基于对偶超图正则化的概念分解算法及其在数据表示中的应用

针对概念分解算法没有同时考虑数据空间和特征属性空间中的高阶几何结构信息的问题,提出了一种基于对偶超图正则化的概念分解算法。该算法通过分别在数据空间和特征属性空间中构建无向加权的拉普拉斯超图正则项,分别反映了数据流形和特征流形的多元几何结构信息,弥补了传统图模型只能表达数据间成对关系的缺陷。采用交替迭代的方法求解算法的目标函数并证明了算法的收敛性。在3个真实数据库(TDT2、PIE、COIL20)上的实验表明,该方法在数据的聚类表示的效果方面优于其他方法。

Hypergraph Dual Regularization Concept Factorization Algorithm and Its Application in Data Representation

The concept factorization(CF) algorithm can not take the geometric structures of both the data manifold and the feature manifold into account simultaneously.And CF algorithm can not consider the high-order relationship among samples.In this paper,a novel algorithm called hypergraph dual regularization concept factorization(DHCF) algorithm was proposed,which encodes the high-order geometric structure information of data and feature spaces by constructing two undirected weighted hypergraph Laplacian regularize term,respectively.By this way,the proposed method can overcome the deficiency that traditional graph model expresses pair-wise relationship only.Moreover,we developed the iterative updating optimization schemes for DHCF,and provided the convergence proof of our optimization scheme.Experimental results on TDT2 document datasets,PIE and COIL20 image datasets demonstrate the effectiveness of our method.