  Dictionary learning for sparse representations has been successful in many
reconstruction tasks. Simplicial learning is an adaptation of dictionary
learning, where subspaces become clipped and acquire arbitrary offsets, taking
the form of simplices. Such adaptation is achieved through additional
constraints on sparse codes. Furthermore, an evolutionary approach can be
chosen to determine the number and the dimensionality of simplices composing
the simplicial, in which most generative and compact simplicials are favored.
This paper proposes an evolutionary simplicial learning method as a generative
and compact sparse framework for classification. The proposed approach is first
applied on a one-class classification task and it appears as the most reliable
method within the considered benchmark. Most surprising results are observed
when evolutionary simplicial learning is considered within a multi-class
classification task. Since sparse representations are generative in nature,
they bear a fundamental problem of not being capable of distinguishing two
classes lying on the same subspace. This claim is validated through synthetic
experiments and superiority of simplicial learning even as a generative-only
approach is demonstrated. Simplicial learning loses its superiority over
discriminative methods in high-dimensional cases but can further be modified
with discriminative elements to achieve state-of-the-art performance in
classification tasks.
