A family of gradient methods using Householder transformation with application to hypergraph partitioning
A family of gradient methods using Householder transformation with application to hypergraph partitioning
复制标题
DOI：
10.1007/s11075-023-01593-y
复制
发表时间：
2023-06
期刊：
影响因子：
--
通讯作者：
Xin Zhang;Jingya Chang;Zhili Ge;Zhou Sheng
中科院分区：
文献类型：
--
作者：
Xin Zhang;Jingya Chang;Zhili Ge;Zhou Sheng
本文提出了一种偶均匀超图的紧致拉普拉斯张量的最小Z-特征对的约束保持算法，其中利用Householder变换，确定了一族具有充分下降的修正共轭方向.此外，我们证明了存在一个积极的步长在新的约束保持更新计划，使沃尔夫条件成立。基于这些性质，我们证明了新算法的收敛性。此外，我们将我们的算法应用于超图划分和图像分割，数值结果表明了所提出算法的效率。
In this paper, we propose a constraint preserving algorithm for the smallestZ-eigenpair of the compact Laplacian tensor of an even-uniform hypergraph, where Householder transform is employed and a family of modified conjugate directions with sufficient descent is determined. Besides, we prove that there exists a positive step size in the new constraint preserving update scheme such that the Wolfe conditions hold. Based on these properties, we prove the convergence of the new algorithm. Furthermore, we apply our algorithm to the hypergraph partitioning and image segmentation, and numerical results are reported to illustrate the efficiency of the proposed algorithm.