现有的子空间聚类方法以数据全局线性分布为前提, 利用先验约束估计未标记数据点的低维子空间, 并将其聚类到相应 组中, 对非线性结构的数据处理存在一定缺陷. 受启发于深度学习以其强大 的非线性学习表征能力在众多应用中取得巨大成功, 文章在数据表示中加入成 对约束, 并运用流形正则化理论, 采用$k$近邻构造全局相似度矩阵, 通过与自 编码器的联合学习, 提出基于流形正则化与成对约束的深度半监督谱聚类算法(MPAE). 该算 法一方面在学习数据的低维表示时同时保留数据的可重构性和局部流形结构的全局特征, 另 一方面将已知样本间的成对约束信息融入目标优化设计, 使学习到的低维特征更具有判别性, 这 在很大程度上提高了所得算法的聚类性能. 实验结果表明文章算法能够取得理想的聚类结果.

Existing subspace clustering methods rest on a global linear data set, which employs prior constraints to estimate underlying subspace of unlabeled data points and clusters them into corresponding groups, thus may fail in handing data with nonlinear structure. Motivated by the huge success achieved by deep learning with its powerful nonlinear representation ability in many applications, in this paper we propose a novel deep simi-supervised spectral clustering approach through joint learning with autoencoder (MPAE), which incorporates regularization of manifold learning and pairwise constraints into the structure of data representation and exploits the $k$-nearest neighbors constraint to construct the similarity matrix. On the one hand, This method preserves the reconstruction and global features of local manifold structure of the data simultaneously, and on the other hand, the pair constraint rules among known samples are integrated into the target optimization design, which makes the learned low-dimensional features more discriminant and improves the clustering performance of the algorithm. Finally, the related clustering algorithm is adopted for clustering. Extensive experiments on several datasets for subspace clustering were conducted. They demonstrated that the proposed algorithm achieves better clustering results.