Fast Online Node Labeling for Very Large Graphs
This work addresses scalability issues in online node labeling for large graphs, offering a more efficient solution for applications like social network analysis, though it is incremental based on prior relaxation techniques.
The paper tackles the online node classification problem for large graphs by proposing FastONL, an algorithm that achieves an approximate regret of O(k√(n^(1+γ))) with per-prediction cost O(vol(S) log 1/ε) and linear memory, improving scalability over existing methods.
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 $\mathcal{O}(\sqrt{n^{1+γ}})$ when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying $\mathcal{O}(k\sqrt{n^{1+γ}})$ 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 $\mathcal{O}(\text{vol}({\mathcal{S}})\log 1/ε)$ locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.