Graph sketching-based Space-efficient Data Clustering

Abstract

In this paper, we address the problem of recovering arbitrary-shaped data clusters from datasets while facing high space constraints, as this is for instance the case in many real-world applications when analysis algorithms are directly deployed on resources-limited mobile devices collecting the data. We present DBMSTClu a new space-efficient density-based non-parametric method working on a Minimum Span-ning Tree (MST) recovered from a limited number of linear measurements i.e. a sketched version of the dissimilarity graph G between the N objects to cluster. Unlike k-means, k-medians or k-medoids algorithms, it does not fail at distin-guishing clusters with particular forms thanks to the property of the MST for expressing the underlying structure of a graph. No input parameter is needed contrarily to DB-SCAN or the Spectral Clustering method. An approximate MST is retrieved by following the dynamic semi-streaming model in handling the dissimilarity graph G as a stream of edge weight updates which is sketched in one pass over the data into a compact structure requiring O(N polylog(N)) space, far better than the theoretical memory cost O(N2) of G. The recovered approximate MST T as input, DBMST-Clu then successfully detects the right number of nonconvex clusters by performing relevant cuts on T in a time linear in N. We provide theoretical guarantees on the quality of the clustering partition and also demonstrate its advantage over the existing state-of-the-art on several datasets.