Fast Online Node Labeling for Very Large Graphs
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This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with 𝒪(n^3) runtime and 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 online relaxation technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret 𝒪(√(n^1+γ)) when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying 𝒪(k√(n^1+γ)) regret based on this relaxation. The key of FastONL is a generalized local push method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is 𝒪(vol(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.
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