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Java實現一元線性回歸

最近在寫一個熒光圖像分析軟件，需要自己擬合方程。一元回歸線公式的算法參考了《Java數值方法》，擬合度R^2（絕對系數）是自己寫的，歡迎討論。計算結果和Excel完全一致。

總共三個文件：

DataPoint.java

/**
* A data point for interpolation and regression.
*/
public class DataPoint
{
/** the x value */ public float x;
/** the y value */ public float y;

    /**
     * Constructor.
     * @param x the x value
     * @param y the y value
     */
    public DataPoint(float x, float y)
    {
        this.x = x;
        this.y = y;

}
}

/**
* A least-squares regression line function.
*/

import java.util.*;
import java.math.BigDecimal;

public class RegressionLine
//implements Evaluatable
{
    /** sum of x */     private double sumX;
    /** sum of y */     private double sumY;
    /** sum of x*x */   private double sumXX;
    /** sum of x*y */   private double sumXY;
    /** sum of y*y */   private double sumYY;
    /** sum of yi-y */   private double sumDeltaY;
    /** sum of sumDeltaY^2 */   private double sumDeltaY2;
    /**誤差 */
    private double sse;
    private double sst;
    private double E;
    private String[] xy ;

    private ArrayList listX ;
    private ArrayList listY ;

    private int XMin,XMax,YMin,YMax;

    /** line coefficient a0 */ private float a0;
    /** line coefficient a1 */ private float a1;

/** number of data points */ private int pn ;
/** true if coefficients valid */ private boolean coefsValid;

    /**
     * Constructor.
     */
    public RegressionLine() {
    XMax = 0;
    YMax = 0;
    pn = 0;
    xy =new String[2];
    listX = new ArrayList();
    listY = new ArrayList();
    }

/**
 * Constructor.
 * @param data the array of data points
 */
 public RegressionLine(DataPoint data[])
 {
 pn = 0;
 xy =new String[2];
 listX = new ArrayList();
 listY = new ArrayList();
 for (int i = 0; i < data.length; ++i) {
 addDataPoint(data[i]);
 }
 }

    /**
     * Return the current number of data points.
     * @return the count
     */
    public int getDataPointCount() { return pn; }

    /**
     * Return the coefficient a0.
     * @return the value of a0
     */
    public float getA0()
    {
        validateCoefficients();
        return a0;
    }

    /**
     * Return the coefficient a1.
     * @return the value of a1
     */
    public float getA1()
    {
        validateCoefficients();
        return a1;
    }

    /**
     * Return the sum of the x values.
     * @return the sum
     */
    public double getSumX() { return sumX; }

    /**
     * Return the sum of the y values.
     * @return the sum
     */
    public double getSumY() { return sumY; }

    /**
     * Return the sum of the x*x values.
     * @return the sum
     */
    public double getSumXX() { return sumXX; }

    /**
     * Return the sum of the x*y values.
     * @return the sum
     */
    public double getSumXY() { return sumXY; }

    public double getSumYY() { return sumYY; }

    public int getXMin() {
  return XMin;
}

public int getXMax() {
return XMax;
}

public int getYMin() {
return YMin;
}

public int getYMax() {
  return YMax;
}

    /**
     * Add a new data point: Update the sums.
     * @param dataPoint the new data point
     */
    public void addDataPoint(DataPoint dataPoint)
    {
        sumX += dataPoint.x;
        sumY += dataPoint.y;
        sumXX += dataPoint.x*dataPoint.x;
        sumXY += dataPoint.x*dataPoint.y;
        sumYY += dataPoint.y*dataPoint.y;

        if(dataPoint.x > XMax){
        XMax = (int)dataPoint.x;
        }
        if(dataPoint.y > YMax){
        YMax = (int)dataPoint.y;
        }

        //把每個點的具體坐標存入ArrayList中，備用

        xy[0] = (int)dataPoint.x+ "";
        xy[1] = (int)dataPoint.y+ "";
        if(dataPoint.x!=0 && dataPoint.y != 0){
        System.out.print(xy[0]+",");
        System.out.println(xy[1]);

        try{
        //System.out.println("n:"+n);
        listX.add(pn,xy[0]);
        listY.add(pn,xy[1]);
        }
        catch(Exception e){
        e.printStackTrace();
        }

        /*
        System.out.println("N:" + n);
        System.out.println("ArrayList listX:"+ listX.get(n));
        System.out.println("ArrayList listY:"+ listY.get(n));
        */
        }
        ++pn;
        coefsValid = false;
     }

/**
 * Return the value of the regression line function at x.
 * (Implementation of Evaluatable.)
 * @param x the value of x
 * @return the value of the function at x
 */
 public float at(int x)
 {
 if (pn < 2) return Float.NaN;

validateCoefficients();
 return a0 + a1*x;
 }

 public float at(float x)
 {
 if (pn < 2) return Float.NaN;

        validateCoefficients();
        return a0 + a1*x;
    }

    /**
     * Reset.
     */
    public void reset()
    {
        pn = 0;
        sumX = sumY = sumXX = sumXY = 0;
        coefsValid = false;
    }

