Benefiting from the effective exploration of the valuable topological pair-wise relationship of data points across multiple views, multi-view subspace clustering (MVSC) has received increasing attention in recent years. However, we observe that existing MVSC approaches still suffer from two limitations that need to be further improved to enhance the clustering effectiveness. Firstly, previous MVSC approaches mainly prioritize extracting multi-view consistency, often neglecting the cross-view discrepancy that may arise from noise, outliers, and view-inherent properties. Secondly, existing techniques are constrained by their reliance on pair-wise sample correlation and pair-wise view correlation, failing to capture the high-order correlations that are enclosed within multiple views. To address these issues, we propose a novel MVSC framework via joiNt crOss-view discrepancy discOvery anD high-order correLation dEtection (NOODLE), seeking an informative target subspace representation compatible across multiple features to facilitate the downstream clustering task. Specifically, we first exploit the self-representation mechanism to learn multiple view-specific affinity matrices, which are further decomposed into cohesive factors and incongruous factors to fit the multi-view consistency and discrepancy, respectively. Additionally, an explicit cross-view sparse regularization is applied to incoherent parts, ensuring the consistency and discrepancy to be precisely separated from the initial subspace representations. Meanwhile, the multiple cohesive parts are stacked into a three-dimensional tensor associated with a tensor-Singular Value Decomposition (t-SVD) based weighted tensor nuclear norm constraint, enabling effective detection of the high-order correlations implicit in multi-view data. Our proposed method outperforms state-of-the-art methods for multi-view clustering on six benchmark datasets, demonstrating its effectiveness.

受益于对跨多个视图的数据点有价值的拓扑成对关系的有效探索，多视图子空间聚类（MVSC）近年来受到越来越多的关注。然而，我们观察到现有的 MVSC 方法仍然存在两个局限性，需要进一步改进以提高聚类有效性。首先，以前的 MVSC 方法主要优先考虑提取多视图一致性，常常忽略可能由噪声、异常值和视图固有属性引起的跨视图差异。其次，现有技术受到对成对样本相关性和成对视图相关性的依赖的限制，无法捕获多个视图中包含的高阶相关性。为了解决这些问题，我们提出了一种新颖的 MVSC 框架，通过连接Ntcr O ss -viewdiscrepancydiscOvery和D高阶相关检测（NOODLE），寻求跨多个特征兼容的信息丰富的目标子空间表示促进下游聚类任务。具体来说，我们首先利用自我表示机制来学习多个特定于视图的亲和力矩阵，该矩阵被进一步分解为内聚因素和不协调因素，以分别适应多视图一致性和差异。此外，显式的跨视图稀疏正则化应用于不相干的部分，确保一致性和差异与初始子空间表示精确分离。同时，多个内聚部分堆叠成一个三维张量，与基于张量奇异值分解（t-SVD）的加权张量核范数约束相关联，从而能够有效检测多视图数据中隐含的高阶相关性。我们提出的方法在六个基准数据集上优于最先进的多视图聚类方法，证明了其有效性。