Clustering by latent dimensions

TL;DR

This paper presents a novel clustering method based on local data dimensionality, called dimensional clustering, which is invariant under transformations and applicable to diverse datasets like dynamical systems and images.

Contribution

Introduces a new clustering approach using pointwise dimension estimation, extending clustering capabilities to datasets with complex local structures.

Findings

Effective in analyzing dynamical systems

Applicable to image and movement data

Invariant under broad transformations

Abstract

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.