🍩 Database of Original & Non-Theoretical Uses of Topology

1. Hyperparameter Optimization of Topological Features for Machine Learning Applications (2019)

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

   Abstract

   This paper describes a general pipeline for generating optimal vector representations of topological features of data for use with machine learning algorithms. This pipeline can be viewed as a costly black-box function defined over a complex configuration space, each point of which specifies both how features are generated and how predictive models are trained on those features. We propose using state-of-the-art Bayesian optimization algorithms to inform the choice of topological vectorization hyperparameters while simultaneously choosing learning model parameters. We demonstrate the need for and effectiveness of this pipeline using two difficult biological learning problems, and illustrate the nontrivial interactions between topological feature generation and learning model hyperparameters.

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   • Biology
   • Protein folding
   • Protein stability
   • Rocklin designs
   • Configuration space
   • Hyperparameter optimization
   • Machine learning
   • Persistence diagrams

2. A Topological Measurement of Protein Compressibility (2015)

   Marcio Gameiro, Yasuaki Hiraoka, Shunsuke Izumi, Miroslav Kramar, Konstantin Mischaikow, Vidit Nanda

   Abstract

   In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure. To identify and understand the relevant topological features within a given protein, we model its molecule as an alpha filtration and hence obtain multi-scale insight into the structure of its tunnels and cavities. The persistence diagrams of this alpha filtration capture the sizes and robustness of such tunnels and cavities in a compact and meaningful manner. From these persistence diagrams, we extract a measure of compressibility derived from those topological features whose relevance is suggested by physical and chemical properties. Due to recent advances in combinatorial topology, this measure is efficiently and directly computable from information found in the Protein Data Bank (PDB). Our main result establishes a clear linear correlation between the topological measure and the experimentally-determined compressibility of most proteins for which both PDB information and experimental compressibility data are available. Finally, we establish that both the topological measurement and the linear correlation are stable with respect to small perturbations in the input data, such as those arising from experimental errors in compressibility and X-ray crystallography experiments.

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   • Molecular structure
   • Protein
   • Protein compressability
   • proteins
   • Alpha filtration
   • Persistence diagrams
   • Persistent homology