In this work, we propose and study a preconditioned framework with a graphic Ginzburg-Landau functional for image segmentation and data clustering by parallel computing. Solving nonlocal models is usually challenging due to the huge computation burden. For the nonconvex and nonlocal variational functional, we propose several damped Jacobi and generalized Richardson preconditioners for the large-scale linear systems within a difference of convex functions algorithms framework. They are efficient for parallel computing with GPU and can leverage the computational cost. Our framework also provides flexible step sizes with a global convergence guarantee. Numerical experiments show the proposed algorithms are very competitive compared to the singular value decomposition based spectral method.

翻译：本文提出并研究了一种基于图Ginzburg-Landau泛函的预条件框架，用于图像分割和数据聚类的并行计算。由于巨大的计算负担，求解非局部模型通常具有挑战性。针对非凸且非局部的变分泛函，我们在凸差函数算法框架中，为大规模线性系统提出了几种阻尼Jacobi和广义Richardson预条件子。这些预条件子在GPU上可高效并行计算，并能有效降低计算成本。我们的框架还提供了灵活的步长选择，并保证了全局收敛性。数值实验表明，与基于奇异值分解的谱方法相比，本文提出的算法具有很强的竞争力。