An Efficient, Parallelized Algorithm for Optimal Conditional Entropy-Based Feature Selection

Author(s)

Estrela, Gustavo ^{[1, 2]} ; Gubitoso, Marco Dimas ^[2] ; Ferreira, Carlos Eduardo ^[2] ; Barrera, Junior ^[2] ; Reis, Marcelo S. ^[1]

Affiliation

^[1] Inst Butantan, Ctr Toxins Immune Response & Cell Signaling CeT, Lab Ciclo Celular, BR-05503900 Butanta, SP - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05503900 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Entropy; v. 22, n. 4 APR 2020.
• Web of Science Citations: 0

Abstract

In Machine Learning, feature selection is an important step in classifier design. It consists of finding a subset of features that is optimum for a given cost function. One possibility to solve feature selection is to organize all possible feature subsets into a Boolean lattice and to exploit the fact that the costs of chains in that lattice describe U-shaped curves. Minimization of such cost function is known as the U-curve problem. Recently, a study proposed U-Curve Search (UCS), an optimal algorithm for that problem, which was successfully used for feature selection. However, despite of the algorithm optimality, the UCS required time in computational assays was exponential on the number of features. Here, we report that such scalability issue arises due to the fact that the U-curve problem is NP-hard. In the sequence, we introduce the Parallel U-Curve Search (PUCS), a new algorithm for the U-curve problem. In PUCS, we present a novel way to partition the search space into smaller Boolean lattices, thus rendering the algorithm highly parallelizable. We also provide computational assays with both synthetic data and Machine Learning datasets, where the PUCS performance was assessed against UCS and other golden standard algorithms in feature selection. (AU)

• FAPESP's process: 16/25959-7 - Design of poset forest-based algorithms for the U-curve optimization problem
• Grantee: Gustavo Estrela de Matos
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• FAPESP's process: 13/07467-1 - CeTICS - Center of Toxins, Immune-Response and Cell Signaling
• Grantee: Hugo Aguirre Armelin
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 15/01587-0 - Storage, modeling and analysis of dynamical systems for e-Science applications
• Grantee: João Eduardo Ferreira
• Support Opportunities: Research Grants - eScience and Data Science Program - Thematic Grants