    /**
     * Validate the coefficients.
     * 計算方程系數 y=ax+b 中的a
     */
    private void validateCoefficients()
    {
        if (coefsValid) return;

        if (pn >= 2) {
            float xBar = (float) sumX/pn;
            float yBar = (float) sumY/pn;

            a1 = (float) ((pn*sumXY - sumX*sumY)
                            /(pn*sumXX - sumX*sumX));
            a0 = (float) (yBar - a1*xBar);
        }
        else {
            a0 = a1 = Float.NaN;
        }

coefsValid = true;
 }

 /**
 * 返回誤差
 */
 public double getR(){
 //遍歷這個list并計算分母
 for(int i = 0; i < pn -1; i++) {
 float Yi= (float)Integer.parseInt(listY.get(i).toString());
 float Y = at(Integer.parseInt(listX.get(i).toString()));
 float deltaY = Yi - Y;
 float deltaY2 = deltaY*deltaY;
 /*
 System.out.println("Yi:" + Yi);
 System.out.println("Y:" + Y);
 System.out.println("deltaY:" + deltaY);
 System.out.println("deltaY2:" + deltaY2);
 */

 sumDeltaY2 += deltaY2;
 //System.out.println("sumDeltaY2:" + sumDeltaY2);

 }

 sst = sumYY - (sumY*sumY)/pn;
 //System.out.println("sst:" + sst);
 E =1- sumDeltaY2/sst;


 return round(E,4) ;
 }

 //用于實現精確的四舍五入
 public double round(double v,int scale){

if(scale<0){
 throw new IllegalArgumentException(
 "The scale must be a positive integer or zero");
 }

 BigDecimal b = new BigDecimal(Double.toString(v));
 BigDecimal one = new BigDecimal("1");
 return b.divide(one,scale,BigDecimal.ROUND_HALF_UP).doubleValue();

    }

    public float round(float v,int scale){

}
}

演示程序：

LinearRegression.java

/**
* Linear Regression
* 
* Demonstrate linear regression by constructing the regression line for a set
* of data points.
*
* require DataPoint.java,RegressionLine.java
*
* 為了計算對于給定數據點的最小方差回線，需要計算SumX,SumY,SumXX,SumXY; (注：SumXX = Sum (X^2))
* 回歸直線方程如下： f(x)=a1x+a0 
* 斜率和截距的計算公式如下：
* n: 數據點個數
* a1=(n(SumXY)-SumX*SumY)/(n*SumXX-(SumX)^2)
* a0=(SumY - SumY * a1)/n
* (也可表達為a0=averageY-a1*averageX)
*
* 畫線的原理：兩點成一直線，只要能確定兩個點即可 
* 第一點：(0,a0) 再隨意取一個x1值代入方程，取得y1，連結(0,a0)和(x1,y1)兩點即可。
* 為了讓線穿過整個圖,x1可以取橫坐標的最大值Xmax，即兩點為(0,a0),(Xmax,Y)。如果y=a1*Xmax+a0,y大于
* 縱坐標最大值Ymax，則不用這個點。改用y取最大值Ymax，算得此時x的值，使用(X,Ymax)，即兩點為(0,a0),(X,Ymax)
*
* 擬合度計算：(即Excel中的R^2)
* *R2 = 1 - E
* 誤差E的計算：E = SSE/SST
* SSE=sum((Yi-Y)^2) SST=sumYY - (sumY*sumY)/n;
* 
*/
public class LinearRegression
{
 private static final int MAX_POINTS = 10;
 private double E;

    /**
* Main program.
*
* @param args
*            the array of runtime arguments
*/
    public static void main(String args[])
    {
        RegressionLine line = new RegressionLine();

        line.addDataPoint(new DataPoint(20, 136));
        line.addDataPoint(new DataPoint(40, 143));
        line.addDataPoint(new DataPoint(60, 152));
        line.addDataPoint(new DataPoint(80, 162));
        line.addDataPoint(new DataPoint(100, 167));

        printSums(line);
        printLine(line);
    }

    /**
* Print the computed sums.
*
* @param line
*            the regression line
*/
    private static void printSums(RegressionLine line)
    {
        System.out.println("\n數據點個數 n = " + line.getDataPointCount());
        System.out.println("\nSum x = " + line.getSumX());
        System.out.println("Sum y = " + line.getSumY());
        System.out.println("Sum xx = " + line.getSumXX());
        System.out.println("Sum xy = " + line.getSumXY());
        System.out.println("Sum yy = " + line.getSumYY());

    }

    /**
* Print the regression line function.
*
* @param line
*            the regression line
*/
    private static void printLine(RegressionLine line)
    {
        System.out.println("\n回歸線公式: y = " +
                           line.getA1() +
                           "x + " + line.getA0());
        System.out.println("擬合度：     R^2 = " + line.getR());
    }

}

posted on 2009-02-22 17:07 風閱讀(1106) 評論(0) 編輯收藏

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Java實現一元線性回歸