A Topological Heat Map for Data Analysis (TopHeat)

Abstract

Topological data analysis provides summaries for the shape of data. Some of these summaries, such as the PI's persistence landscape, are feature maps and kernels, and can be easily combined with standard methods of statistics and machine learning. However, these topological summaries can be difficult for non-experts to interpret. In this project, we produced a new summary, that may be visualized as a heat map on the underlying data. We developed theory for this heat map, showing that it is stable under perturbations of the input. Furthermore, we showed how to combine this summary with statistics and machine learning and applied it to synthetic data and real data.

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Document Details

Document Type
Technical Report
Publication Date
Jan 05, 2023
Accession Number
AD1224710

Entities

Organizations

  • University of Florida

Tags

Readers

  • Atmospheric Science/Meteorology
  • Business Analytics
  • Computer Vision.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference