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arXiv · 1805.09949

Topological Data Analysis of Decision Boundaries with Application to Model Selection

Karthikeyan Natesan Ramamurthy·Kush R. Varshney·Krishnan Mody
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Abstract

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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Karthikeyan Natesan Ramamurthy, Kush R. Varshney, Krishnan Mody. 2018-05-25. Topological Data Analysis of Decision Boundaries with Application to Model Selection. https://arxiv.org/abs/1805.09949

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