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Thomas Weighill

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3 papers

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AAAI Conference 2025 Conference Paper

Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance

Ranthony A. Clark
Tom Needham
Thomas Weighill

Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to embed the data into some other manifold or metric space in order to better reflect the geometry or topology of the point cloud. We propose a general method for manifold-valued multidimensional scaling based on concepts from optimal transport. In particular, we establish theoretical connections between the recently introduced semi-relaxed Gromov-Wasserstein (srGW) framework and multidimensional scaling by solving the Monge problem in this setting. We also derive novel connections between srGW distance and Gromov-Hausdorff distance. We apply our computational framework to analyze ensembles of political redistricting plans for states with two Congressional districts, achieving an effective visualization of the ensemble as a distribution on a circle which can be used to characterize typical neutral plans, and to flag outliers.

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AAAI Conference 2023 Short Paper

Persistent Homology through Image Segmentation (Student Abstract)

Joshua Slater
Thomas Weighill

The efficacy of topological data analysis (TDA) has been demonstrated in many different machine learning pipelines, particularly those in which structural characteristics of data are highly relevant. However, TDA's usability in large scale machine learning applications is hindered by the significant computational cost of generating persistence diagrams. In this work, a method that allows this computationally expensive process to be approximated by deep neural networks is proposed. Moreover, the method's practicality in estimating 0-dimensional persistence diagrams across a diverse range of images is shown.

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AAAI Conference 2023 Short Paper

Toplogical Data Analysis Detects and Classifies Sunspots (Student Abstract)

Aidan Lytle
Neil Pritchard
Alicia Aarnio
Thomas Weighill

In our technology-dependent modern world, it is imperative to monitor the Sun for space weather threats to critical infrastructure. Topological data analysis (TDA) is a new set of mathematical techniques used in data analysis and machine learning. We demonstrate that TDA can robustly detect and classify solar surface and coronal activity. This technique is a promising step toward future application in predictive space weather modeling.

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