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Explainable Graph Spectral Clustering of text documents.

Bartłomiej Starosta1, Mieczysław A Kłopotek1, Sławomir T Wierzchoń1

  • 1Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland.

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Summary

This study bridges graph spectral clustering (GSC) with document content, enabling explainable AI for text document analysis. We link spectral embeddings to term vector spaces for interpretable clustering results.

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Area of Science:

  • Data Science
  • Machine Learning
  • Natural Language Processing

Background:

  • Spectral clustering methods excel at identifying complex clusters but lack interpretability, especially in text document analysis.
  • The spectral space embedding in graph spectral clustering (GSC) often lacks a clear connection to the original document content, hindering user understanding.
  • Explaining clustering outcomes is crucial for practical applications, particularly when dealing with high-dimensional text data.

Purpose of the Study:

  • To develop a theoretical framework connecting graph spectral clustering results to document content.
  • To propose methods for explaining cluster membership in graph spectral clustering applied to text documents.
  • To establish a link between spectral embeddings and term vector spaces for enhanced interpretability.

Main Methods:

  • Constructing a theoretical bridge between graph spectral clustering (GSC) and document content using cosine similarity in tf or tfidf representations.
  • Proposing K-embedding and [Formula: see text]-embedding as methods to link spectral space to term vector space.
  • Analyzing combinatorial and normalized Laplacian based graph spectral clustering.

Main Results:

  • Demonstrated approximate equivalence between combinatorial Laplacian embedding and K-embedding with term vector space embedding.
  • Showcased good approximation of K-embedding for Laplacian embedding under various conditions.
  • Established perfect equivalence between normalized Laplacian embedding and [Formula: see text]-embedding with (weighted) term vector space embedding.

Conclusions:

  • A theoretical bridge is successfully constructed between textual content and clustering results for both combinatorial and normalized Laplacian based GSC.
  • The proposed K-embedding and [Formula: see text]-embedding provide interpretable links to document content.
  • This work enhances the explainability of spectral clustering for text document analysis.