http://www.cnblogs.com/wzm-xu/p/4062266.html
多元线性回归----Java简单实现
学习Andrew N.g的机器学习课程之后的简单实现.
课程地址：https://class.coursera.org/ml-007
不大会编辑公式，所以略去具体的推导，有疑惑的同学去看看Andrew 的课程吧，顺带一句，Andrew的课程实在是很赞。
如果还有疑问，feel free to contact me via emails or QQ.
LinearRegression.java
import java.io.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException; public class LinearRegression {
/*
* 训练数据示例：
* x0 x1 x2 y
1.0 1.0 2.0 7.2
1.0 2.0 1.0 4.9
1.0 3.0 0.0 2.6
1.0 4.0 1.0 6.3
1.0 5.0 -1.0 1.0
1.0 6.0 0.0 4.7
1.0 7.0 -2.0 -0.6
注意！！！！x1，x2，y三列是用户实际输入的数据，x0是为了推导出来的公式统一，特地补上的一列。
x0,x1,x2是“特征”，y是结果 h(x) = theta0 * x0 + theta1* x1 + theta2 * x2 theta0,theta1,theta2 是想要训练出来的参数 此程序采用“梯度下降法” *
*/ private double [][] trainData;//训练数据，一行一个数据，每一行最后一个数据为 y
private int row;//训练数据 行数
private int column;//训练数据 列数 private double [] theta;//参数theta private double alpha;//训练步长
private int iteration;//迭代次数 public LinearRegression(String fileName)
{
int rowoffile=getRowNumber(fileName);//获取输入训练数据文本的 行数
int columnoffile = getColumnNumber(fileName);//获取输入训练数据文本的 列数 trainData = new double[rowoffile][columnoffile+1];//这里需要注意，为什么要+1，因为为了使得公式整齐，我们加了一个特征x0，x0恒等于1
this.row=rowoffile;
this.column=columnoffile+1; this.alpha = 0.001;//步长默认为0.001
this.iteration=100000;//迭代次数默认为 100000 theta = new double [column-1];//h(x)=theta0 * x0 + theta1* x1 + theta2 * x2 + .......
initialize_theta(); loadTrainDataFromFile(fileName,rowoffile,columnoffile);
}
public LinearRegression(String fileName,double alpha,int iteration)
{
int rowoffile=getRowNumber(fileName);//获取输入训练数据文本的 行数
int columnoffile = getColumnNumber(fileName);//获取输入训练数据文本的 列数 trainData = new double[rowoffile][columnoffile+1];//这里需要注意，为什么要+1，因为为了使得公式整齐，我们加了一个特征x0，x0恒等于1
this.row=rowoffile;
this.column=columnoffile+1; this.alpha = alpha;
this.iteration=iteration; theta = new double [column-1];//h(x)=theta0 * x0 + theta1* x1 + theta2 * x2 + .......
initialize_theta(); loadTrainDataFromFile(fileName,rowoffile,columnoffile);
} private int getRowNumber(String fileName)
{
int count =0;
File file = new File(fileName);
BufferedReader reader = null;
try {
reader = new BufferedReader(new FileReader(file));
while ( reader.readLine() != null)
count++;
reader.close();
} catch (IOException e) {
e.printStackTrace();
} finally {
if (reader != null) {
try {
reader.close();
} catch (IOException e1) {
}
}
}
return count; } private int getColumnNumber(String fileName)
{
int count =0;
File file = new File(fileName);
BufferedReader reader = null;
try {
reader = new BufferedReader(new FileReader(file));
String tempString = reader.readLine();
if(tempString!=null)
count = tempString.split(" ").length;
reader.close();
} catch (IOException e) {
e.printStackTrace();
} finally {
if (reader != null) {
try {
reader.close();
} catch (IOException e1) {
}
}
}
return count;
} private void initialize_theta()//将theta各个参数全部初始化为1.0
{
for(int i=0;i<theta.length;i++)
theta[i]=1.0;
} public void trainTheta()
{
int iteration = this.iteration;
while( (iteration--)>0 )
{
//对每个theta i 求 偏导数
double [] partial_derivative = compute_partial_derivative();//偏导数
//更新每个theta
for(int i =0; i< theta.length;i++)
theta[i]-= alpha * partial_derivative[i];
}
} private double [] compute_partial_derivative()
{
double [] partial_derivative = new double[theta.length];
for(int j =0;j<theta.length;j++)//遍历，对每个theta求偏导数
{
partial_derivative[j]= compute_partial_derivative_for_theta(j);//对 theta i 求 偏导
}
return partial_derivative;
}
private double compute_partial_derivative_for_theta(int j)
{
double sum=0.0;
for(int i=0;i<row;i++)//遍历 每一行数据
{
sum+=h_theta_x_i_minus_y_i_times_x_j_i(i,j);
}
return sum/row;
}
private double h_theta_x_i_minus_y_i_times_x_j_i(int i,int j)
{
double[] oneRow = getRow(i);//取一行数据，前面是feature，最后一个是y
double result = 0.0; for(int k=0;k< (oneRow.length-1);k++)
result+=theta[k]*oneRow[k];
result-=oneRow[oneRow.length-1];
result*=oneRow[j];
return result;
}
private double [] getRow(int i)//从训练数据中取出第i行，i=0，1，2，。。。，（row-1）
{
return trainData[i];
} private void loadTrainDataFromFile(String fileName,int row, int column)
{
for(int i=0;i< row;i++)//trainData的第一列全部置为1.0（feature x0）
trainData[i][0]=1.0; File file = new File(fileName);
BufferedReader reader = null;
try {
reader = new BufferedReader(new FileReader(file));
String tempString = null;
int counter = 0;
while ( (counter<row) && (tempString = reader.readLine()) != null) {
String [] tempData = tempString.split(" ");
for(int i=0;i<column;i++)
trainData[counter][i+1]=Double.parseDouble(tempData[i]);
counter++;
}
reader.close();
} catch (IOException e) {
e.printStackTrace();
} finally {
if (reader != null) {
try {
reader.close();
} catch (IOException e1) {
}
}
}
} public void printTrainData()
{
System.out.println("Train Data:\n");
for(int i=0;i<column-1;i++)
System.out.printf("%10s","x"+i+" ");
System.out.printf("%10s","y"+" \n");
for(int i=0;i<row;i++)
{
for(int j=0;j<column;j++)
{
System.out.printf("%10s",trainData[i][j]+" ");
}
System.out.println();
}
System.out.println();
} public void printTheta()
{
for(double a:theta)
System.out.print(a+" ");
} }
TestLinearRegression.java
public class TestLinearRegression {
public static void main(String[] args) {
// TODO Auto-generated method stub
LinearRegression m = new LinearRegression("trainData",0.001,1000000);
m.printTrainData();
m.trainTheta();
m.printTheta();
}
}trainData文件中是训练数据，默认最后一列是y，比如：
1.0 2.0 7.2
2.0 1.0 4.9
3.0 0.0 2.6
4.0 1.0 6.3
5.0 -1.0 1.0
6.0 0.0 4.7
7.0 -2.0 -0.6
前两列是“feature”，最后一列，也就是第三列是y
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