Fast kernel spectral clustering

Spectral clustering suffers from a scalability problem in both memory usage and computational time when the number of data instances N is large. To solve this issue, we present a fast spectral clustering algorithm able to effectively handle millions of datapoints at a desktop PC scale. The proposed technique relies on a kernel-based formulation of the spectral clustering problem, also known as kernel spectral clustering. In this framework, the Nystrom approximation of the feature map of size m, with m << N, is used to solve the primal optimization problem. This leads to a reduction of time complexity from O(N-3) to O(mN) and space complexity from O(N-2) to O(mN). The effectiveness of the proposed algorithm in terms of computational efficiency and clustering quality is illustrated on several datasets. (C) 2017 Published by Elsevier B.V.