Exploiting sparsity to improve the accuracy of Nyström-based large-scale spectral clustering

The Nyström method is a matrix approximation technique that has shown great promise in speeding up spectral clustering. However, when the input matrix is sparse, we show that the traditional Nyström method requires a prohibitively large number of samples to obtain a good approximation. We propose a novel sampling approach to select the landmark points used to compute the Nyström approximation. We show that the proposed sampling approach obeys the same error bound as in Bouneffouf and Birol (2015). To control sample complexity, we propose a selective densification step based on breadth-first traversal. We show that the proposed densification does not change the optimal clustering. Results on real world datasets show that by combining the proposed sampling and densification schemes, we can obtain better accuracy compared to other techniques used for the Nyström method while using significantly fewer samples.