Soal 2 Machine Learning

IMPLEMENTING LINEAR REGRESSION WITH ONE VARIABLE USING MATLAB 

Referensi : https://www.coursera.org/learn/machine-learning

1. Aplikasi Matlab

       Ini adalah Implementasi Algoritma Regresi Linier dengan satu variabel menggunakan matlab.

Algoritma memprediksi keuntungan yang bisa diperoleh dari kota tergantung pada populasinya.

Listing Program :

clear; close all; clc;

% read the training data

data = load('examples.txt');

% initialize Matrices and Variables

X = data(:, 1);     % featue matrix

y = data(:, 2);     % results matrix

m = length(y);      % number of training examples

theta = zeros(2, 1);     % initial weights

iterations = 1500;  % Iterations needed for Gradient Descent

alpha = 0.01;       % Learning Rate

% Plot the Data

plot(X, y, 'rx', 'MarkerSize', 10);

title('Training Examples');

xlabel('Population in 10,000');

ylabel('Profit in $10,000');

% Compute the Cost Function

X = [ones(m, 1), data(:, 1)];

J = ComputeCost(X, y, theta);

% Run Gradient Descent

[theta, Js] = GradientDescent(X, y, theta, alpha, iterations);

hold on;

plot(X(:, 2), X * theta, '-');

legend('Training data', 'Linear regression');

hold off;

% plotting the cost function

plot(1: iterations, J_history, '-b');

% Predicting Profits

fprintf('Prediction for 35000:\t%f\n', ([1, 3.5] * theta) * 10000);

fprintf('Prediction for 70000:\t%f\n', ([1, 7] * theta) * 10000);

Program Computasi Cost :

function J = ComputeCost(X, y, theta)

    % Prepare Variables

    m = length(y);

   

    % Calculate Hypothesis

    h = X * theta;

   

    % Calculate Cost

    J = 1 / (2 * m) * sum((h - y) .^ 2);

end

Cost Function Formula :

Hypothesis Formula :

Ini disebut (vektorisasi), yang lebih efisien dari loop, kami hanya kalkulus vektor hipotesis dengan mengalikan setiap baris dalam Contoh matriks dengan theta vektor kolom

Gradient Descend Formula :

Program Descent Gradient :

function [theta, Js] = GradientDescent(X, y, theta, alpha, iterations)

    % Prepare Variables

    m = length(y);

    Js = zeros(iterations, 1);

   

    for i = 1 : iterations,

        h = X * theta;

        t1 = theta(1) - (alpha * (1 / m) * sum(h - y));

        t2 = theta(2) - (alpha * (1 / m) * sum((h - y) .* X(:, 2)));

        theta(1) = t1;

        theta(2) = t2;

       

        Js(i) = ComputeCost(X, y, theta);

    end

end

Hasil dari training Desicion Tree adalah seperti gambar :

Untuk Grafik hasil dari Program pada Matlab :

VIDEO PENJELASAN

Link Datasheet : Download

Link Program : Download

Link Computation : Download

Link Descent Gradient : Download