A new rank correlation coefficient for information retrieval

In the field of information retrieval, one is often faced with the problem of computing the correlation between two ranked lists. The most commonly used statistic that quantifies this correlation is Kendall's Τ. Often times, in the information retrieval community, discrepancies among those items having high rankings are more important than those among items having low rankings. The Kendall's Τ statistic, however, does not make such distinctions and equally penalizes errors both at high and low rankings.In this paper, we propose a new rank correlation coefficient, AP correlation (Τap), that is based on average precision and has a probabilistic interpretation. We show that the proposed statistic gives more weight to the errors at high rankings and has nice mathematical properties which make it easy to interpret. We further validate the applicability of the statistic using experimental data.