In this article, we focus on utilizing the idea of co-clustering algorithms to address the subspace clustering problem. In recent years, co-clustering methods have been developed greatly with many important applications, such as document clustering and gene expression analysis. Different from the traditional graph-based methods, co-clustering can utilize the bipartite graph to extract the duality relationship between samples and features. It means that the bipartite graph can obtain more information than other traditional graph methods. Therefore, we proposed a novel method to handle the subspace clustering problem by combining dictionary learning with a bipartite graph under the constraint of the (normalized) Laplacian rank. Besides, to avoid the effect of redundant information hiding in the data, the original data matrix is not used as the static dictionary in our model. By updating the dictionary matrix under the sparse constraint, we can obtain a better coefficient matrix to construct the bipartite graph. Based on Theorem 2 and Lemma 1, we further speed up our algorithm. Experimental results on both synthetic and benchmark datasets demonstrate the superior effectiveness and stability of our model.

中文翻译：

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通过约束拉普拉斯秩学习子空间聚类的最佳二分图


在本文中，我们重点讨论利用共聚类算法的思想来解决子空间聚类问题。近年来，共聚类方法得到了很大的发展，具有许多重要的应用，例如文档聚类和基因表达分析。与传统的基于图的方法不同，共聚类可以利用二分图来提取样本和特征之间的对偶关系。这意味着二分图比其他传统图方法可以获得更多的信息。因此，我们提出了一种在（归一化）拉普拉斯秩约束下将字典学习与二部图相结合来处理子空间聚类问题的新方法。此外，为了避免数据中隐藏冗余信息的影响，我们的模型中不使用原始数据矩阵作为静态字典。通过在稀疏约束下更新字典矩阵，我们可以获得更好的系数矩阵来构造二分图。基于定理2和引理1，我们进一步加速了我们的算法。合成数据集和基准数据集的实验结果证明了我们模型的卓越有效性和稳定性。