Now showing items 1-4 of 4
Topological techniques for characterization of patterns in differential equations
Author(s):Neville, Rachel A.
Complex data can be challenging to untangle. Recent advances in computing capabilities has allowed for practical application of tools from algebraic topology, which have proven to be useful for qualitative and quantitative ...
Patterns in dynamics
Author(s):Motta, Francis Charles
In this paper we introduce and explore the idea of persistent homology (PH) and discuss several applications of this computational topology tool beyond its intended purpose. In particular we apply persistence to data ...
Algorithms for feature selection and pattern recognition on Grassmann manifolds
This dissertation presents three distinct application-driven research projects united by ideas and topics from geometric data analysis, optimization, computational topology, and machine learning. We first consider ...
Persistent homology of the logistic map: an exploration of chaos
Given a discrete sampling of points, how can one reconstruct the underlying geometric object? Further, the question arises how can one discern between noise and sampling distortion and important topological features. ...