You see a set of wagons - I see one train: Towards a unified view of local and global arbitrarily oriented subspace clusters

Having data with a high number of features raises the need to detect clusters which exhibit within subspaces of features a high similarity. These subspaces can be arbitrarily oriented which gave rise to arbitrarily-oriented subspace clustering (AOSC) algorithms. In the diversity of such algorithms some are specialized at detecting clusters which are global, across the entire dataset regardless of any distances, while others are tailored at detecting local clusters. Both of these views (local and global) are obtained separately by each of the algorithms. While from an algebraic point of view, none of both representations can claim to be the true one, it is vital that domain scientists are presented both views, enabling them to inspect and decide which of the representations is closest to the domain specific reality. We propose in this work a framework which is capable to detect locally dense arbitrarily oriented subspace clusters which are embedded within a global one. We also first introduce definitions of locally and globally arbitrarily oriented subspace clusters. Our experiments illustrate that this approach has no significant impact on the cluster quality nor on the runtime performance, and enables scientists to be no longer limited exclusively to either of the local or global views.