Dimensionality reduction with adaptive graph

作     者：Lishan QIAO Limei ZHANG Songcan CHEN 

作者机构：Department of Mathematics Science Liaocheng University Liaocheng 252000 China Department of Computer Science and Engineering Nanjing University of Aeronautics & Astronautics Nanjing 210016 China 

出 版 物：《Frontiers of Computer Science》 (中国计算机科学前沿（英文版）)

年 卷 期：2013年第7卷第5期

页      面：745-753页

核心收录：

学科分类：0810[工学-信息与通信工程] 0808[工学-电气工程] 08[工学] 080203[工学-机械设计及理论] 0802[工学-机械工程] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 080201[工学-机械制造及其自动化] 

基　　金：Jiangsu Qing Lan Project National Natural Science Foundation of China, NSFC, (61170151) Natural Science Foundation of Jiangsu Province, (BK2011728) Natural Science Foundation of Shandong Province, (ZR2010FL011, ZR2012FQ005) 

主　　题：Dimensionality reduction graph construction face recognition 

摘      要：Graph-based dimensionality reduction （DR） methods have been applied successfully in many practical problems, such as face recognition, where graphs play a crucial role in modeling the data distribution or structure. However, the ideal graph is, in practice, difficult to discover. Usually, one needs to construct graph empirically according to various motivations, priors, or assumptions; this is inde- pendent of the subsequent DR mapping calculation. Different from the previous works, in this paper, we attempt to learn a graph closely linked with the DR process, and propose an al- gorithm called dimensionality reduction with adaptive graph （DRAG）, whose idea is to, during seeking projection matrix, simultaneously learn a graph in the neighborhood of a pre- specified one. Moreover, the pre-specified graph is treated as a noisy observation of the ideal one, and the square Frobenius divergence is used to measure their difference in the objective function. As a result, we achieve an elegant graph update for- mula which naturally fuses the original and transformed data information. In particular, the optimal graph is shown to be a weighted sum of the pre-defined graph in the original space and a new graph depending on transformed space. Empirical results on several face datasets demonstrate the effectiveness of the proposed algorithm.