摘要：

随着多媒体和数据采集技术的快速发展, 多视角数据越来越常见。相比于单视角数据, 多视角数据可以提供更丰富的描述信息, 提高样本结构信息的挖掘效率。针对多视角子空间聚类任务, 提出基于双跨视角相关性检测的多视角子空间聚类算法。首先, 考虑噪声干扰和高维数据冗余性对多视角聚类效果的影响, 采用线性投影变换来获得原始数据的低维低冗余潜在表示, 并利用其进行自表示学习获得准确的子空间表示。其次, 为了充分挖掘多视角数据的互补性信息, 对潜在特征表示和子空间表示进行跨视角相关性关系检测, 具体为: 将多视角潜在特征视为低层次表示, 利用希尔伯特-施密特独立性准则(HSIC)探索和保留多视角特征的多样性属性; 对于包含一致的高层次聚类结构信息的多视角子空间表示, 引入低秩张量约束充分捕获跨视角高阶相关性关系和互补性信息。最后, 采用增广拉格朗日乘子交替方向极小化算法求解模型的优化问题。在真实数据上的实验结果表明, 与对比方法中的次优方法相比, 该算法在6个基准数据集上的聚类准确率分别提高了3.00、3.60、1.90、2.00、7.50和1.90百分点, 该结果验证了该算法的优越性和有效性。

关键词: 多视角子空间聚类, 双跨视角相关性检测, 低秩张量学习, 张量核范数, 一致性, 互补性

Abstract:

With the rapid advancement of multimedia and data collection technologies, multi-view data is becoming increasingly prevalent. Unlike single-view data, multi-view data offers richer descriptive information and enhances the efficiency of structural information mining. In response to the multi-view clustering challenge, this study proposes a multi-view subspace clustering algorithm based on dual cross-view correlation detection. Considering the effects of noise disturbance and high-dimensional data redundancy on multi-view clustering, the proposed algorithm employs linear projection transformation to derive a potential low-redundancy representation of the original data. The accurate view-specific subspace representation is learned from the latent feature representation based on the self-representation property. To fully leverage the complementary information present in multi-view data, the proposed algorithm simultaneously detects cross-view correlations in both feature and subspace representations. Specifically, latent features are treated as low-level representations, enabling their diversity to be explored and retained by the Hilbert-Schmidt Independence Criterion (HSIC). For high-level clustering structures, the proposed algorithm ensures consistency among multi-view subspace representations by imposing a low-rank tensor constraint, which facilitates the exploration of high-order correlations and complementary information. The study employs an alternating direction minimization strategy with an augmented Lagrange multiplier to address the optimization problem. Experimental results on real datasets demonstrate that the proposed algorithm significantly outperforms suboptimal methods, achieving improvements in clustering accuracy of 3.00, 3.60, 1.90, 2.00, 7.50, and 1.90 percentage points across six benchmark datasets, respectively. These results validate the superiority and effectiveness of the algorithm.

Key words: multi-view subspace clustering, dual cross-view correlation detection, low-rank tensor learning, tensor nuclear norm, consistency, complementarity