# 2003 ComparingTopKLists

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- (Fagin et al., 2003b) ⇒ Ronald Fagin, Ravi Kumar, and D. Sivakumar. (2003). “Comparing Top k Lists.” In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003).

**Subject Headings:** Ranking Function, Ranking Algorithm, TF-IDF Ranking Function.

## Notes

## Cited By

- ~371 http://scholar.google.com/scholar?q=%22Comparing+Top+k+Lists.%22+2003
- ~59 http://portal.acm.org/citation.cfm?id=644108.644113&preflayout=flat#citedby

## Quotes

### Abstract

Motivated by several applications, we introduce various distance measures between "top k lists." Some of these distance measures are metrics, while others are not. For each of these latter distance measures: we show that it is "almost" a metric in the following two seemingly unrelated aspects:

- step-(i) it satisfies a relaxed version of the polygonal (hence, triangle) inequality, and
- step-(ii) there is a metric with positive constant multiples that bounds our measure above and below.

This is not a coincidence---we show that these two notions of almost being a metric are the same. Based on the second notion, we define two distance measures to be equivalent if they are bounded above and below by constant multiples of each other. We thereby identify a large and robust equivalence class of distance measures.

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