前一阶段做了关于大西洋鲑鱼肉色分级的研究，通过对颜色特征的分析，发现一些具有与等级间呈线性关系的特征。故利用这些特征进行多元线性回归。利用回归求参数的方法主要有最小二乘和迭代等，本文利用最小二乘和模拟退火对参数寻优，具体算法可参见任何一种介绍机器学习的资料，这里不再赘述。本训练样本数为101个，有3个特征。

1. 最小二乘法

% linear regression

% least squares data = [x1,x2,....,xn, y]

function theta = mylinearregress(data)

[m, n] = size(data);

one = ones(m,1);

y = data(:,n);

X = [one,data(:,1:n-1)];

theta = (X'*X)\(X'*y); % theta为线性模型系数

2. 模拟退火法

% linear regression % Simulated Annealing

% LMS algorithm  h = theta(1) + theta(2) * x1 + theta(3) * x2 + theta(4) * x3;

function theta = LMS_SA(data)

[m, n] = size(data);

one = ones(m,1);

X = [one,data(:,1:n-1)];

y = data(:,n);

theta0 = [1,1,1,1]';

H0 = 0.5*(X * theta0 - y)'* (X * theta0 - y);

alpha = 0.0000001;

T = 1;

T_min = 0.01;

while T > T_min

    t0 = 0;

    t1 = 0;

    while t1 < 100 && t0 < 1000

        t = zeros(1,n);

       for j = 1:m

         for k =1:n

           t(k) = t(k) + (y(j) - X(j, :) * theta0) * X(j, k);

         end

       end

       theta1 = theta0 + alpha * t';

       H1 =0.5*(X * theta1 - y)'* (X * theta1 - y);

    if H1 - H0 < 0

       theta0 = theta1;

       H0 = H1;

    elseif exp((H1 - H0)/T) > rand(0,1)

       theta0 = theta1;

       H0 = H1;

    else

       t0 = t0 + 1;

    end

       t1 = t1 + 1;

    end

    T = 0.99 * T;

end

theta = theta0;

一般情况下，模拟退火只能找到相对的最优值。所以，利用模拟退火获得的回归模型的预测准确率较差。但相对于单纯的只使用梯度下降算法而言已经具有很大的优势。

3. C#与matlab混合编程

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

using System.IO;

using System.Collections;

using matPrj;

using MathWorks.MATLAB.NET.Arrays;

using MathWorks.MATLAB.NET.Utility;

namespace myLinearRegression

{

    class Program

    {

        static void Main(string[] args)

        {

            myMathclass myfun = new myMathclass();

            StreamReader objReader = new StreamReader("test.txt");

            string sLine = "";

            double[] data = new double[404];

            int count = 0;

            

            while ((sLine = objReader.ReadLine()) != null)

            {

                foreach (string str in sLine.Split('\t'))

                {

                    data[count] = Convert.ToDouble(str);

                    count++;

                }

            }

            double[] theta = new double[4];

            MWNumericArray m_data = new MWNumericArray(101, 4, data);

            MWArray[] output = new MWArray[1];

            MWArray[] input = new MWArray[1] { m_data };

            myfun.mylinearregress(1,ref output,input);

            MWNumericArray x = output[0] as MWNumericArray;

            theta = (double[])x.ToArray();

        }

    }

}

将.m文件在matlab下转换成.DLL文件，然后将该文件与ManagedCPPAPI.netmodule和MWArray.dll文件放到C#工程的bin\debug下即可。