machine-learning-01 线性回归模拟
跟随吴恩达老师学习机器学习，利用Octave开源软件，快速实现模型建立与函数实现，开启了我在机器学习领域的大门。今天是机器学习的第一个编程作业——线性回归。希望和大家一起学习，共同进步。
I.Simple Octave function：返回5*5的矩阵
1.下载好ex1文件并load到Octave中
2.编写warmUpExercise.m文件
function A = warmUpExercise()%WARMUPEXERCISE Example function in octave% A = WARMUPEXERCISE() is an example function that returns the 5x5 % identity matrixA = eye(5);% ============= YOUR CODE HERE ==============% Instructions: Return the 5x5 identity matrix % In octave, we return values by defining which variables% represent the return values (at the top of the file)% and then set them accordingly. % ===========================================end
3.在Octave中运行warmwarmUpExercise函数
II.Linear regression with one variable
单特征值的线性回归预测，ex1data1中包含了97组数据，每组有两个数据用“，”分割，一个为x变量，一个为y因变量。
1.将数据load到Octave中 & 编写plotData.m文件
data = load('ex1data1.txt'); % read comma separated dataX = data(:, 1); y = data(:, 2);m = length(y); % number of training examples function plotData(x, y)plot(x, y, 'bx', 'MarkerSize', 10); % Plot the dataylabel('Profit in $10,000s'); % Set the y?axis labelxlabel('Population of City in 10,000s');end 2.运行poltData函数
3.Gradient Descent
%初始值设定X = [ones(m, 1), data(:,1)]; % Add a column of ones to xtheta = zeros(2, 1); % initialize fitting parametersiterations = 1500;alpha = 0.01;
%computeCost函数编写function J = computeCost(X, y, theta)m = length(y); % number of training examplesJ = sum(power(X*theta-y,2)/(2*m));end
运行得到期望值32.07
%计算theta_0,theta_1 & 编写gradientDescent函数%num_iters ---> iterationsfunction [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)m = length(y); % number of training examplesJ_history = zeros(num_iters, 1);for iter = 1:num_iters theta1=theta(1,1)-alpha/m*sum(X*theta-y); theta2=theta(2,1)-alpha/m*sum((X*theta-y) .* X(:,2)); theta(1,1)=theta1; theta(2,1)=theta2;J_history(iter) = computeCost(X, y, theta);endend
计算预测值
predict1 = [1, 3.5]theta; predict2 = [1, 7]theta;
4.通过gradientDescent求出的theta值画出拟合曲线
III.Visualizing->understand better gradientDescent function
将数据与回归直线的误差J转化为三维像小山一样的模型，我们通过梯度下降算法找到极小值点，利用等高线图像，在凹线中心的地方为最好的拟合点，更好的理解梯度下降算法的原理。
%初始化变量% Grid over which we will calculate Jtheta0_vals = linspace(-10, 10, 100);theta1_vals = linspace(-1, 4, 100);% initialize J_vals to a matrix of 0'sJ_vals = zeros(length(theta0_vals), length(theta1_vals));% Fill out J_valsfor i = 1:length(theta0_vals) for j = 1:length(theta1_vals) t = [theta0_vals(i); theta1_vals(j)]; J_vals(i,j) = computeCost(X, y, t); endend
%3-d误差模型figure;surf(theta0_vals, theta1_vals, J_vals)
%误差等高线模型figurecontour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20)) %画20条等高线，每条等高线的值根据theta0,theta1,J,在10^(-2)和10^3依次对应一个值hold on;plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);
笔者能力有限，哪里理解的不好请大家不要吝啬指出，不胜感激。