Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix represents the graph structure and is vital to the performance of semi-supervised graph-based clustering. However, existing methods adopt a static affinity matrix to learn the low-dimensional representations of data points and do not optimize the affinity matrix during the learning process. In this paper, we propose a novel dynamic graph structure learning method for semi-supervised clustering. In this method, we simultaneously optimize the affinity matrix and the low-dimensional representations of data points by leveraging the given pairwise constraints. Moreover, we propose an alternating minimization approach with proven convergence to solve the proposed nonconvex model. During the iteration process, our method cyclically updates the low-dimensional representations of data points and refines the affinity matrix, leading to a dynamic affinity matrix (graph structure). Specifically, for the update of the affinity matrix, we enforce the data points with remarkably different low-dimensional representations to have an affinity value of 0. Furthermore, we construct the initial affinity matrix by integrating the local distance and global self-representation among data points. Experimental results on eight benchmark datasets under different settings show the advantages of the proposed approach.
翻译:现有大多数半监督的基于图形的集群方法利用监督信息,办法是改进亲和矩阵,或直接限制数据点的低维表示方式; 亲和矩阵代表图形结构,对于半监督的基于图形的集群工作至关重要; 然而,现有方法采用静态的亲和矩阵方法,以学习数据点的低维表示方式,而不是在学习过程中优化亲和矩阵; 在本文件中,我们为半监督的集群提出一个新的动态图形结构学习方法; 在这种方法中,我们利用给定的对口限制,优化亲和低维对数据点的表示方式; 此外,我们建议采用一种交替最小化方法,并证明能够一致地解决拟议的非对口图形模式; 在循环过程中,我们的方法周期性地更新数据点的低维的表述方式,并且不优化亲和关系矩阵; 具体地,为了更新亲和受监督的集群,我们用截然不同的低维基面表示方式来优化数据点和低维度表示数据点的低维度表示方式; 此外,我们建议采用一种交替最小的最小化方法,以整合全球8个基点的自我代表模式为基础,我们根据不同的实验性模型构建了数据结构构建了数据。