Cumulated relative position: a metric for ranking evaluation

The development of multilingual and multimedia information access systems calls for proper evaluation methodologies to ensure that they meet the expected user requirements and provide the desired effectiveness. IR research offers a strong evaluation methodology and a range of evaluation metrics, such as MAP and (n)DCG. In this paper, we propose a new metric for ranking evaluation, the CRP. We start with the observation that a document of a given degree of relevance may be ranked too early or too late regarding the ideal ranking of documents for a query. Its relative position may be negative, indicating too early ranking, zero indicating correct ranking, or positive, indicating too late ranking. By cumulating these relative rankings we indicate, at each ranked position, the net effect of document displacements, the CRP. We first define the metric formally and then discuss its properties, its relationship to prior metrics, and its visualization. Finally we propose different visualizations of CRP by exploiting a test collection to demonstrate its behavior.