Unsupervised feature selection with evolutionary sparsity

The ℓ_2,0-norm is playing an increasingly important role in unsupervised feature selection. However, existing algorithm for optimization problem with ℓ_2,0-norm constraint has two problems: First, they cannot automatically determine the sparsity, also known as the number of key features. Second, they have the risk of converging towards local optima, therefore selecting trivial (less informative) features. To address these problems, this paper proposes an unsupervised feature selection method with evolutionary sparsity (EVSP), which integrates the feature selection process with a sparse projection matrix and population search mechanisms into a unified unsupervised feature selection framework. Specifically, the level of sparsity is encoded as population individuals, and subsequently, a multi-objective evolutionary algorithm based on binary encoding is introduced to recursively determine the optimal level of sparsity, thus unsupervisedly guiding the learning of an optimal row-sparse projection matrix. Moreover, by utilizing the feature weights learned through sparse projection, a two-stage strategy called the mutation-repair operator is designed to steer the evolution of the population, aiming to generate high-quality candidate solutions. Comprehensive experiments on eleven benchmark datasets, with a maximum dimensionality of 10304 features and a maximum size of 9298 samples, demonstrate that the proposed EVSP method can effectively determine the optimal sparsity level, significantly outperforming several state-of-the-art methods.