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Filtration-Based Representation Learning for Temporal Graphs

Samrik Chowdhury, Siddharth Pritam, Rohit Roy, Madhav Cherupilil Sajeev

TL;DR

<3-5 sentence high-level summary> Temporal graphs are challenging to analyze due to evolving connectivity and timing. This work introduces a filtration-based representation using δ-temporal motifs to capture multi-scale temporal structure without snapshotting, enabling persistent homology and graph-filtration kernels to operate directly on temporal data. The authors prove stability under several randomized reference models, provide an efficient O(|E| d_max) averaging algorithm, and demonstrate strong, node-label-free classification performance on real and synthetic datasets. This approach offers a scalable, robust framework for dynamic network analysis with broad applicability to epidemic, social, and signaling systems.

Abstract

In this work, we introduce a filtration on temporal graphs based on $δ$-temporal motifs (recurrent subgraphs), yielding a multi-scale representation of temporal structure. Our temporal filtration allows tools developed for filtered static graphs, including persistent homology and recent graph filtration kernels, to be applied directly to temporal graph analysis. We demonstrate the effectiveness of this approach on temporal graph classification tasks.

Filtration-Based Representation Learning for Temporal Graphs

TL;DR

<3-5 sentence high-level summary> Temporal graphs are challenging to analyze due to evolving connectivity and timing. This work introduces a filtration-based representation using δ-temporal motifs to capture multi-scale temporal structure without snapshotting, enabling persistent homology and graph-filtration kernels to operate directly on temporal data. The authors prove stability under several randomized reference models, provide an efficient O(|E| d_max) averaging algorithm, and demonstrate strong, node-label-free classification performance on real and synthetic datasets. This approach offers a scalable, robust framework for dynamic network analysis with broad applicability to epidemic, social, and signaling systems.

Abstract

In this work, we introduce a filtration on temporal graphs based on -temporal motifs (recurrent subgraphs), yielding a multi-scale representation of temporal structure. Our temporal filtration allows tools developed for filtered static graphs, including persistent homology and recent graph filtration kernels, to be applied directly to temporal graph analysis. We demonstrate the effectiveness of this approach on temporal graph classification tasks.

Paper Structure

This paper contains 34 sections, 11 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our Approach:
  3. Our Contribution:
  4. Related work:
  5. Preliminaries
  6. Temporal Network
  7. Temporal Graphs:
  8. $\delta$-Temporal Motifs:
  9. Topological Data Analysis
  10. Simplicial Complex:
  11. Filtration:
  12. Persistent Homology:
  13. PSS Kernel and Graph Filtration Kernel
  14. Kernel for Persistence Diagrams:
  15. Graph Filtration Kernel:
  16. ...and 19 more sections

Figures (5)

  • Figure 1: Multiple time labels are separated by commas.
  • Figure 2: All four possible 3-node 3-edge motifs of Figure \ref{['fig:mulit_temporal_graph']} are depicted here. Note that the temporal edges between $B$ and $C$ and $B$ and $F$ differ in their respective timestamps. The two left motifs satisfy $\delta = 6$, while the two right motifs satisfy $\delta = 5$.
  • Figure 3: The first figure on the left shows a single-labeled temporal graph, followed by the corresponding average and minimum filtrations derived from it in the next two figures.
  • Figure 4: An example of a single step in the RE procedure involves shuffling the edges $BC$ and $FE$ to $BF$ and $CE$, respectively, while maintaining their original time stamps.
  • Figure 5: Comparison of the PH and filtered-kernel pipelines across datasets. The reported accuracy scores are averaged over multiple runs, with only marginal variation across trials.