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Topological Data Analysis of Decision Boundaries with Application to Model Selection

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arxiv 1805.09949 v1 pith:JGDRTJOW submitted 2018-05-25 stat.ML cs.LG

Karthikeyan Natesan Ramamurthy , Kush R. Varshney , Krishnan Mody This is my paper · ORCID
classification stat.MLcs.LG
keywords complexdecisionlabeledanalysisboundarieshomologyvietoris-ripsapplication
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We propose the labeled \v{C}ech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide theoretical conditions and analysis for recovering the homology of a decision boundary from samples. Our main objective is quantification of deep neural network complexity to enable matching of datasets to pre-trained models; we report results for experiments using MNIST, FashionMNIST, and CIFAR10.

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Cited by 1 Pith paper

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  1. Concept Boundary Vectors

    cs.LG 2024-12 conditional novelty 6.0 of 10

    Concept boundary vectors are derived from the boundary between latent concept clusters, and the paper reports they capture semantic relationships better than concept activation vectors.

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