The practical visual data do not necessarily lie in linear subspaces, so deep convolutional subspace clustering network is proposed to segment the practical visual data into multiple categories accurately. The original convolutional subspace clustering network contains the stacked convolutional encoder module, the stacked convolutional decoder module and the self-expression module. We firstly alter the self-expression module, i.e., add a new k-block diagonal regularizer to the weights of the self-expression module. It means that the \(\ell _1\) or \(\ell _2\) regularizer is abandoned. The k-block diagonal regularizer is proposed to directly pursue the block diagonal matrix, so introducing this regularizer to the self-expression module will make the learned representation matrix conform with the block diagonal matrix better. Secondly, we add a new spectral clustering module to this convolutional subspace clustering network, in which the spectral clustering result is used to supervise the learning of the representation matrix. This subspace structured regularizer is introduced to the spectral clustering module, which further refines the learned representation matrix. Experimental results on three challenging datasets have demonstrated that the proposed deep learning based subspace clustering method achieves the better clustering effect over the state-of-the-arts.

实际视觉数据不一定位于线性子空间中，因此提出了深度卷积子空间聚类网络来将实际视觉数据准确地分割成多个类别。原始卷积子空间聚类网络包含堆叠卷积编码器模块、堆叠卷积解码器模块和自我表达模块。我们首先改变自我表达模块，即在自我表达模块的权重上添加一个新的k块对角线正则化器。这意味着\(\ell _1\)或\(\ell _2\)正则化器被放弃。该ķ-block diagonal regularizer 被提出来直接追求block对角矩阵，所以在self-expression模块中引入这个regularizer会使学习到的表示矩阵更好地符合block对角矩阵。其次，我们在这个卷积子空间聚类网络中添加了一个新的谱聚类模块，其中谱聚类结果用于监督表征矩阵的学习。这种子空间结构的正则化器被引入到谱聚类模块中，进一步细化了学习到的表示矩阵。在三个具有挑战性的数据集上的实验结果表明，所提出的基于深度学习的子空间聚类方法比现有技术实现了更好的聚类效果。