Abstract Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance. This paper proposes a graph learning framework to preserve both the local and global structure of data. Specifically, our method uses the self-expressiveness of samples to capture the global structure and adaptive neighbor approach to respect the local structure. Furthermore, most existing graph-based methods conduct clustering and semi-supervised classification on the graph learned from the original data matrix, which doesn’t have explicit cluster structure, thus they might not achieve the optimal performance. By considering rank constraint, the achieved graph will have exactly c connected components if there are c clusters or classes. As a byproduct of this, graph learning and label inference are jointly and iteratively implemented in a principled way. Theoretically, we show that our model is equivalent to a combination of kernel k-means and k-means methods under certain condition. Extensive experiments on clustering and semi-supervised classification demonstrate that the proposed method outperforms other state-of-the-art methods.

中文翻译：

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用于聚类和半监督分类的结构化图学习

摘要 在过去的十年中，图在对各种问题中的结构和交互进行建模方面变得越来越流行。基于图的聚类和半监督分类技术已经显示出令人印象深刻的性能。本文提出了一个图学习框架来保留数据的局部和全局结构。具体来说，我们的方法使用样本的自我表达来捕捉全局结构和自适应邻居方法来尊重局部结构。此外，现有的大多数基于图的方法对从原始数据矩阵中学习到的图进行聚类和半监督分类，没有明确的聚类结构，因此可能无法达到最佳性能。通过考虑秩约束，如果有 c 个集群或类，则所实现的图将恰好具有 c 个连接组件。作为其副产品，图学习和标签推理以一种有原则的方式联合和迭代实施。从理论上讲，我们证明了我们的模型在一定条件下等效于核 k-means 和 k-means 方法的组合。对聚类和半监督分类的大量实验表明，所提出的方法优于其他最先进的方法。