# Graph sketching-based Space-efficient Data Clustering

## TL;DR

This paper introduces DBMSTClu, a space-efficient, non-parametric clustering method that uses a sketched MST from limited measurements to accurately identify arbitrary-shaped clusters on resource-constrained devices.

## Contribution

It presents a novel MST-based clustering algorithm that operates under strict space constraints using streaming sketches, without requiring input parameters.

## Key findings

- Effective at identifying non-convex clusters.
- Requires significantly less memory than traditional methods.
- Outperforms state-of-the-art on multiple datasets.

## Abstract

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 $\mathcal{G}$ 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 $\mathcal{G}$ as a stream of edge weight updates which is sketched in one pass over the data into a compact structure requiring $O(N \operatorname{polylog}(N))$ space, far better than the theoretical memory cost $O(N^2)$ of $\mathcal{G}$. The recovered approximate MST $\mathcal{T}$ as input, DBMSTClu then successfully detects the right number of nonconvex clusters by performing relevant cuts on $\mathcal{T}$ 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.