As an effective convex relaxation of the rank minimization model, the tensor nuclear norm minimization based multi-view clustering methods have been attracting more and more interest in recent years. However, most existing clustering methods regularize each singular value equally, restricting their capability and flexibility in tackling many practical problems, where the singular values should be treated differently. To address this problem, we propose a novel weighted tensor nuclear norm minimization (WTNNM) based method for multi-view spectral clustering. Specifically, we firstly calculate a set of transition probability matrices from different views, and construct a 3-order tensor whose lateral slices are composed of probability matrices. Secondly, we learn a latent high-order transition probability matrix by using our proposed weighted tensor nuclear norm, which directly considers the prior knowledge of singular values. Finally, clustering is performed on the learned transition probability matrix, which well characterizes both the complementary information and high-order information embedded in multi-view data. An efficient optimization algorithm is designed to solve the optimal solution. Extensive experiments on five benchmarks demonstrate that our method outperforms the state-of-the-art methods.

作为秩最小化模型的有效凸松弛，基于张量核范数最小化的多视图聚类方法近年来引起了越来越多的关注。但是，大多数现有的聚类方法均等地对每个奇异值进行正则化，从而限制了它们在解决许多实际问题时的能力和灵活性，在实际问题中应区别对待奇异值。为了解决这个问题，我们提出了一种新颖的基于加权张量核规范最小化（WTNNM）的多视图谱聚类方法。具体来说，我们首先从不同的角度计算一组转移概率矩阵，然后构造一个三阶张量，其横向切片由概率矩阵组成。其次，我们通过使用我们提出的加权张量核范数来学习潜在的高阶跃迁概率矩阵，该矩阵直接考虑了奇异值的先验知识。最后，对学习的转移概率矩阵进行聚类，它很好地刻画了嵌入在多视图数据中的互补信息和高阶信息。设计了一种有效的优化算法来求解最优解。在五个基准上进行的大量实验表明，我们的方法优于最新方法。设计了一种有效的优化算法来求解最优解。在五个基准上进行的大量实验表明，我们的方法优于最新方法。设计了一种有效的优化算法来求解最优解。在五个基准上进行的大量实验表明，我们的方法优于最新方法。