2013/05/16 by Saba Emrani, Emrani, Saba, Thanos Gentimis +3 · 1 citation
Computer Science · Mathematics · #55N35 #55N99 #55U99 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1305.3879
openalex publication_date 2013/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The objective of this study is to detect and quantify the periodic behavior of the signals using topological methods. We propose to use delay-coordinate embeddings as a tool to measure the periodicity of signals. Moreover, we use persistent homology for analyzing the structure of point clouds of delay-coordinate embeddings. A method for finding the appropriate value of delay is proposed based on the autocorrelation function of the signals. We apply this topological approach to wheeze signals by introducing a model based on their harmonic characteristics. Wheeze detection is performed using the first Betti numbers of a few number of landmarks chosen from embeddings of the signals.