A spectral clustering approach for online and streaming applications

In this paper, we present a spectral clustering method for online and streaming applications. Here, we note that the rank of the coefficients of the eigenvector of the graph Laplacian govern, together with the weights of the adjacency matrix, the assignment of the data to clusters. Thus, we adopt a sampling without replacement strategy, where, at each sampling step, we select those data instances which are most relevant to the clustering process. To do this, we 'sparsify' the eigenvector making use of a Minorisation-Maximisation approach. This not only allows to cluster the data under consideration after the sampling has been effected, but also permits the optimisation in hand to be performed making use of a gradient descent approach with a closed form iterate. Moreover, the method presented here is quite general in nature and can be employed in other settings which hinge in an L-0 regularised penalty function. We discuss the use of our approach for the assessment of node centrality and document binarisation. We also illustrate the utility of our method for purposes of background subtraction and compare our results with those yielded by alternatives elsewhere in the literature.