In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pairwise constraints synchronously. Besides, we use the local geometry structure of input samples to complement the global low-rank prior to achieve better affinity matrix learning. The proposed model is formulated as a Laplacian graph regularized convex low-rank tensor representation problem, which is further solved with an alternative iterative algorithm. In addition, we propose to refine the affinity matrix with the augmented pairwise constraints. Comprehensive experimental results on eight commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods. The code is publicly available at https://github.com/GuanxingLu/Subspace-Clustering.

翻译：在这封信中,我们提出一种新的半监督的子空间集群方法,它能够同时增加初始监督信息,并构建一个歧视性的亲和矩阵。通过代表有限的监督信息量,作为双向制约矩阵,我们观察到集群的理想亲和矩阵与理想的双向制约矩阵具有相同的低层次结构。因此,我们把两个矩阵堆叠成一个3-D Exor,其中对促进亲和矩阵构建施加全球低层次限制,并同步增加初始对对称限制。此外,我们使用输入样本的本地几何结构来补充全球低层次输入样本,从而在进行更好的亲和矩阵学习之前实现更好的全球低级别。拟议模型是作为拉普拉克图形正统的低层锥形模型的形成,用替代的迭接算法进一步解决这个问题。此外,我们提议用强化的双向制约来改进亲和直通性矩阵。八个常用基准数据集的全面实验结果显示了我们的方法优于现状方法。该代码在 https://githu/Subxluing.com 公开提供 https://gustrubu/Subxluing.