黎曼流形的距离均方差最小降维改进算法  

Minimum squared mean distance based on dimension reduction of Riemannian manifold

作　　者：高恩芝[1,2] 王士同[1] 

机构地区：[1]江南大学数字媒体学院,江苏无锡214122 [2]江苏省信息融合软件工程技术研究开发中心,江苏无锡214405

出　　处：《计算机工程与应用》2013年第2期198-202,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.60704047);国家自然科学基金重大研究计划项目(No.9082002);江苏省信息融合软件工程技术研究开发中心开放基金

摘　　要：TRIMAP算法重新定义了图上距离的表达形式,并用近邻点对的测地距离的误差和作为衡量投影函数好坏的标准,通过这种方法可以较好地找到所需的从高维空间到低维空间转换的媒介,但是这种衡量标准不能很好地表达出TRIMAP中定义的图上距离与投影到低维空间中两点实际距离的对比关系。针对这个不足,采用了一个新的衡量标准表达式,定义一个参数m来代表对比关系,以此来解决这个缺陷,从而更好地获得最佳投影,提高识别率。实验结果表明,在ORL人脸图像的分类识别问题中获得了较好的识别性能。The TRIMAP algorithm redefines the expression of the distance on the graph, and in order to measure the quality of the projection functions, considers the squared error sum of all pair wise geodesic. This way can better find what is needed from high-dimensional space to low-dimensional vector space conversion. But this measure can＇ t be well express the contrast relation- ship between graph distance which is defined in TRIMAP algorithm and actual distance which is projected to low dimensional space. Aiming at this deficiency, this paper uses a new standard expression and defines a parameter m to represent relationship in order to solve the defect, get the best projection and improve the recognition rate. The preliminary experimental results show that it can get a better recognition performance in the ORL face image classification and recognition problem.

关 键 词：数据降维 流形学习 测地距离 等距离映射算法 局部线性嵌入 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]