判别性增强的稀疏子空间聚类

稀疏关系表示(SRR)是一种性能良好的子空间聚类算法，其利用一个数据样本和所有样本间的邻域关系作为新特征来学习自表示系数，由自表示系数矩阵构建相似度矩阵并通过谱聚类得到聚类结果。同时考虑相似度矩阵的稀疏性和聚集性，在SRR算法基础上提出一个判别性增强的稀疏子空间聚类模型。对邻域关系矩阵的自表示矩阵采用平方F范数代替SSR中的核范数，降低模型求解难度，并在邻域关系矩阵的自表示矩阵中引入新的正则项，保证自表示矩阵的类间判别性和邻域关系矩阵的类内聚集性，进一步优化聚类性能。实验结果表明：与SSC、LRR、LSR、BDR-B、SRR等模型相比，该模型具有较好的聚类性能；在MNIST、USPS、ORL数据集上，聚类错误率较SRR模型分别下降9.6、14.1、3.8个百分点；在Extended Yale B数据集上，针对2、3、5、8、10类聚类问题的聚类错误率较SRR模型分别下降0.39、0.72、1.32、2.73、3.28个百分点。

Discriminant Enhanced Sparse Subspace Clustering

The Sparse Relation Representation(SRR) algorithm shows good clustering performance.It uses the neighborhood relation between a data sample and other samples as new features to learn the self-representation coefficient, which is then used to construct the affinity matrix;spectral clustering is finally applied to realize segmentation.Considering both the sparsity and aggregation of a similarity matrix, this study proposes a discriminant-enhanced sparse subspace clustering model based on the SSR algorithm.The study's novelty is two-fold:first, to overcome the complexity induced by the nuclear norm in SSR, it uses the squared F norm to regularize the self-representation matrix;second, it introduces a new regularization term that can guarantee the inter-class discrimination of the self-expression coefficient matrix and grouping effect of the neighborhood relation matrix.The experimental results show that compared with SSC, LRR, LSR, BDR-B, SRR, and other models, this model has better clustering performance.On MNIST, USPS, and ORL datasets, the clustering error rate of this model is 9.6, 14.1, and 3.8 percentage points lower than that of the SRR model, respectively;on the Extended Yale B dataset, the clustering error rates of the model in the 2, 3, 5, 8, and 10 cluster problems are 0.39, 0.72, 1.32, 2.73, and 3.28 percentage points lower than in the SRR model, respectively.