  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.
