Optimal column subset selection for image classification by genetic algorithms

Abstract

Many problems in operations research can be solved by combinatorial optimization. Fixed-length subset selection is a family of combinatorial optimization problems that involve selection of a set of unique objects from a larger superset. Feature selection, p-median problem, and column subset selection problem are three examples of hard problems that involve search for fixed-length subsets. Due to their high complexity, exact algorithms are often infeasible to solve real-world instances of these problems and approximate methods based on various heuristic and metaheuristic (e.g. nature-inspired) approaches are often employed. Selecting column subsets from massive data matrices is an important technique useful for construction of compressed representations and low rank approximations of high-dimensional data. Search for an optimal subset of exactly k columns of a matrix, \(A^{m\times n}\), \(k < n\), is a well-known hard optimization problem with practical implications for data processing and mining. It can be used for unsupervised feature selection, dimensionality reduction, data visualization, and so on. A compressed representation of raw real-world data can contribute, for example, to reduction of algorithm training times in supervised learning, to elimination of overfitting in classification and regression, to facilitation of better data understanding, and to many other benefits. This paper proposes a novel genetic algorithm for the column subset selection problem and evaluates it in a series of computational experiments with image classification. The evaluation shows that the proposed modifications improve the results obtained by artificial evolution.