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<p>In recent years, deep matrix factorization (DMF) has garnered significant attention for its effectiveness in various artificial intelligence applications. However, conventional DMF frameworks face two key limitations: (1) an inability to effectively uncover complex latent patterns in high-dimensional data spaces, and (2) insufficient preservation of data geometric structures. These limitations lead to suboptimal solution smoothness and algorithmic instability. To address these challenges, we propose a novel variant of deep nonnegative matrix factorization called deep hypergraph regularized <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44443_2025_321_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> smooth semi-nonnegative matrix factorization (DHGLpSNMF). This method incorporates hypergraph-based geometric regularization to enhance solution stability and structural coherence. We introduce an efficient optimization framework using forward-backward splitting operators to handle the multivariate objective function. Theoretical analysis rigorously proves the convergence of our method to critical points under specified conditions. Extensive experiments on four real-world benchmark datasets demonstrate the superiority of our approach. Our method achieves statistically significant improvements over six established baselines across ACC, NMI and ARI benchmarks. These results demonstrate the method’s efficacy in enhancing solution stability and structural coherence, thus providing valuable insights for ongoing research.</p>

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Deep hypergraph regularized \(L_{p}\) smooth semi-nonnegative matrix factorization for hierarchical clustering analysis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月6日

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  • Shunli Li,
  • Ling Wang,
  • Mingjun Bai

摘要

In recent years, deep matrix factorization (DMF) has garnered significant attention for its effectiveness in various artificial intelligence applications. However, conventional DMF frameworks face two key limitations: (1) an inability to effectively uncover complex latent patterns in high-dimensional data spaces, and (2) insufficient preservation of data geometric structures. These limitations lead to suboptimal solution smoothness and algorithmic instability. To address these challenges, we propose a novel variant of deep nonnegative matrix factorization called deep hypergraph regularized \(L_{p}\) L p smooth semi-nonnegative matrix factorization (DHGLpSNMF). This method incorporates hypergraph-based geometric regularization to enhance solution stability and structural coherence. We introduce an efficient optimization framework using forward-backward splitting operators to handle the multivariate objective function. Theoretical analysis rigorously proves the convergence of our method to critical points under specified conditions. Extensive experiments on four real-world benchmark datasets demonstrate the superiority of our approach. Our method achieves statistically significant improvements over six established baselines across ACC, NMI and ARI benchmarks. These results demonstrate the method’s efficacy in enhancing solution stability and structural coherence, thus providing valuable insights for ongoing research.