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Open AccessArticle

Feature Selection based on the Local Lift Dependence Scale

Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Junior Barrera was supported by grants 2013/07467-1 and 2015/01587-0, São Paulo Research Foundation (FAPESP).
Entropy 2018, 20(2), 97;
Received: 11 November 2017 / Revised: 19 January 2018 / Accepted: 25 January 2018 / Published: 30 January 2018
This paper uses a classical approach to feature selection: minimization of a cost function applied on estimated joint distributions. However, in this new formulation, the optimization search space is extended. The original search space is the Boolean lattice of features sets (BLFS), while the extended one is a collection of Boolean lattices of ordered pairs (CBLOP), that is (features, associated value), indexed by the elements of the BLFS. In this approach, we may not only select the features that are most related to a variable Y, but also select the values of the features that most influence the variable or that are most prone to have a specific value of Y. A local formulation of Shannon’s mutual information, which generalizes Shannon’s original definition, is applied on a CBLOP to generate a multiple resolution scale for characterizing variable dependence, the Local Lift Dependence Scale (LLDS). The main contribution of this paper is to define and apply the LLDS to analyse local properties of joint distributions that are neglected by the classical Shannon’s global measure in order to select features. This approach is applied to select features based on the dependence between: i—the performance of students on university entrance exams and on courses of their first semester in the university; ii—the congress representative party and his vote on different matters; iii—the cover type of terrains and several terrain properties. View Full-Text
Keywords: feature selection; local lift dependence scale; mutual information; variable dependence; variable selection feature selection; local lift dependence scale; mutual information; variable dependence; variable selection
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Marcondes, D.; Simonis, A.; Barrera, J. Feature Selection based on the Local Lift Dependence Scale. Entropy 2018, 20, 97.

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