Simplex-based dimension estimation of topological manifolds

Tasaki, Hirohisa; Lenz, Reiner; Chao, Jinhui

doi:10.1109/icpr.2016.7900194

Cited by 3 publications

(1 citation statement)

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“…Simplex and simplicial complex based data applications are becoming popular in literature as data analysis receives more and more topological considerations [16,17,18,19,20]. Moreover, utilizing simplices for data applications is not a completely new idea from the perspective of sparse representations [21,22].…”

Section: Related Workmentioning

confidence: 99%

Evolutionary Simplicial Learning as a Generative and Compact Sparse Framework for Classification

Oktar,

Turkan

2020

Preprint

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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.

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Section: Related Workmentioning

confidence: 99%