Clustering by latent dimensions
This provides a new clustering approach for researchers analyzing complex datasets where local dimensionality varies, though it appears incremental in extending existing dimension estimation techniques.
The paper tackles the problem of clustering data points based on local dimensionality, introducing dimensional clustering that uses pointwise dimension estimated via nearest neighbor distances. The method is demonstrated on dynamical systems, images, and human movements, showing applicability across diverse datasets.
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em 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 $n^{\text{th}}$ nearest neighbor. We demonstrate the applicability of our technique to the analysis of dynamical systems, images, and complex human movements.