Classification Via Simplicial Learning

Dictionary learning for sparse representations is generative in nature, hence discriminative modifications are commonly observed for classification problems. Classical dictionary learning bears a fundamental problem of not being capable of distinguishing two different classes lying on the same subspace, that cannot be resolved by any discriminative modification. This paper proposes an evolutionary simplicial learning method as a generative and compact sparse framework that solves the aforementioned problem for classification. Simplicial learning is an adaptation of conventional dictionary learning, in which subspaces designated by dictionary elements take the form of simplices through additional constraints on sparse codes. On top, an evolutionary approach is developed to determine the dimensionality and the number of simplices composing the simplicial. The proposed evolutionary learning is considered within multi-class classification tasks through synthetic and handwritten digit datasets and the superiority of it even as a generative-only approach is demonstrated. Simplicial learning loses its superiority over discriminative methods in high-dimensional real-world cases but can further be modified with discriminative elements to achieve state-of-the-art for classification.