SpEx: A Spectral Approach to Explainable Clustering

TL;DR

This paper introduces a spectral graph partitioning method for explainable clustering that can fit explanation trees to any clustering or dataset, offering a flexible and general approach.

Contribution

It proposes a novel spectral approach to explainable clustering, enabling fitting explanation trees to arbitrary clusterings or datasets, and unifies prior algorithms under a graph partitioning framework.

Findings

Favorable performance compared to baselines on multiple datasets

Flexible method applicable to any clustering or dataset

Unifies previous algorithms within a spectral graph framework

Abstract

Explainable clustering by axis-aligned decision trees was introduced by Moshkovitz et al. (2020) and has gained considerable interest. Prior work has focused on minimizing the price of explainability for specific clustering objectives, lacking a general method to fit an explanation tree to any given clustering, without restrictions. In this work, we propose a new and generic approach to explainable clustering, based on spectral graph partitioning. With it, we design an explainable clustering algorithm that can fit an explanation tree to any given non-explainable clustering, or directly to the dataset itself. Moreover, we show that prior algorithms can also be interpreted as graph partitioning, through a generalized framework due to Trevisan (2013) wherein cuts are optimized in two graphs simultaneously. Our experiments show the favorable performance of our method compared to baselines on a range of datasets.