Explaining Clusters Using Minimal Weighted Edge Coverage

NIMA SAFAEI

Keywords: Clustering, Explainability, Graph Theory, Minimal Edge Covering

TL;DR: A Linear Integer Programming model is proposed to create explainable clusters inspired by the graph theory's Minimal Edge Covering problem

Abstract: Current clustering techniques in unsupervised learning lack interpretability. This is primarily because clustering represents a combinatorial optimization problem that becomes exponentially complex in large-dimensional spaces. Consequently, most clustering algorithms employ intricate mathematical computations, statistical assumptions, distance approximations, and data transformations in ways that diminish their interpretability. This study introduces a Linear Integer Programming model to optimize the balance between interpretability and quality, drawing inspiration from the graph theory's Minimal Edge Covering problem. An edge cover is a set of graph edges ensuring each vertex of the graph is incident to at least one edge of the set; the challenge lies in determining the smallest set possible. By adopting this approach, data can be grouped into clusters in the form of tree-like structures, enhancing our comprehension of the clustering process. If the edges are weighted to represent dissimilarities or distances, the problem becomes the Minimum Weighted Edge Covering (MWEC) problem.

Submission Number: 66