如何分析稀疏邻接矩阵? [英] How to analyse a sparse adjacency matrix?

问题描述

我正在研究稀疏邻接矩阵，其中大多数像元为零，而有些像个零散，两个像元之间的每个关系都有一个非常长的多项式描述，并且手动分析它们很费时.我的老师建议使用Gröbnerbases 的纯代数方法，但是在继续之前，我想从纯计算机科学和编程的角度来了解如何分析稀疏邻接矩阵?是否存在一些数据挖掘工具可以对其进行分析?

I am researching sparse adjacency matrices where most cells are zeros and some ones here-and-there, each relationship between two cells has a polynomial description that can be very long and their analysis manually time-consuming. My instructor is suggesting purely algebraic method in terms of Gröbner bases but before proceeding I would like to know from purely computer science and programming perspective about how to analyse sparse adjacency matrices? Does there exist some data mining tools to analyse them?

推荐答案

多元多项式计算和Gröbner基础是一个活跃的研究领域. 1991年，Sturmfels在稀疏消除理论中概述了所得的方法和GR方法.在 2015年7月的会议，可可粉分析.

Multivariate polynomial computation and Gröbner basis is an active research area. In 1991, Sturmfels in Sparse elimination theory outlined the resultant methods and GR methods. In 2015 July conference, CoCoa analysis.

SE在这方面收集了很棒的资料，例如 M2中的GR计算分析，在这里您可以找到分步指南书中概述的分步示例和不同的答案.对于稀疏矩阵，存在基于GR基础的稀疏矩阵算法，例如Faugère的F4和基于Buchberger算法的F5算法.

SE is gathering awesome material on this such as GR computational analysis in M2 where you an find step-by-step examples outlined in the books and different answers. For sparse matrices, there are sparse matrix algorithms built with GR bases such as Faugère's F4 and F5 algorithms that is based on Buchberger algorithm.

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