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Spectral clustering methods are known for their ability to represent clustersof diverse shapes, densities etc. However, results of such algorithms, whenapplied e.g. to text documents, are hard to explain to the user, especially dueto embedding in the spectral space which has no obvious relation to documentcontents. Therefore there is an urgent need to elaborate methods for explainingthe outcome of the clustering. This paper presents a contribution towards thisgoal. We present a proposal of explanation of results of combinatorialLaplacian based graph spectral clustering. It is based on showing (approximate)equivalence of combinatorial Laplacian embedding, $K$-embedding (proposed inthis paper) and term vector space embedding. Hence a bridge is constructedbetween the textual contents and the clustering results. We provide theoreticalbackground for this approach. We performed experimental study showing that$K$-embedding approximates well Laplacian embedding under favourable blockmatrix conditions and show that approximation is good enough under otherconditions.

Explainable Graph Spectral Clustering of Text Documents