Papers › Graph sketching-based Space-efficient Data Clustering
Graph sketching-based Space-efficient Data Clustering
Anne Morvan, Krzysztof Choromanski, Cédric Gouy-Pailler, Jamal Atif
In this paper, we address the problem of recovering arbitrary-shaped data clusters from datasets while facing \emph{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 \emph{non-parametric} method working on a Minimum Spanning Tree (MST) recovered from a limited number of linear measurements i.e. a \emph{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 distinguishing 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 DBSCAN or the Spectral Clustering method. An approximate MST is retrieved by following the dynamic \emph{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, DBMSTClu 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.
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