Explainable Graph Spectral Clustering of Text Documents

TL;DR

This paper introduces a method to explain spectral clustering results on text documents by linking spectral embeddings to term vector space, enhancing interpretability of clustering outcomes.

Contribution

It proposes a novel $K$-embedding that approximates Laplacian spectral embedding and connects it to textual content, with theoretical and experimental validation.

Findings

$K$-embedding closely approximates Laplacian embedding under certain conditions

The approach effectively bridges spectral clustering results with document content

Experimental results confirm the approximation quality in various scenarios

Abstract

Spectral clustering methods are known for their ability to represent clusters of diverse shapes, densities etc. However, results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to embedding in the spectral space which has no obvious relation to document contents. Therefore there is an urgent need to elaborate methods for explaining the outcome of the clustering. This paper presents a contribution towards this goal. We present a proposal of explanation of results of combinatorial Laplacian based graph spectral clustering. It is based on showing (approximate) equivalence of combinatorial Laplacian embedding, $K$-embedding (proposed in this paper) and term vector space embedding. Hence a bridge is constructed between the textual contents and the clustering results. We provide theoretical background for this approach. We performed experimental study showing that $K$-embedding approximates well Laplacian embedding under favourable block matrix conditions and show that approximation is good enough under other conditions.