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09/19/2023
O(k)-Equivariant Dimensionality Reduction on Stiefel Manifolds
Many real-world datasets live on high-dimensional Stiefel and Grassmanni...
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04/28/2023
Topological Data Analysis of Electroencephalogram Signals for Pediatric Obstructive Sleep Apnea
Topological data analysis (TDA) is an emerging technique for biological ...
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12/16/2022
Learning on Persistence Diagrams as Radon Measures
Persistence diagrams are common descriptors of the topological structure...
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12/14/2022
Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction
The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Joh...
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06/13/2022
Fiberwise dimensionality reduction of topologically complex data with vector bundles
Datasets with non-trivial large scale topology can be hard to embed in l...
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04/25/2021
Move Schedules: Fast persistence computations in sparse dynamic settings
The standard procedure for computing the persistent homology of a filter...
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04/15/2021
Approximate and discrete Euclidean vector bundles
We introduce ε-approximate versions of the notion of Euclidean vector bu...
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03/08/2021
Sliding Window Persistence of Quasiperiodic Functions
A function is called quasiperiodic if its fundamental frequencies are li...
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10/13/2019
Adaptive template systems: Data-driven feature selection for learning with persistence diagrams
Feature extraction from persistence diagrams, as a tool to enrich machin...
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10/12/2019
Künneth Formulae in Persistent Homology
The classical Künneth formula in algebraic topology describes the homolo...
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05/01/2019
Coordinatizing Data With Lens Spaces and Persistent Cohomology
We introduce here a framework to construct coordinates in finite Lens sp...
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02/19/2019
Approximating Continuous Functions on Persistence Diagrams Using Template Functions
The persistence diagram is an increasingly useful tool arising from the ...
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11/28/2018
Topological Time Series Analysis
Time series are ubiquitous in our data rich world. In what follows I wil...
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09/25/2018
Sparse Circular Coordinates via Principal Z-Bundles
We present in this paper an application of the theory of principal bundl...
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09/19/2018
Twisty Takens: A Geometric Characterization of Good Observations on Dense Trajectories
In nonlinear time series analysis and dynamical systems theory, Takens' ...
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09/10/2018
A Brief History of Persistence
Persistent homology is currently one of the more widely known tools from...
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03/23/2018