Graph-based clustering aims to partition the data according to a similarity graph, which has shown impressive performance on various kinds of tasks. The quality of similarity graph largely determines the clustering results, but it is difficult to produce a high-quality one, especially when data contain noises and outliers. To solve this problem, we propose a robust rank constrained sparse learning (RRCSL) method in this article. The L2,1-norm is adopted into the objective function of sparse representation to learn the optimal graph with robustness. To preserve the data structure, we construct an initial graph and search the graph within its neighborhood. By incorporating a rank constraint, the learned graph can be directly used as the cluster indicator, and the final results are obtained without additional postprocessing. In addition, the proposed method cannot only be applied to single-view clustering but also extended to multiview clustering. Plenty of experiments on synthetic and real-world datasets have demonstrated the superiority and robustness of the proposed framework.

中文翻译：

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鲁棒的秩受限稀疏学习：用于单视图和多视图聚类的基于图的框架。

基于图的聚类旨在根据相似度图对数据进行分区，该相似度图在各种任务上均表现出令人印象深刻的性能。相似度图的质量在很大程度上决定了聚类结果，但是很难生成高质量的图，尤其是当数据包含噪声和异常值时。为了解决这个问题，本文提出了一种鲁棒的秩约束稀疏学习（RRCSL）方法。L2,1-范数被用于稀疏表示的目标函数中，以学习具有鲁棒性的最优图。为了保留数据结构，我们构造了一个初始图并在其邻域内搜索该图。通过合并秩约束，可以将学习到的图直接用作聚类指标，并且无需其他后处理即可获得最终结果。此外，该方法不仅可以应用于单视图聚类，而且可以扩展到多视图聚类。在合成和真实数据集上进行的大量实验证明了所提出框架的优越性和鲁棒性。