Topological feature selection for time series data

Autor:	Bubenik, Peter, Bush, Johnathan
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Topology Mathematics - Optimization and Control 55N31
Druh dokumentu:	Working Paper
Popis:	We use tools from applied topology for feature selection on vector-valued time series data. We employ persistent homology and sliding window embeddings to quantify the coordinated dynamics of time series. We describe an algorithm for gradient descent to assign scores, or weights, to the variables of the time series based on their contribution to the dynamics as quantified by persistent homology; the result is a convex combination of a subset of the variables. In this setting, we prove persistence vineyards are piecewise linear and we give a simple formula for the derivatives of the vines. We demonstrate our method of topological feature selection with synthetic data and C. elegans neuronal data. Comment: 15 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.17494 Zobrazit plný text záznamu View this record from Arxiv