Author:
Oballe Christopher,Boothe David,Franaszczuk Piotr J.,Maroulas Vasileios
Abstract
<p style='text-indent:20px;'>We propose ToFU, a new trainable neural network unit with a persistence diagram dissimilarity function as its activation. Since persistence diagrams are topological summaries of structures, this new activation measures and learns the topology of data to leverage it in machine learning tasks. We showcase the utility of ToFU in two experiments: one involving the classification of discrete-time autoregressive signals, and another involving a variational autoencoder. In the former, ToFU yields competitive results with networks that use spectral features while outperforming CNN architectures. In the latter, ToFU produces topologically-interpretable latent space representations of inputs without sacrificing reconstruction fidelity.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference50 articles.
1. H. Adams, T. Emerson, M. Kirby, R. Neville and C. Peterson, et al., Persistence images: A stable vector representation of persistent homology, J. Mach. Learn. Res., 18 (2017), 35pp.
2. R. J. Adler, S. Agami.Modelling persistence diagrams with planar point processes, and revealing topology with bagplots, J. Appl. Comput. Topol., 3 (2019), 139-183.
3. J.-B. Bardin, G. Spreemann, K. Hess.Topological exploration of artificial neuronal network dynamics, Network Neuroscience, 3 (2019), 725-743.
4. E. Berry, Y.-C. Chen, J. Cisewski-Kehe, B. T. Fasy.Functional summaries of persistence diagrams, J. Appl. Comput. Topol., 4 (2020), 211-262.
5. C. A. N. Biscio, J. Møller.The accumulated persistence function, a new useful functional summary statistic for topological data analysis, with a view to brain artery trees and spatial point process applications, J. Comput. Graph. Statist., 28 (2019), 671-681.
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