Since data are collected from a range of sources via different techniques, multiview clustering has become an emerging technique for unsupervised data classification. However, most existing soft multiview clustering methods only consider the pairwise correlations and ignore high-order correlations among multiple views. To integrate more comprehensive information from different views, this article innovates a fuzzy clustering model using the low-rank tensor to address the multiview data clustering problem. Our method first conducts a standard fuzzy clustering on different views of the data separately. Then, the obtained soft partition results are aggregated as the new data to be handled by a Kullback-Leibler (KL) divergence-based fuzzy model with low-rank tensor constraints. The KL divergence function, which replaces the traditional minimized Euclidean distance, can enhance the robustness of the model. More importantly, we formulate fuzzy partition matrices of different views as a third-order tensor. So, a low-rank tensor is introduced as a norm constraint in the KL divergence-based fuzzy clustering to obtain dexterously high-order correlations of different views. The minimization of the final model is convex and we present an efficient augmented Lagrangian alternating direction method to handle this problem. Specially, the global membership is derived by using tensor factorization. The efficiency and superiority of the proposed approach are demonstrated by the comparison with state-of-the-art multiview clustering algorithms on many multiple-view data sets.

中文翻译：

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多视图数据的低秩张量正则化模糊聚类


由于数据是通过不同的技术从一系列来源收集的，因此多视图聚类已成为无监督数据分类的新兴技术。然而，大多数现有的软多视图聚类方法仅考虑成对相关性，而忽略了多个视图之间的高阶相关性。为了整合来自不同视图的更全面的信息，本文创新了一种使用低秩张量的模糊聚类模型来解决多视图数据聚类问题。我们的方法首先分别对数据的不同视图进行标准模糊聚类。然后，将获得的软划分结果聚合为新数据，由具有低秩张量约束的基于散度的 Kullback-Leibler (KL) 模糊模型处理。 KL散度函数代替了传统的最小化欧氏距离，可以增强模型的鲁棒性。更重要的是，我们将不同视图的模糊划分矩阵表示为三阶张量。因此，在基于KL散度的模糊聚类中引入低秩张量作为范数约束，以灵活地获得不同视图的高阶相关性。最终模型的最小化是凸的，我们提出了一种有效的增强拉格朗日交替方向方法来处理这个问题。特别地，全局隶属度是通过使用张量分解得出的。通过与许多多视图数据集上最先进的多视图聚类算法进行比较，证明了所提出方法的效率和优越性。