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Deep Basis Non-Negative Matrix Factorization with Multi-Centroid Contrastive Learning
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DOI：10.3390/math14091452.png)
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Abstract
En 中文
Non-negative Matrix Factorization (NMF) is a fundamental technique in unsupervised learning for data representation and clustering tasks. Although deep NMF methods have been developed to uncover hierarchical latent features, many existing approaches primarily rely on coefficient-matrix-based decomposition or single-centroid representations. This often limits the integration of intra-class structural features during deep decomposition, resulting in ambiguous and incomplete local feature representations. Moreover, these frameworks often exhibit feature blurring and inadequate discriminability across hierarchical levels. This paper introduces a novel Deep Basis Non-negative Matrix Factorization with Multi-Centroid Contrastive Learning (DBMCNMF) algorithm that addresses these limitations through innovative architectural design. The proposed method integrates multi-centroid representation learning with contrastive regularization constraints within a deep basis matrix factorization framework. The algorithm uses Gaussian similarity measures to establish attractive and repulsive regularization terms that preserve manifold topology while promoting discriminative clustering. DBMCNMF uses multiple centroids instead of single-centroid methods to comprehensively cover complex data distributions and capture local geometric structures that are typically inaccessible to conventional methods. The proposed model is evaluated on several benchmark image datasets. The results indicate that DBMCNMF consistently outperforms traditional single-centroid methods by achieving higher clustering accuracy and preserving the underlying manifold structure more effectively.
Keywords:
Non-negative Matrix Factorization (NMF)
deep matrix factorization (DMF)
contrastive learning
multi-centroid clustering