44 citations · 109 across the 21 of their papers we have counts for
6 papers · 1 filter
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…
Sparse Circular Coordinates via Principal -Bundles
Jose A. Perea
We present in this paper an application of the theory of principal bundles to the problem of nonlinear dimensionality reduction in data analysis. More explicitly, we derive, from a…
Twisty Takens: A Geometric Characterization of Good Observations on Dense Trajectories
Boyan Xu, Christopher J. Tralie, Alice Antia +2
In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a…
Chatter Classification in Turning Using Machine Learning and Topological Data Analysis
Firas A. Khasawneh, Elizabeth Munch, Jose A. Perea
Chatter identification and detection in machining processes has been an active area of research in the past two decades. Part of the challenge in studying chatter is that machining…