2017/07/20 by Mustafa Hajij, Hajij, Mustafa, Bei Wang +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Alzheimer's disease research and treatments #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graphics (cs.GR) #Metabolomics and Mass Spectrometry Studies #Topological and Geometric Data Analysis #cs.CG #cs.GR
paper · pdf · doi:10.48550/arxiv.1707.06683
openalex publication_date 2017/07/20 · arxiv created 2017/10/03 · arxiv updated 2017/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into metric spaces, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether persistence-based similarity measure as a graph metric satisfies a set of well-established, desirable properties for graph metrics.