Subspace clustering aims at discovering the intrinsic structure of data in unsupervised fashion. As ever in most of approaches, an affinity matrix is constructed by learning from original data or the corresponding hand-crafted feature with some constraints on the self-expressive matrix (SEM), which is then followed by spectral clustering algorithm. Based on successful applications of deep technologies, it has become popular to simultaneously accomplish deep feature and self-representation learning for subspace clustering. However, deep feature and SEM in previous deep methods are lack of precise constraints, which is sub-optimal to conform with the linear subspace model. To address this, we propose an approach, namely sparse and low-rank regularized deep subspace clustering (SLR-DSC). In the proposed SLR-DSC, an end-to-end framework is proposed by introducing sparse and low-rank constraints on deep feature and SEM respectively. The sparse deep feature and low-rank regularized SEM implemented via fully-connected layers are encouraged to facilitate a more informative affinity matrix. In order to solve the nuclear norm minimization problem, a sub-gradient computation strategy is utilized to cater to the chain rule. Experiments on the data sets demonstrate that our method significantly outperforms the competitive unsupervised subspace clustering approaches.

子空间聚类旨在以无监督的方式发现数据的固有结构。与大多数方法一样，通过从原始数据或相应的手工特征中学习（对自表达矩阵（SEM）有所约束）来构造亲和力矩阵，然后再进行光谱聚类算法。基于深层技术的成功应用，同时完成用于子空间聚类的深层特征和自表示学习变得流行。但是，以前的深度方法中的深度特征和SEM缺乏精确的约束，因此与线性子空间模型相符的次优。为了解决这个问题，我们提出了一种方法，即稀疏和低秩正则化深度子空间聚类（SLR-DSC）。在拟议的SLR-DSC中，通过在深度特征和扫描电镜上分别引入稀疏约束和低秩约束，提出了端到端框架。鼓励通过完全连接的层实现稀疏的深度特征和低等级的正则化SEM，以促进信息量更大的亲和力矩阵。为了解决核规范最小化问题，采用次梯度计算策略来满足链式规则。在数据集上进行的实验表明，我们的方法明显优于竞争性无监督子空间聚类方法。次梯度计算策略用于迎合链式规则。在数据集上进行的实验表明，我们的方法明显优于竞争性无监督子空间聚类方法。次梯度计算策略用于迎合链式规则。在数据集上进行的实验表明，我们的方法明显优于竞争性无监督子空间聚类方法。