Clustering by latent dimensions

2018/05/28 by Shohei Hidaka, Hidaka, Shohei, Neeraj Kashyap +1
Computer Science · Mathematics · #Advanced Vision and Imaging #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Morphological variations and asymmetry #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1805.10759

openalex publication_date 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^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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