Compressive Spectral Clustering
This work addresses the scalability problem for practitioners using spectral clustering on large networks, though it is incremental as it builds on existing graph signal processing results.
The authors tackled the computational intensity of spectral clustering for large datasets by proposing a method that speeds up the last two steps using graph signal processing techniques, achieving a gain in computation time that can reach several orders of magnitude while controlling approximation error.
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features to separate objects into k classes. Each of these three steps becomes computationally intensive for large N and/or k. We propose to speed up the last two steps based on recent results in the emerging field of graph signal processing: graph filtering of random signals, and random sampling of bandlimited graph signals. We prove that our method, with a gain in computation time that can reach several orders of magnitude, is in fact an approximation of spectral clustering, for which we are able to control the error. We test the performance of our method on artificial and real-world network data.