Hyperparameter Optimization of Topological Features for Machine Learning Applications

Motta, Francis C.; Harer, John; Leiby, Nick; Marinozzi, Franco; Novotney, Scott; Rocklin, Gabe; Singer, Jed; Strickland, Devin; Vaughn, Matthew; Tralie, Christopher J.; Bedini, Rossella; Bini, Fabiano; Bini, Gilberto; Eramian, Hamed; Gameiro, Marcio; Haase, Steve; Haddox, Hugh K.

doi:10.1109/icmla.2019.00185

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…A main goal of topological data analysis (TDA) is to characterize the structure of an object-usually a point cloudthrough its topological features. In particular, persistent homology [2,21] is a family of techniques that detect and summarize multiscale topological features and has been applied to a wide variety of applications including timeseries data [10,24], image processing [31], machine learning [19], and artificial intelligence [3,17]. Complementing the study of point-cloud data, another line of research involves utilizing the TDA toolset to study complex systems, for which applications include the analysis of spreading processes over social networks [28], network neuroscience [5,25], mechanical-force networks [12], jamming in granular material [13], molecular structure [16], and DNA folding [7].…”

Section: Introductionmentioning

confidence: 99%

Persistent homology of convection cycles in network flows

Le¹,

Taylor²

2021

Preprint

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Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and characterization of convective/cyclic/chiral flows over networks, particularly those that arise for irreversible Markov chains (MCs). As two applications, we study convection cycles arising under the PageRank algorithm, and we investigate chiral edges flows for a stochastic model of a bi-monomer's configuration dynamics. Our experiments highlight how system parameters-e.g., the teleportation rate for PageRank and the transition rates of external and internal state changes for a monomer-can act as homology regularizers of convection, which we summarize with persistence barcodes and homological bifurcation diagrams. Our approach establishes a new connection between the study of convection cycles and homology, the branch of mathematics that formally studies cycles, which has diverse potential applications throughout the sciences and engineering.

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