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最小二乘法的Java实现
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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));
}
}
