有向加权网络上基于模式的谱聚类研究

项目名称： 有向加权网络上基于模式的谱聚类研究

项目编号： No.61463039

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 其他

项目作者： 苏木亚

作者单位： 内蒙古大学

项目金额： 45万元

中文摘要： 有向加权网络上基于模式的聚类结构在计算机科学、电子商务和经济学等诸多领域蕴藏着巨大的潜在应用价值。谱聚类方法具有有效、易于执行等优点，并且可将模块度函数的优化问题转化为矩阵的谱分解问题。因此，本项目拟用谱聚类方法挖掘有向加权网络上基于模式的聚类结构。首先，利用马尔科夫链模型和随机游走理论构造相对通用并且具有理论支撑的谱聚类矩阵，使其能够被用来发现有向加权网络上基于模式的聚类结构。其次，利用矩阵分析理论、马尔科夫链模型和Lumpability定理估计聚类数目，并建立有向加权网络上基于模式的谱聚类模型；利用数据弯曲和正则化方法增强谱聚类矩阵的鲁棒性，在此基础上建立有向加权网络上基于模式的抗噪声谱聚类模型；根据划分结果的稳定性建立聚类效果评价指标；利用矩阵分析理论和优化理论进一步挖掘各个类之间的关系，建立有向加权网络上基于模式的图近似谱聚类模型。最后，利用所建立的模型分析金融风险传播问题。

中文关键词： 数据挖掘；有向加权网络；基于模式的聚类结构；谱聚类

英文摘要： Pattern-based clustering structures on directed weighted networks have important application values in many domains, including computer science, electronic commerce and economics. Spectral clustering method either has advanteges of effevtiveness and easy implementation or an optimazation framework for the modularity function. For this reason, spectral clustering method will be used to detect pattern-based clustering structures of directed weighed networks. First, Markov chain model and random walk theory will be used to construct relatively common and theoretically supported spectral clustering matrix, which can be used to detect pattern-based clustering structures of directed weighed networks. Then, cluster number will be estimated based on matrix theory, Markov chain model and Lumpability theorem, pattern-based spectral clustering model in directed weighed networks will also be proposed; We will propose noise robust pattern-based spectral clustering model in directed weighed networks based on data wraping and regularization framework; The models will be evaluated based on stability of the clustering results. Matrix theory and optimization theory will be used to detect relation of the clusters further, and pattern-based graph approximation spectral clustering model in directed weighed networks will be proposed. Finally, the proposed models will be used to analyze financial risk transmission problems.

英文关键词： data mining;directed weighted network;pattern-based clustering structure;spectral clustering