Khatri-Rao Clustering for Data Summarization

2026-02-17

AI Summary

This work addresses the challenge of balancing conciseness and accuracy in centroid-based clustering when the number of clusters is large. To this end, we propose a novel Khatri-Rao clustering paradigm that, for the first time, incorporates the Khatri-Rao structure into clustering by assuming cluster centroids are generated through tensor-product interactions among multiple compact prototype sets. This formulation yields a more compact yet accurate data summary. We develop both a Khatri-Rao k-Means algorithm and a deep clustering framework that jointly leverage representation learning and tensor decomposition principles. Extensive experiments demonstrate that our approach significantly reduces summary size while maintaining or even improving clustering accuracy, outperforming standard k-Means and existing deep clustering methods.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Data Compression
• Natural Language Processing: Summarization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

As datasets continue to grow in size and complexity, finding succinct yet accurate data summaries poses a key challenge. Centroid-based clustering, a widely adopted approach to address this challenge, finds informative summaries of datasets in terms of few prototypes, each representing a cluster in the data. Despite their wide adoption, the resulting data summaries often contain redundancies, limiting their effectiveness particularly in datasets characterized by a large number of underlying clusters. To overcome this limitation, we introduce the Khatri-Rao clustering paradigm that extends traditional centroid-based clustering to produce more succinct but equally accurate data summaries by postulating that centroids arise from the interaction of two or more succinct sets of protocentroids. We study two central approaches to centroid-based clustering, namely the well-established k-Means algorithm and the increasingly popular topic of deep clustering, under the lens of the Khatri-Rao paradigm. To this end, we introduce the Khatri-Rao k-Means algorithm and the Khatri-Rao deep clustering framework. Extensive experiments show that Khatri-Rao k-Means can strike a more favorable trade-off between succinctness and accuracy in data summarization than standard k-Means. Leveraging representation learning, the Khatri-Rao deep clustering framework offers even greater benefits, reducing even more the size of data summaries given by deep clustering while preserving their accuracy.

Problem

• data summarization
• centroid-based clustering
• redundancy
• Khatri-Rao clustering
• succinctness

Innovation

• Khatri-Rao clustering
• data summarization
• protocentroids
• k-Means
• deep clustering