多变量的线性回归（梯度下降，Python语言，MATLAB语言）

Python版：

import numpy as np

import matplotlib.pyplot as plt

a = np.loadtxt('ex1data2.txt')

print(a.shape)

X=a[:,0:2]
y=a[:,2:3]
m=y.shape[0]
l=X.shape[1]
print(m,l)

X0=np.ones(m)

def featureNormalize(X,l):
    X_norm=X
    mu=np.mean(X,0)
    print(mu)
    sigma=np.std(X)
    X_norm=(X-mu)/sigma
    print(X_norm.shape)

    return X_norm

X_norm=featureNormalize(X,l)

X=X_norm

#将两个数组合并成一个数组，在右方加上另一个数组的方法：np.c_[a,b]或者np.hstack[a,b]
X=np.c_[X0,X]
n=X.shape[1]
print(y.shape)
print(n)
print(type(X))

#将两个数组合并成一个数组，按上下合并用：np.r_[a,b] or np.vstack[a,b]

theta=np.zeros((n,1))

alpha=1

iterations=8500

def gradientdescentmulti(theta,alpha,iterations,X,y,m):
    J_h=np.zeros((iterations,1))
    for i in range (0,iterations):
        y_hat=np.dot(X,theta)

        bb=np.dot(X.transpose(),(y_hat-y))

        theta=theta-alpha/m * bb
        J=sum((y_hat-y)**2)/(2*m)
        J_h[i,:]=J

    return theta,J_h

(theta,J_h)=gradientdescentmulti(theta,alpha,iterations,X,y,m)
print(theta)

print(J_h)

x2=np.arange(iterations)
plt.plot(x2,J_h)
plt.title("costfunction")

plt.show()

MATLAB版：

clear ; close all; clc


fprintf('Loading data ...\n');


%% Load Data
data = load('ex1data2.txt');
X = data(:, 1:2);
y = data(:, 3);

m = length(y);

[X mu sigma] = featureNormalize(X);      % 均值0，标准差1
% Add intercept term to X

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

alpha = 0.01;
num_iters = 8500;
% Init Theta and Run Gradient Descent 
theta = zeros(3, 1);

[theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);

figure;
plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
xlabel('Number of iterations');

ylabel('Cost J');

function [X_norm, mu, sigma] = featureNormalize(X)

    X_norm = X;
    mu = zeros(1, size(X, 2));      % mean value 均值   size(X,2)  列数

    sigma = zeros(1, size(X, 2));   % standard deviation  标准差

    mu = mean(X,1);       %  mean value 
    sigma = std(X);     %  standard deviation

    X_norm  = (X - repmat(mu,size(X,1),1)) ./  repmat(sigma,size(X,1),1);

end

function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
    m = length(y); % number of training examples
    J_history = zeros(num_iters, 1);
    for iter = 1:num_iters
        theta = theta - alpha / m * X' * (X * theta - y); 
        J_history(iter) = computeCostMulti(X, y, theta);
    end

end

function J = computeCostMulti(X, y, theta)
    m = length(y); % number of training examples
    J = 0;
    J = sum((X * theta - y).^2) / (2*m);    
end

多变量线性回归测试数据集：https://download.youkuaiyun.com/download/qq_20406597/10370017