SUBCLU

SUBCLU is an algorithm for clustering high-dimensional data by Karin Kailing, Hans-Peter Kriegel and Peer Kröger. It is a subspace clustering algorithm that builds on the density-based clustering algorithm DBSCAN. SUBCLU can find clusters in axis-parallel subspaces, and uses a bottom-up, greedy strategy to remain efficient.

Approach

SUBCLU uses a monotonicity criteria: if a cluster is found in a subspace $S$, then each subspace $T\subseteq S$ also contains a cluster. However, a cluster $C\subseteq DB$ in subspace $S$ is not necessarily a cluster in $T\subseteq S$, since clusters are required to be maximal, and more objects might be contained in the cluster in $T$ that contains $C$. However, a density-connected set in a subspace $S$ is also a density-connected set in $T\subseteq S$.

This downward-closure property utilized by SUBCLU in a way similar to the Apriori algorithm: first, all 1-dimensional subspaces are clustered. All clusters in a higher-dimensional subspace will be subsets of the clusters detected in this first clustering. SUBCLU hence recursively produces $k+1$-dimensional candidate subspaces by combining $k$-dimensional subspaces with clusters sharing $k-1$ attributes. After pruning irrelevant candidates, DBSCAN is applied to the candidate subspace to find out if it still contains clusters. If it does, the candidate subspace is used for the next combination of subspaces.