Feature selection for high-dimensional data using a multivariate search space reduction strategy based scatter search

In feature selection, the increasing of the dimensionality and the complexity of feature interactions make the problem challenging. Furthermore, searching for an optimal subset of features from a high-dimensional feature space is known to be an NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{N}\mathcal{P}$$\end{document}-hard problem. To improve the efficiency and effectiveness of the search algorithm, feature grouping has emerged as a way to reduce the search space by clustering features according to a measure. In this work we propose to reduce the search space by applying a greedy algorithm, called Multivariate Greedy Predominant Groups Generator (MGPGG). MGPGG extends the idea of the Greedy Predominant Groups Generator (GPGG) algorithm by taking into account feature interaction among three or more features. For this purpose, MGPGG uses the Multivariate Symmetrical Uncertainty (MSU) to group features that share information about the class label. We also propose a Scatter Search strategy that integrates MGPGG to find small subsets of features with high predictive power. The proposed algorithm, called Multivariate Predominant Group-based Scatter Search (MPGSS), is tested on high-dimensional data from biomedical and text-mining fields. The proposal is compared with state-of-the-art feature selection strategies. Results show that MPGSS is competitive since it is capable of finding small subsets of features while keeping high predictive classification models.