🤖 AI Summary
This study addresses the effectiveness of topological feature extraction for univariate time series classification by mapping time series into graph structures using five complex network methods, including visibility graphs, transition graphs, and proximity graphs. Persistent diagrams are generated via Vietoris–Rips filtration and persistent homology, then vectorized using persistence landscapes and topological statistics. The work reveals that both the choice of network construction and distance metric critically influence classification performance: diffusion distance consistently outperforms shortest-path distance, and optimal graph representations vary across signal types. Furthermore, the robustness of topological features under noise is empirically validated. Experiments on twelve UCR benchmark datasets demonstrate that while no single network construction universally dominates, diffusion distance consistently yields superior results.
📝 Abstract
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and horizontal visibility graphs), transition, and proximity) and the graph is converted to a dissimilarity matrix from which a Vietoris-Rips filtration yields persistence diagrams. These diagrams are vectorized into fixed-length features through persistence landscapes and topological summary statistics. By standardizing the downstream processing, differences in classification performance are attributable to the network construction and distance metric alone. Experiments on twelve UCR benchmarks show that (i) no single construction dominates: the optimal graph type depends on the signal's discriminative structure; (ii) the graph distance metric is a first-order design choice, with diffusion distance uniformly outperforming shortest-path alternatives; and (iii) persistence-based features degrade gracefully under noise, consistent with the classical stability theorem of persistent homology.