斯皮尔曼等级相关性-Spearman Rank Correlation

一、简介

在机器学习中，当要预测不同的机器学习算法在同一个学习任务上的性能时，需要使用序相关系数对真实的性能排序与预测的性能排序进行比较，本文介绍了其中一种秩相关系数——斯皮尔曼等级相关性。

公式：

其中：di=xi-yi表示两个排序之间的差值；

            n:表示样本的大小，即机器学习算法的数量；

二、代码实现

1.计算斯皮尔曼等级相关性

package recommendation.featureExtraction;

import java.math.BigDecimal;

/**
 * spearman rank correlation
 * refer to soruce from http://en.wikipedia.org/wiki/Spearman_rank_correlation
 * @author LiuKai 2014.07.06
 */
public class SpearmanRankCorrelation {

	/*
	 * rang between [-1, 1];
	 * Inappropriate static <>.
	 * "There is almonst no chance that we'd want Math.max to be polymorphic"
	 */
	public static double correlation(int[] base, int[] other) {
		
		if (base.length != other.length) {
			System.err.println("The length of array base and other must be equal!");
			return 0.0;
		}
		if (base.length <= 1) {
			System.err.println("The length of both of the arrays must be equal!");
			System.exit(-1);
		}
		BigDecimal bg = new BigDecimal(1-(6.0*sumOfSquareDiff(base, other)/(power(base.length, 3)-base.length)));
		return bg.setScale(4, BigDecimal.ROUND_HALF_UP).doubleValue();
	}
	
	private static double sumOfSquareDiff(int[] a, int[] b) {
		
		double sum = 0.0;
		for (int i = 0; i < a.length; i++) 
			sum += power((a[i]-b[i]), 2);
		return sum;
	}
	
	/*
	 * Method should do one thing 
	 * <>
	 */
	private static double power(double base, int exp) {
		
		if (base == 0)
			return 0.0;
		double result = 1.0;
		for (int i = 0; i < exp; i++)
			result *= base;
		return result;
	}
}

2.测试斯皮尔曼等级相关系数

package recommendation.featureExtraction;

/**
 * Test SpearmanRankCorrelation.class
 * @author Administrator
 *
 */
public class TestSpearman {
	
	public static void main(String[] args) {
		int[] base = {1, 2, 3, 4, 5};
		int[] other1 = {1, 2, 3, 4, 5};
		int[] other2 = FisherYatesShuffle.shuffle(base.clone());
		int[] other3 = {5, 4, 3, 2, 1};
		System.out.println(SpearmanRankCorrelation.correlation(base, other1));	
		System.out.println(SpearmanRankCorrelation.correlation(base, other2));
		System.out.println(SpearmanRankCorrelation.correlation(base, other3));
	}
}

3.辅助类费雪耶兹随机置乱算法

具体见另一篇博客：http://blog.csdn.net/lhkaikai/article/details/25627161

package recommendation.featureExtraction;

import java.util.Random;

/*
 * Fisher-Yates shuffle, also known as the Knuth shuffle, is an algorithm for generating
 * a random permutation of a finite set-in plain terms, for randomly shuffling the set.
 */
public class FisherYatesShuffle {
	
	public static int[] shuffle(int[] array) {
		for (int i = array.length - 1; i > 0; i--) {
			int rand = (new Random()).nextInt(i+1);
			int temp = array[i];
			array[i] = array[rand];
			array[rand] = temp;
		}
		return array;
	}
	
	public static void main(String[] args) {
		
		int[] array1= {1, 2, 3, 4, 5};
		int[] array2 = shuffle(array1);
		for(int elem: array2)
			System.out.print(elem + " ");
		System.out.println();
	}
}

三、实验测试结果