我有以下问题。

我有一组元素，我可以通过一定的算法排序的。该排序是好的，但价格昂贵。

I have a set of elements that I can sort by a certain algorithm A . The sorting is good, but very expensive.

还有一个算法B中可以近似A的结果是要快得多，但排序不会完全相同。

There is also an algorithm B that can approximate the result of A. It is much faster, but the ordering will not be exactly the same.

以A的输出作为金标准我需要导致对相同的数据采用B的错误的有意义的估计。

Taking the output of A as a 'golden standard' I need to get a meaningful estimate of the error resulting of the use of B on the same data.

任何人都可以请提出任何资源，我可以看看，以解决我的问题？ 在此先感谢！

Could anyone please suggest any resource I could look at to solve my problem? Thanks in advance!

编辑：

根据要求：添加一个例子来说明情况： 如果数据的前10个英文字母，

As requested : adding an example to illustrate the case : if the data are the first 10 letters of the alphabet,

A输出：A，B，C，D，E，F，G，H，I，J

A outputs : a,b,c,d,e,f,g,h,i,j

B输出：A，B，D，C，E，G，H，F，J，I

B outputs : a,b,d,c,e,g,h,f,j,i

什么是导致错误的可能措施，这将让我调整算法B的内部参数，以获得结果更接近A的输出？

What are the possible measures of the resulting error, that would allow me to tune the internal parameters of algorithm B to get result closer to the output of A?

推荐答案

我想你想要的是 Spearman秩相关系数 。利用指数[排名]载体两个分类法（完美 A 和近似 B ），你计算的等级相关 RHO 范围从-1（完全不同）到1（完全一样）：

Spearman's rho

I think what you want is Spearman's rank correlation coefficient. Using the index [rank] vectors for the two sortings (perfect A and approximate B), you calculate the rank correlation rho ranging from -1 (completely different) to 1 (exactly the same):

其中d（i）是A和B之间的每个字符在行列的差

where d(i) are the difference in ranks for each character between A and B

您可以定义你的错误的措施，因为距离 D：=（1-RHO）/ 2

You can defined your measure of error as a distance D := (1-rho)/2.