Fast multiscale clustering and manifold identification

We present a novel multiscale clustering algorithm inspired by algebraic multigrid techniques. Our method begins with assembling data points according to local similarities. It uses an aggregation process to obtain reliable scale-dependent global properties, which arise from the local similarities. As the aggregation process proceeds, these global properties affect the formation of coherent clusters. The global features that can be utilized are for example density, shape, intrinsic dimensionality and orientation. The last three features are a part of the manifold identification process which is performed in parallel to the clustering process. The algorithm detects clusters that are distinguished by their multiscale nature, separates between clusters with different densities, and identifies and resolves intersections between clusters. The algorithm is tested on synthetic and real data sets, its running time complexity is linear in the size of the data set.