Machine_Learning（logistic回归习题：matlab版）

偏执的太偏执、 2022-11-27 00:48 38阅读 0赞

## logistic回归习题：matlab版 ##

**线性可分**  
ex2.m

close all;clear all;clc;
    
    data = load('E:\ML_exercise\ex2\ex2data1.txt');
    X=data(:,1:2);
    y=data(:,3);
    %plotData(X,y);
    m=length(y);
    X=[ones(m,1),X];
    theta = zeros(3,1);
    init_cost = costFunction(X,y,theta)
    
    options = optimset('GradObj','on','MAxIter',400);%GradObj告诉fminunc损失和梯度
    [theta,cost,flag] = fminunc(@(t)(costFunction(X,y,t)),theta,options);
    
    plotDecisionBoundary(X,y,theta);
    
    %预测
    pro = sigmoid([1 45 85] * theta)
    
    p = predict(X,theta);
    %准确率
    accuracy = mean(p == y)

plotData.m

function plotData(X,y)
    %display a 2-dimension plot
        figure;hold on;
        
        pos=find(y==1);
        neg=find(y==0);
        plot(X(pos,1),X(pos,2),'k+','LineWidth',2,'MarkerSize',7);
        plot(X(neg,1),X(neg,2),'ko','MarkerFaceColor','y','MarkerSize',7);
        legend('Admitted','Not Admitted','fontsize',6);
        xlabel('Exam 1 score');
        ylabel('Exam 2 score');
        hold off;
    end

sigmoid.m

function result = sigmoid(z)
    %sigmoid函数
        %result = zeros(size(z));
        result = power(1+exp(-z),-1);
    end

costFunction.m

function [J,grad] = costFunction(X,y,theta)
    %损失函数
        m = length(X);
        A = sigmoid(X*theta);
        J = -(y'*log(A)+(1-y)'*log(1-A)) / m;
        
        grad = ((A-y)'*X)' ./ m; 
    end

plotDecisionBoundary.m

function plotDecisionBoundary(X,y,theta)
    
    plotData(X(:,2:3), y);
    hold on
    
    % if分支，处理目标3.1（X特征个数2，令其为x2、x3，分别对应图中的x轴和y轴）
    if size(X, 2) <= 3 
        plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
        plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
    
        plot(plot_x, plot_y)
        
        legend('Admitted', 'Not admitted', 'Decision Boundary','fontsize',6)
        axis([30, 100, 30, 100])
        
    % else分支，处理目标3.2（X特征个数＞2）
    else
        u = linspace(-1, 1.5, 50);
        v = linspace(-1, 1.5, 50);
        z = zeros(length(u), length(v));
        for i = 1:length(u)
            for j = 1:length(v)
                z(i,j) = mapFeature(u(i), v(j))*theta;
            end
        end
    
        z = z'; 
    
        contour(u, v, z, [0, 0], 'LineWidth', 2)
    end
    hold off
    
    end

**线性不可分**  
ex2\_reg.m

close all;clear all;clc;
    
    data = load('E:\ML_exercise\ex2\ex2data2.txt');
    X=data(:,1:2);
    y=data(:,3);
    
    %plotData_reg(X,y);
    x1=X(:,1);
    x2=X(:,2);
    X=mapFeature(x1,x2);
    
    %初始化
    lamda=1;
    theta=zeros(size(X,2),1);
    [cost,grad] = costFunctionReg(X,y,theta,lamda);
    
    options = optimset('GradObj','on','MaxIter',400);
    [theta,cost,flag] = fminunc(@(t)(costFunctionReg(X,y,t,lamda)),theta,options)
    
    %决策边界
    plotDecisionBoundary(X,y,theta);
    
    p = predict(X,theta);
    %准确率
    accuracy = mean(p == y)

plotData\_reg.m

function plotData_reg(X,y)
        figure;hold on;
        pos = find(y==1);
        neg = find(y==0);
        
        plot(X(pos,1),X(pos,2),'k+','LineWidth',2,'MarkerSize',5);
        plot(X(neg,1),X(neg,2),'ko','MarkerFaceColor','y','MarkerSize',5);
        xlabel('Microchip Test 1');
        ylabel('Microchip Test 2');
        legend('y=1','y=2');
        hold off;
    end

mapFeature.m

function out = mapFeature(x1,x2)
        power = 6;
        out = ones(size(x1(:,1)));
        for i=1:power
            for j=0:i
                out(:,end+1) = (x1.^(i-j).*(x2.^j));
            end
        end
    end

costFunctionReg.m

function [J,grad] = costFunctionReg(X,y,theta,lamda)
    %损失函数
        m = length(X);
        A = sigmoid(X*theta);
        theta(1,1)=0;%规则化项不计算theta0
        reg = theta'*theta*(lamda/(2*m));%正则化项
        J = -(y'*log(A)+(1-y)'*log(1-A))/m + reg;
        grad = ((A-y)'*X)' ./ m + theta.*(lamda/m);
    end