
- % For this part of the exercise, you will need to change some
- % parts of the code below for various experiments (e.g., changing
- % learning rates).
- %
- %% Initialization
- %% ================ Part 1: Feature Normalization ================
- %% Clear and Close Figures
- clear ; close all; clc
- fprintf('Loading data ...\n');
- %% Load Data
- data = load('ex1data2.txt');
- X = data(:, 1:2);
- y = data(:, 3);
- m = length(y);
- % Print out some data points
- fprintf('First 10 examples from the dataset: \n');
- fprintf(' x = [%.0f %.0f], y = %.0f \n', [X(1:10,:) y(1:10,:)]');
- fprintf('Program paused. Press enter to continue.\n');
- pause;
- % Scale features and set them to zero mean
- fprintf('Normalizing Features ...\n');
- [X mu sigma] = featureNormalize(X);
- % Add intercept term to X
- X = [ones(m, 1) X];
- %% ================ Part 2: Gradient Descent ================
- % ====================== YOUR CODE HERE ======================
- % Instructions: We have provided you with the following starter
- % code that runs gradient descent with a particular
- % learning rate (alpha).
- %
- % Your task is to first make sure that your functions -
- % computeCost and gradientDescent already work with
- % this starter code and support multiple variables.
- %
- % After that, try running gradient descent with
- % different values of alpha and see which one gives
- % you the best result.
- %
- % Finally, you should complete the code at the end
- % to predict the price of a 1650 sq-ft, 3 br house.
- %
- % Hint: By using the 'hold on' command, you can plot multiple
- % graphs on the same figure.
- %
- % Hint: At prediction, make sure you do the same feature normalization.
- %
- fprintf('Running gradient descent ...\n');
- % Choose some alpha value
- alpha = 0.01;
- num_iters = 400;
- % Init Theta and Run Gradient Descent
- theta = zeros(3, 1);
- [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);
- % Plot the convergence graph
- figure;
- plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
- xlabel('Number of iterations');
- ylabel('Cost J');
- % Display gradient descent's result
- fprintf('Theta computed from gradient descent: \n');
- fprintf(' %f \n', theta);
- fprintf('\n');
- % Estimate the price of a 1650 sq-ft, 3 br house
- % ====================== YOUR CODE HERE ======================
- % Recall that the first column of X is all-ones. Thus, it does
- % not need to be normalized.
- price = 0; % You should change this
- % ============================================================
- fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
- '(using gradient descent):\n $%f\n'], price);
- fprintf('Program paused. Press enter to continue.\n');
- pause;
- %% ================ Part 3: Normal Equations ================
- fprintf('Solving with normal equations...\n');
- % ====================== YOUR CODE HERE ======================
- % Instructions: The following code computes the closed form
- % solution for linear regression using the normal
- % equations. You should complete the code in
- % normalEqn.m
- %
- % After doing so, you should complete this code
- % to predict the price of a 1650 sq-ft, 3 br house.
- %
- %% Load Data
- data = csvread('ex1data2.txt');
- X = data(:, 1:2);
- y = data(:, 3);
- m = length(y);
- % Add intercept term to X
- X = [ones(m, 1) X];
- % Calculate the parameters from the normal equation
- theta = normalEqn(X, y);
- % Display normal equation's result
- fprintf('Theta computed from the normal equations: \n');
- fprintf(' %f \n', theta);
- fprintf('\n');
- % Estimate the price of a 1650 sq-ft, 3 br house
- % ====================== YOUR CODE HERE ======================
- price = 0; % You should change this
- % ============================================================
- fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
- '(using normal equations):\n $%f\n'], price);
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