2024/08/17 by Hao Li, Hao Jiang, Li, Hao +7 · 1 citation
Computer Science · Engineering · #Algebraic Topology (math.AT) #FOS: Computer and information sciences #FOS: Mathematics #Geoscience and Mining Technology #Machine Learning (cs.LG) #Neural Networks and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2408.09123
openalex publication_date 2024/08/17 · openalex created_date 2024/09/14 · openalex updated_date 2026/07/28
Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.