A Novel Genetic Algorithm Approach for Discriminative Subspace Optimization

Image set representation by subspace methods has shown to be effective for several image processing tasks, such as classifying multiple images and videos. A subspace exploits the geometrical structure in which images are distributed, representing the image set with a fixed dimension giving more statistical robustness to input noise and compactness to the images. The mutual subspace method (MSM) and its extensions, the Orthogonal Mutual Subspace method (OMSM), and the Generalized Difference Subspace (GDS) are the most prominent subspace methods employed. However, these methods require solving a nonlinear optimization which lacks a closed-form solution. In this paper, we present a metaheuristic-based approach for discriminative subspace optimization. We develop a Genetic Algorithm (GA) for integrating OMSM and GDS discriminative subspaces. The initialization strategy and the genetic operators of the GA provide quality of objective function value of solutions and preserve their feasibility without any extra repair step. We validated our approach on four object recognition datasets. Results show that our optimization method outperforms related methods in accuracy and highlights the use of evolutionary algorithms for subspace optimization. Code: https://github.com/bernardo-gatto/Evolving_manifold.