Spectral Clustering via Graph Filtering: Consistency on the High-Dimensional Stochastic Block Model
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Spectral clustering is amongst the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen-decomposition of the n×n graph Laplacian matrix to extract its k leading eigenvectors, where k is the desired number of clusters among n objects. This is prohibitively complex to implement for very large datasets. However, it has recently been shown that it is possible to bypass the eigen-decomposition by computing an approximate spectral embedding through graph filtering of random signals. In this paper, we prove that spectral clustering performed via graph filtering can still recover the planted clusters consistently, under mild conditions. We analyse the effects of sparsity, dimensionality and filter approximation error on the consistency of the algorithm.
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