An Algorithm for Determining the Topological Dimensionality of Point Clusters

Abstract

The main thrust of this paper is to present a new algorithm for the analysis of structure in multivariate data point clusters from the standpoint of intrinsic (topological) dimensionality.

The method is based on the unfolding of a minimum spanning tree laid over the data, using a barycentric transformation. Visual display of the transformed data is provided by nonlinear mappings.

The methodological aspects of dimensionality analysis are briefly discussed. The algorithm and its implementation are described, and computed results are given using test data selected from previously published examples.

Index Terms

~Clustering, intrinsic dimensionality, minimum spanning tree, multidimensional scaling, nonlinear mapping, topological dimensionality.