Clustering by latent dimensions
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This paper introduces a new clustering technique, called dimensional clustering, which clusters each data point by its latent pointwise dimension, which is a measure of the dimensionality of the data set local to that point. Pointwise dimension is invariant under a broad class of transformations. As a result, dimensional clustering can be usefully applied to a wide range of datasets. Concretely, we present a statistical model which estimates the pointwise dimension of a dataset around the points in that dataset using the distance of each point from its n^th nearest neighbor. We demonstrate the applicability of our technique to the analysis of dynamical systems, images, and complex human movements.
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