Fast Online Node Labeling for Very Large Graphs

• URL: http://arxiv.org/abs/2305.16257v2
• Date: Sun, 28 May 2023 14:16:44 GMT
• Title: Fast Online Node Labeling for Very Large Graphs
• Authors: Baojian Zhou, Yifan Sun, Reza Babanezhad
• Abstract summary: Current methods either invert a graph kernel runtime matrix with $mathcalO(n3)$ or $mathcalO(n2)$ space complexity or sample a large volume of random spanning trees. We propose an improvement based on the textitonline relaxation technique introduced by a series of works.
• Score: 11.700626862639131
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with $\mathcal{O}(n^3)$ runtime and $\mathcal{O}(n^2)$ space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the \textit{online relaxation} technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret $\mathcal{O}(\sqrt{n^{1+\gamma}})$ when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying $\mathcal{O}(k\sqrt{n^{1+\gamma}})$ regret based on this relaxation. The key of FastONL is a \textit{generalized local push} method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is $\mathcal{O}(\text{vol}({\mathcal{S}})\log 1/\epsilon)$ locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

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