Genetic Algorithm for the Column Subset Selection Problem

Abstract

The column subset selection problem is a wellknown hard optimization problem of selecting an optimal subset of k columns from the matrix A m×n , k < n, so that the cost function is minimized. The problem is of practical importance for data mining and processing since it can be used for unsupervised feature selection, dimension reduction, and many other applications. This work proposes a new genetic algorithm for the column subset selection problem and evaluates it in a series of computational experiments.

Multimodal Stereoscopic Movie Summarization Conforming to Narrative Characteristics

“…In [57], a metaheuristic approach based on a genetic algorithm is successfully employed for the approximate solution of the CSSP, by directly using Equation (2) as a fitness function. The method is evaluated on several small, randomly generated matrices and is shown to produce good results for a fixed small value of C. In this work, the same metaheuristic approach was adopted and adapted into the proposed pipeline, so that MSP could be modelled and solved as a CSSP.…”

Movie shot selection preserving narrative properties

“…In [19], a metaheuristic approach based on a genetic algorithm is successfully employed for the approximate solution of the CSSP, by directly using Equation (1) as a fitness function. The method is evaluated on several small, randomly generated matrices and is shown to produce good results for a fixed small value of C. In this work, the same metaheuristic approach was adopted and adapted into the proposed pipeline, so that MSP could be modelled and solved as a CSSP.…”

“…An order-preserving variant of 1-point crossover [19] is utilized as the main genetic operator. Specifically, in order to combine parent chromosomes c l and c m , a random position k is selected as crossover point and is inspected for suitability.…”

“…An order-preserving variant of mutation [19] is employed as the second genetic operator. Specifically, the k-th gene of a chromosome c n , with an assigned valued of c n k , is randomly selected and replaced by a value determined by the neighbouring genes, according to Equation (5):…”

“…A genetic algorithm is employed to approximate an optimal solution and, as in [19], each candidate is encoded in the form of a sequence of column indices sorted in increasing order. Every such chromosome is of length C. Roulette selection at each iteration is adopted as the mating pool formation strategy.…”