ClusterGraph: a new tool for visualization and compression of multidimensional data

TL;DR

ClusterGraph introduces a topological data analysis-based method to enhance clustering outputs, revealing global data structures and improving visualization and understanding of high-dimensional datasets.

Contribution

The paper presents ClusterGraph, a novel topological approach that adds a global structure layer to clustering results, aiding visualization and analysis of high-dimensional data.

Findings

Provides a new topological data analysis layer for clustering outputs

Enhances visualization of global data structures

Offers measures to evaluate the quality of the representation

Abstract

Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered data into lower dimensional space. This family of methods, while preserving local structures and features, often misses the global structure of the dataset. Clustering techniques are another class of methods operating on the data in the ambient space. They group together points that are similar according to a fixed similarity criteria, however unlike dimensionality reduction techniques, they do not provide information about the global organization of the data. Leveraging ideas from Topological Data Analysis, in this paper we provide an additional layer on the output of any clustering algorithm. Such data structure, ClusterGraph, provides information about the global layout of clusters, obtained from the considered clustering algorithm. Appropriate measures are provided to assess the quality and usefulness of the obtained representation. Subsequently the ClusterGraph, possibly with an appropriate structure--preserving simplification, can be visualized and used in synergy with state of the art exploratory data analysis techniques.