Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the ever-increasing computational challenges, graph coarsening can be potentially applied for preprocessing a given hypergraph by aggressively aggregating its vertices (nodes). However, state-of-the-art hypergraph partitioning (clustering) methods that incorporate heuristic graph coarsening techniques are not optimized for preserving the structural (global) properties of hypergraphs. In this work, we propose an efficient spectral hypergraph coarsening scheme (HyperSF) for well preserving the original spectral (structural) properties of hypergraphs. Our approach leverages a recent strongly-local max-flow-based clustering algorithm for detecting the sets of hypergraph vertices that minimize ratio cut. To further improve the algorithm efficiency, we propose a divide-and-conquer scheme by leveraging spectral clustering of the bipartite graphs corresponding to the original hypergraphs. Our experimental results for a variety of hypergraphs extracted from real-world VLSI design benchmarks show that the proposed hypergraph coarsening algorithm can significantly improve the multi-way conductance of hypergraph clustering as well as runtime efficiency when compared with existing state-of-the-art algorithms.
翻译:测高仪使多路高顺序关系出现模型问题。 然而, 多数现有高光谱算法的计算成本可能在很大程度上取决于输入高光计的大小。 为了应对不断增加的计算挑战, 图形粗化可能会通过大力集聚其脊椎( 节点) 来用于预处理特定高光谱。 但是, 包含超光速图形粗化技术的高光谱分隔( 集成) 方法并不是用来保存高光谱结构( 全球) 特性的优化。 在这项工作中, 我们提议一个高效的光谱高光谱剖析计划( HyperSF), 以妥善保存高光谱的原有光谱( 结构) 特性。 我们的方法可以借助最近非常本地的以最大流为基础的集成算算法来检测能够尽量减少削减比率的超高光谱垂直( 集合) 。 为了进一步提高算法效率, 我们建议采用与原始高光谱高光谱剖面图相匹配的光谱分析方法, 我们的实验结果, 用来对高光谱系统系统进行对比, 将高光谱分析, 系统压数据分析系统设计,, 将高空基数据分析比比地基数据基数据分析系统,,, 将高空基数据分析系统 显示高空基数据分析,, 显示高空基数据基数据分析,, 显示高空基数据基数据分析, 显示高空基比。