Abstract Subspace clustering methods have been extensively studied in recent years. For 2-dimensional (2D) data, existing subspace clustering methods usually convert 2D examples to vectors, which severely damages inherent structural information and relationships of the original data. In this paper, we propose a novel subspace clustering method, named KTRR, for 2D data. The KTRR provides us with a way to learn the most representative 2D features from 2D data in learning data representation. In particular, the KTRR performs 2D feature learning and low-dimensional representation construction simultaneously, which renders the two tasks to mutually enhance each other. 2D kernel is introduced to the KTRR, which renders the KTRR to have enhanced capability of capturing nonlinear relationships from data. An efficient algorithm is developed for its optimization with provable decreasing and convergent property in objective value. Extensive experimental results confirm the effectiveness and efficiency of our method.

中文翻译：

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子空间聚类的核二维岭回归

摘要 近年来，子空间聚类方法得到了广泛的研究。对于二维（2D）数据，现有的子空间聚类方法通常将二维示例转换为向量，这严重破坏了原始数据的固有结构信息和关系。在本文中，我们提出了一种新的子空间聚类方法，名为 KTRR，用于二维数据。KTRR 为我们提供了一种在学习数据表示中从二维数据中学习最具代表性的二维特征的方法。特别是，KTRR 同时执行 2D 特征学习和低维表示构建，这使得这两个任务相互增强。KTRR 中引入了 2D 核，这使得 KTRR 具有增强的从数据中捕获非线性关系的能力。开发了一种有效的算法来优化其目标值的可证明递减和收敛特性。大量的实验结果证实了我们方法的有效性和效率。