In the graph-based learning method, the data graph or similarity matrix reveals the relationship between data, and reflects similar attributes within a class and differences between classes. Inspired by Davis–Kahan Theorem that the stability of matrix eigenvector space depends on its spectral distance (i.e. its eigenvalue gap), in this paper, we propose a global local affinity matrix model with low rank subspace sparse representation (GLAM-LRSR) based on global information of eigenvalue gap and local distance between samples. This method approximate the similarity matrix with ideally diagonal block structure from the perspective of maximizing the eigenvalue gap, and the local distance between data is utilized as a regular term to prevent the eigenvalue gap from being too large to ensure the efficacy of similarity matrix. We have shown that the combination of subspace (LRSR) partitioning method such as Sparse Subspace Clustering(SSC) and the similarity matrix constructed by GLAM can improve the accuracy of subspace clustering, and that the similarity matrix constructed by GLAM-LRSR can be successfully applied to graph-based semi-supervised classification task. Our experiments on synthetic data as well as the real-world datasets for face clustering, face recovery and motion segmentation have clearly demonstrate the significant advantages of GLAM-LRSR and its effectiveness.

在基于图的学​​习方法中，数据图或相似度矩阵揭示了数据之间的关系，并反映了类内的相似属性和类之间的差异。受到戴维斯-卡汉定理的启发，矩阵特征向量空间的稳定性取决于其光谱距离（即特征值间隙），在本文中，我们提出了一种基于低阶子空间稀疏表示的全局局部亲和矩阵模型（GLAM-LRSR）。特征值差距和样本之间局部距离的全局信息。从最大化特征值间隙的角度出发，该方法用理想的对角线块结构近似相似矩阵，并且数据之间的局部距离被用作规则项，以防止特征值间隙太大以确保相似矩阵的有效性。我们已经表明，将稀疏子空间聚类（S稀疏子空间聚类，SSC）等子空间（LRSR）划分方法与GLAM构造的相似度矩阵相结合，可以提高子空间聚类的准确性，并且可以成功应用GLAM-LRSR构造的相似度矩阵基于图的半监督分类任务 我们在合成数据以及用于人脸聚类，人脸恢复和运动分割的真实世界数据集上的实验清楚地证明了GLAM-LRSR的显着优势及其有效性。GLAM-LRSR构建的相似度矩阵可以成功地应用于基于图的半监督分类任务。我们在合成数据以及用于人脸聚类，人脸恢复和运动分割的真实世界数据集上的实验清楚地证明了GLAM-LRSR的显着优势及其有效性。GLAM-LRSR构建的相似度矩阵可以成功地应用于基于图的半监督分类任务。我们在合成数据以及用于人脸聚类，人脸恢复和运动分割的真实世界数据集上的实验清楚地证明了GLAM-LRSR的显着优势及其有效性。