最小二乘法的Java实现

最小二乘法原理十分简单，这里不再赘述。对于预测公式y' = a * x + b，最优解如下

double a = Sxy / Sxx;

double b = yAvg - a * xAvg;

double r = Sxy / Math.sqrt(Sxx * Syy);

其中，r为相关系数，绝对值越大，线性相关性越大。对f(a, b) = (y - y')^2求极值，即可得到上述解。

package coshaho.learn;

import java.util.HashMap;
import java.util.Map;
import java.util.Random;

/**
 * 最小二乘法
 * @author coshaho
 *
 */
public class MyLineRegression 
{
    /**
     * 最小二乘法
     * @param X
     * @param Y
     * @return y = ax + b, r
     */
    public Map<String, Double> lineRegression(double[] X, double[] Y)
    {
        if(null == X || null == Y || 0 == X.length 
                || 0 == Y.length || X.length != Y.length)
        {
            throw new RuntimeException();
        }
        
        // x平方差和
        double Sxx = varianceSum(X);
        // y平方差和
        double Syy = varianceSum(Y);
        // xy协方差和
        double Sxy = covarianceSum(X, Y);
        
        double xAvg = arraySum(X) / X.length;
        double yAvg = arraySum(Y) / Y.length;
        
        double a = Sxy / Sxx;
        double b = yAvg - a * xAvg;
        
        // 相关系数
        double r = Sxy / Math.sqrt(Sxx * Syy);
        Map<String, Double> result = new HashMap<String, Double>();
        result.put("a", a);
        result.put("b", b);
        result.put("r", r);
        
        return result;
    }
    
    /**
     * 计算方差和
     * @param X
     * @return
     */
    private double varianceSum(double[] X)
    {
        double xAvg = arraySum(X) / X.length;
        return arraySqSum(arrayMinus(X, xAvg));
    }
    
    /**
     * 计算协方差和
     * @param X
     * @param Y
     * @return
     */
    private double covarianceSum(double[] X, double[] Y)
    {
        double xAvg = arraySum(X) / X.length;
        double yAvg = arraySum(Y) / Y.length;
        return arrayMulSum(arrayMinus(X, xAvg), arrayMinus(Y, yAvg));
    }
    
    /**
     * 数组减常数
     * @param X
     * @param x
     * @return
     */
    private double[] arrayMinus(double[] X, double x)
    {
        int n = X.length;
        double[] result = new double[n];
        for(int i = 0; i < n; i++)
        {
            result[i] = X[i] - x;
        }
        
        return result;
    }
    
    /**
     * 数组求和
     * @param X
     * @return
     */
    private double arraySum(double[] X)
    {
        double s = 0 ;
        for( double x : X ) 
        {
            s = s + x ;
        }
        return s ;
    }
    
    /**
     * 数组平方求和
     * @param X
     * @return
     */
    private double arraySqSum(double[] X)
    {
        double s = 0 ;
        for( double x : X ) 
        {
            s = s + Math.pow(x, 2) ; ;
        }
        return s ;
    }
    
    /**
     * 数组对应元素相乘求和
     * @param X
     * @return
     */
    private double arrayMulSum(double[] X, double[] Y)
    {
        double s = 0 ;
        for( int i = 0 ; i < X.length ; i++ ) 
        {
            s = s + X[i] * Y[i] ;
        }
        return s ;
    }
    
    public static void main(String[] args)
    {
        Random random = new Random();    
        double[] X = new double[20];
        double[] Y = new double[20];
        
        for(int i = 0; i < 20; i++)
        {
            X[i] = Double.valueOf(Math.floor(random.nextDouble() * 97));
            Y[i] = Double.valueOf(Math.floor(random.nextDouble() * 997));
        }
        
        System.out.println(new MyLineRegression().lineRegression(X, Y));
    }
}