Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications

Abstract. Algebraic Multigrid (AMG) methods were developed originally for nu-merically solving Partial Differential Equations (PDE), not necessarily on structured grids. In the last two decades solvers inspired by the AMG approach, were devel-oped for non PDE problems, including data and image analysis problems, such as clustering, segmentation, quantization and others. These solvers share a common principle in that there is a crosstalk between fine and coarse representations of the problems, with flow of information in both directions, fine-to-coarse and coarse-to-fine. This paper surveys some of these problems and the AMG-inspired algorithms for their solution