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

Area of Science:

• Data Science
• Applied Mathematics
• Computer Science

Background:

• High-dimensional data analysis is crucial across applied sciences.
• Dimensionality reduction techniques often fail to capture global data structure.
• Clustering methods group data but lack global organizational insights.

Purpose of the Study:

• To introduce a novel data structure, ClusterGraph, to represent the global organization of clusters.
• To provide a method that complements existing clustering algorithms.
• To enable better understanding and visualization of high-dimensional data structures.

Main Methods:

• Leveraging concepts from Topological Data Analysis.
• Developing the ClusterGraph data structure to layer on clustering algorithm outputs.
• Defining measures to assess the quality and utility of the ClusterGraph representation.

Main Results:

• ClusterGraph successfully captures the global layout of clusters derived from any clustering algorithm.
• The proposed measures effectively evaluate the quality of the ClusterGraph representation.
• ClusterGraph facilitates synergistic use with exploratory data analysis techniques.

Conclusions:

• ClusterGraph offers a valuable addition to clustering, providing global data organization insights.
• The structure can be simplified and visualized for enhanced exploratory data analysis.
• This approach improves the understanding of complex, high-dimensional datasets.