The deviation of a set of strings

Abstract

This paper introduces the concept of set deviation as a tool to characterise the deviation of a set of strings around its set median. The set deviation is defined as the set median of the positive edit sequences between any string and the set median. We show that the set deviation has the same properties as the classic second-order statistical moment. This approach is generalised to higher-order-moments of a set of strings. We then show how the set deviation can be efficiently used in well-known statistical algorithms to improve the computation of the set median of a set of strings, illustrating this concept with several examples, particularly in post-processing of texts extracted from video sequences.