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:在这项工作中,我们提出并研究了一个具有图格林斯布-朗道功能的预条件框架,用于通过并行计算进行图像分割和数据聚类。解决非局部模型通常是具有巨大的计算负担的。对于非凸和非局部变分函数,我们提出了几个阻尼Jacobi和广义Richardson预处理器,用于差分函数算法框架内的大规模线性系统。它们在GPU上进行并行计算非常有效,并可以利用计算成本。我们的框架还提供了灵活的步长和全局收敛保证。数值实验表明,与基于奇异值分解的光谱方法相比,所提出的算法非常具有竞争力。