量子主成分分析算法  

Quantum Principal Component Analysis Algorithm

作　　者：阮越[1,2] 陈汉武[1,3] 刘志昊[1] 张俊[1] 朱皖宁[1] 

机构地区：[1]东南大学计算科学与工程学院,南京210096 [2]安徽工业大学计算机学院,安徽马鞍山243005 [3]东南大学计算机网络和信息集成教育部重点实验室,南京210096

出　　处：《计算机学报》2014年第3期666-676,共11页Chinese Journal of Computers

基　　金：国家自然科学基金(61170321);高等学校博士学科点专项科研基金(20110092110024);东南大学计算机网络和信息集成教育部重点实验室开放基金(K93-9-2010-18)资助

摘　　要：主成分分析(Principal Component Analysis,PCA)是模式识别领域,尤其是人脸识别中一种应用广泛的重要算法.然而,在此算法及其后续的改造算法中始终存在两个主要问题:(1)降维处理后的特征空间依然较大;(2)用于比较两幅人脸特征相似性的测度方法计算量较大,从而导致算法在识别阶段的时间效率较差.该文基于量子信息的相关理论与方法,并受算术编码基本思想的启发,提出了量子PCA算法.设计了一种人脸特征编码方案,进一步压缩了降维处理后的特征空间;将两幅人脸特征的相似性测度方法改为在某一阈值条件下的等值判定;应用Grover算法修改识别阶段的处理流程,使得算法的时间效率有了显著提高.Principal Component Analysis （PCA） is an important method used widely in pattern recognition, especially in human face recognition. However, two shortcomings exist in it and its upgraded versions. One is large feature space even after the procedure of dimension reduction; the other is heavy computation burden of the method which is used to compare the feature similarity of two faces. Therefore, these two reasons lead to poor time efficiency during the recognition phase. Based on quantum information theory and inspired by the main idea of Arithmetic Code, a novel quantum PCA algorithm was proposed in this paper. A quantum encoding method of human face features was designed to compress feature space after the procedure of dimension reduction; the calculation method used to compare the feature similarity of two faces was modified to the method of equivalence determination under a certain threshold; the recognition procedure was revised by Grover algorithm. So, these reformations enhance the algorithm＇s time efficiency greatly.

关 键 词：主成分分析 人脸识别 量子计算 算术编码 Grover算法中图法 

分 类 号：TP302[自动化与计算机技术—计算机系统结构]