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Unified Multi-view Data Clustering: Simultaneous Learning of Consensus Coefficient Matrix and Similarity Graph

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Abstract

Integrating data from multiple sources or views has become increasingly common in data analysis, particularly in fields like healthcare, finance, and social sciences. However, clustering such multi-view data poses unique challenges due to the heterogeneity and complexity of the data sources. Traditional clustering methods are often unable to effectively leverage the information from different views, leading to suboptimal clustering results. To address this challenge, multi-view clustering techniques have been developed, aiming to integrate information from multiple views to improve clustering performance. These techniques typically involve learning a similarity matrix for each view and then combining these matrices to form a consensus similarity matrix, which is subsequently used for clustering. However, existing approaches often suffer from limitations such as the need for manual tuning of parameters and the inability to effectively capture the underlying structure of the data. In this paper, we propose a novel approach for multi-view clustering that addresses these limitations by jointly learning the consensus coefficient matrix and similarity graph. Unlike existing methods that follow a sequential approach of first learning the coefficient matrix and then constructing the similarity graph, our approach simultaneously learns both matrices, ensuring a more regularized consensus graph. Additionally, our method automatically adjusts the weight of each view, eliminating the need for manual parameter tuning. Our approach involves several key steps. First, we formulate an optimization problem that jointly optimizes the consensus coefficient matrix, unified spectral projection matrix, coefficient matrix, and soft cluster assignment matrix. We then propose an efficient algorithm to solve this optimization problem, which involves iteratively updating the matrices until convergence. To learn the consensus coefficient matrix and similarity graph, we leverage techniques from matrix factorization and graph-based learning. Specifically, we use a self-representation technique to learn the coefficient matrix (regularization graPh) and a graph regularization technique to learn the similarity graph. By jointly optimizing these matrices, we ensure that the resulting consensus graph is more regularized and better captures the underlying structure of the data. We evaluate our approach on several public image datasets, comparing it against state-of-the-art multi-view clustering methods. Our experimental results demonstrate that our approach consistently outperforms existing methods in terms of clustering accuracy and robustness. Additionally, we conduct sensitivity analysis to evaluate the impact of different hyperparameters on the clustering performance. We present a novel approach for multi-view data clustering that jointly learns the consensus coefficient matrix and similarity graph. By simultaneously optimizing these matrices, our approach achieves better clustering performance compared to existing methods. Our results demonstrate the effectiveness and robustness of our approach across different datasets, highlighting its potential for real-world applications in various domains.

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Data Availability

No datasets were generated or analyzed during the current study.

Notes

  1. https://cam-orl.co.uk/facedatabase.html

  2. http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php

  3. https://www.researchgate.net/publication/335857675

  4. https://archive.ics.uci.edu/ml/datasets/Multiple+Features

  5. http://yann.lecun.com/exdb/MNIST/

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Authors and Affiliations

  1. University of the Basque Country UPV/EHU, San Sebastian, Spain

    F. Dornaika, S. El Hajjar & N. Barrena

  2. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    F. Dornaika

  3. Léonard de Vinci Pôle Universitaire, Research Center, 92 916, Paris La Défense, France

    J. Charafeddine

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  1. F. Dornaika
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  3. J. Charafeddine
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Contributions

S. H. and J. C. was involved in data curation, software development, and executing the experiments. F. D. contributed to the methodology, investigation, and supervision. J. C. and N.B. participated in the review of the paper. All authors contributed to writing the paper.

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Correspondence to F. Dornaika.

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Dornaika, F., El Hajjar, S., Charafeddine, J. et al. Unified Multi-view Data Clustering: Simultaneous Learning of Consensus Coefficient Matrix and Similarity Graph. Cogn Comput 17, 38 (2025). https://doi.org/10.1007/s12559-024-10392-z

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