Sergio Jimenez¹, Fabio A. Gonzalez¹, and Alexander Gelbukh²

¹ Departamento de Ingeniería de Sistemas e Industrial of the Universidad Nacional de Colombia, Bogota, Colombia. (e-mail: fagonzalezo@unaledu.co, sergiojimenezvargas@gmail.com).

² Centro de Investigación en Computación, Instituto Politécnico Nacional, México City, México. (e-mail: gelbukh@gelbukh.com).

Manuscript received on February 17, 2015.
Accepted for publication on May 27, 2015. ]]> Published on June 15, 2015.

Abstract

Soft cardinality is a generalization of the classic set cardinality (i.e., the number of elements in a set), which exploits similarities between elements to provide a "soft" counting of the number of elements in a collection. This model is so general that can be used interchangeability as cardinality function in resemblance coefficients such as Jaccard's, Dice's, cosine and others. Beyond that, cardinality-based features can be extracted from pairs of objects being compared to learn adaptive similarity functions from training data. This approach can be used for comparing any object that can be represented as a set or bag. We and other international teams used soft cardinality to address a series of natural language processing (NLP) tasks in the recent SemEval (semantic evaluation) competitions from 2012 to 2014. The systems based on soft cardinality have always been among the best systems in all the tasks in which they participated. This paper describes our experience in that journey by presenting the generalities of the model and some practical techniques for using soft cardinality for NLP problems.

Key words: Similarity measure, soft computing, set cardinality, semantics, natural language processing.

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ACKNOWLEDGMENT

The second author acknowledges the support of LACCIR R1212LAC006 under the project "Multimodal image retrieval to support medical case-based scientific literature search." The third author acknowledges the support of the Mexican Government via SNI, CONACYT, and the Instituto Politécnico Nacional, SIP-IPN grants 20152100 and 20152095.

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