Optimal Boolean lattice-based algorithms for the U-curve optimization problem

Author(s)

Reis, Marcelo S. ^{[1, 2]} ; Estrela, Gustavo ^{[3, 1, 2]} ; Ferreira, Carlos Eduardo ^[3] ; Barrera, Junior ^{[3, 2]}

Affiliation

^[1] Inst Butantan, Lab Especial Ciclo Celular, Sao Paulo - Brazil

^[2] Inst Butantan, Ctr Toxins Immune Response & Cell Signaling CeTIC, Sao Paulo - Brazil

^[3] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

• Document type: Journal article
• Source: INFORMATION SCIENCES; v. 471, p. 97-114, JAN 2019.
• Web of Science Citations: 0

Abstract

The U-curve optimization problem is characterized by a decomposable in U-shaped curves cost function over the chains of a Boolean lattice. This problem can be applied to model the classical feature selection problem in Machine Learning. In this paper, we point out that the firstly proposed algorithm to tackle the U-curve problem, the RBM algorithm, is in fact suboptimal. We also present two new algorithms: UCS, which is actually optimal to tackle this problem; and UCSR, a variation of UCS that solves a special case of the U-curve problem and relies on a reduced, ordered binary decision diagram to control the search space. We provide results of two computational assays with these new algorithms: first, W-operator design for filtering of binary images; second, linear SVM design for classification of data sets from the UCI Machine Learning Repository. We show that, in these assays, UCS and UCSR outperformed an exhaustive search and also three widely used heuristics: the SFFS sequential selection, the BFS graph-based search, and the CHCGA genetic algorithm. Finally, we analyze the obtained results and point out improvements that might enhance the performance of these two novel algorithms. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/07467-1 - CeTICS - Center of Toxins, Immune-Response and Cell Signaling
• Grantee: Hugo Aguirre Armelin
• Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 11/50761-2 - Models and methods of e-Science for life and agricultural sciences
• Grantee: Roberto Marcondes Cesar Junior
• Support type: Research Projects - Thematic Grants
• FAPESP's process: 14/23564-0 - Studies of efficient data structures to tackle the U-curve optimization problem
• Grantee: Gustavo Estrela de Matos
• Support type: Scholarships in Brazil - Scientific Initiation