基于双线性谱惩罚与结构对齐的不完备多视图聚类方法

    An Incomplete Multiview Clustering Method Based on Bilinear Spectral Penalty and Structural Alignment

    • 摘要: 多视图聚类在实际应用中常面临视图缺失的问题。现有聚类方法往往难以兼顾低秩图结构的全局一致性与计算开销。此外,在处理高缺失率数据时,因为忽视了视图间公共样本的几何对齐,现有方法对一致性信息的利用往往不足。为了解决上述问题,本文提出了一种基于双线性谱惩罚与结构对齐的不完备多视图聚类方法(Incomplete Multiview Clustering Method Based on Bilinear Spectral Penalty and Structural Alignment, SPIMC-SA)。首先,该算法在自适应图学习框架下,引入双线性矩阵分解策略替代传统的核范数约束,将低秩约束的求解从奇异值分解转化为小规模因子矩阵的优化,提升了低秩约束子问题求解效率;其次,引入流形正则化项以挖掘数据内部的局部几何结构,弥补了矩阵分解方法对局部拓扑保持的不足;再次,设计了显式的跨视图结构对齐机制,利用公共样本作为锚点,强制不同视图的自表示系数在子空间层面保持一致,从而有效校准视图间的分布偏差;最后,设计了一个基于交替方向乘子法的统一优化框架,对所有变量进行联合求解。实验表明,本文方法在多个基准数据集上取得了优于现有方法的聚类性能,例如在BBCSport数据集10%和50%缺失率下,本文方法准确率分别达到93.25%和78.62%。本文方法为不完备多视图聚类提高求解效率与聚类鲁棒性提供了一种有效途径。

       

      Abstract: Multiview clustering frequently encounters missing views in practical applications, where existing methods struggle to balance the global consistency of low-rank graph structures with computational efficiency, and tend to underutilize consensus information under high missing rates due to neglecting geometric alignment among common samples across views. To address these issues, an incomplete multiview clustering method based on bilinear spectral penalty and structural alignment (SPIMC-SA) is proposed. Within an adaptive graph learning framework, a bilinear matrix factorization strategy replaces traditional nuclear norm constraints, transforming the low-rank subproblem from singular value decomposition into the optimization of smaller factor matrices to improve efficiency; a manifold regularization term then captures local geometric structure to compensate for the limited topology preservation of matrix factorization; and an explicit cross-view structural alignment mechanism uses common samples as anchors to enforce consistency of self-representation coefficients at the subspace level, calibrating distribution deviations between views. All variables are jointly solved under a unified ADMM framework. Experiments on multiple benchmark datasets show that SPIMC-SA achieves superior clustering performance with stronger robustness under high missing rates; for example, on BBCSport it achieves 93.25% and 78.62% accuracy at 10% and 50% missing rates respectively, providing an effective approach that balances solving efficiency and clustering robustness for incomplete multiview clustering under missing-data scenarios.

       

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