3 citations · 4 across the 3 of their papers we have counts for
9 papers
Adaptive template systems: Data-driven feature selection for learning with persistence diagrams
Luis Polanco, Jose A. Perea
Feature extraction from persistence diagrams, as a tool to enrich machine learning techniques, has received increasing attention in recent years. In this paper we explore an adapti…
Künneth Formulae in Persistent Homology
Hitesh Gakhar, Jose A. Perea
The classical Künneth formula in algebraic topology describes the homology of a product space in terms of that of its factors. In this paper, we prove Künneth-type theorems for the…
Coordinatizing Data With Lens Spaces and Persistent Cohomology
Luis Polanco, Jose A. Perea
We introduce here a framework to construct coordinates in \emph{finite} Lens spaces for data with nontrivial 1-dimensional persistent cohomology, . Said coo…
Geometric Data Analysis Across Scales via Laplacian Eigenvector Cascading
Joshua L. Mike, Jose A. Perea
We develop here an algorithmic framework for constructing consistent multiscale Laplacian eigenfunctions (vectors) on data. Consequently, we address the unsupervised machine learni…
Topological Time Series Analysis
Jose A. Perea
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights f…
A Brief History of Persistence
Jose A. Perea
Persistent homology is currently one of the more widely known tools from computational topology and topological data analysis. We present in this note a brief survey on the evoluti…