Dominant Eigenvalue-Eigenvector Pair Estimation via Graph Infection
We present a novel method to estimate the dominant eigenvalue and eigenvector pair of any non-negative real matrix via graph infection. The key idea in our technique lies in approximating the solution to the first-order matrix ordinary differential equation (ODE) with the Euler method. Graphs, which can be weighted, directed, and with loops, are first converted to its adjacency matrix A. Then by a naive infection model for graphs, we establish the corresponding first-order matrix ODE, through which A’s dominant eigenvalue is revealed by the fastest growing term. When there are multiple dominant eigenvalues of the same magnitude, the classical power iteration method can fail. In contrast, our method can converge to the dominant eigenvalue even when same-magnitude counterparts exist, be it complex or opposite in sign. We conduct several experiments comparing the convergence between our method and power iteration. Our results show clear advantages over power iteration for tree graphs, bipartite graphs, directed graphs with periods, and Markov chains with spider-traps. To our knowledge, this is the first work that estimates dominant eigenvalue and eigenvector pair from the perspective of a dynamical system and matrix ODE. We believe our method can be adopted as an alternative to power iteration, especially for graphs.
Thu 20 JulDisplayed time zone: London change
11:00 - 12:30 | ICGT Session 6: ApplicationsResearch Papers at Willow Chair(s): Kazunori Ueda Waseda University Remote Participants: Zoom Link, YouTube Livestream | ||
11:00 30mTalk | A Rule-Based Procedure for Graph Query Solving Research Papers Dominique Duval Université Grenoble Alpes, P: Rachid Echahed University of Grenoble - CNRS, Frederic Prost Université Grenoble Alpes DOI | ||
11:30 30mTalk | Formalization and analysis of BPMN using graph transformation systemsICGT Best Applications Paper Research Papers P: Tim Kräuter Western Norway University of Applied Sciences, Adrian Rutle Western Norway University of Applied Sciences, Harald König University of Applied Sciences, FHDW Hannover and Western Norway University of Applied Sciences, Yngve Lamo Western Norway University of Applied Sciences DOI Pre-print File Attached | ||
12:00 30mTalk | Dominant Eigenvalue-Eigenvector Pair Estimation via Graph Infection Research Papers P: Kaiyuan Yang University of Zurich, Li Xia National University of Singapore, Y.C. Tay National University of Singapore DOI Pre-print |