CSpace  > 数学所
Locality preserving projection on SPD matrix Lie group: algorithm and analysis
Li, Yangyang1,2; Lu, Ruqian1
2018-09-01
发表期刊SCIENCE CHINA-INFORMATION SCIENCES
ISSN1674-733X
卷号61期号:9页码:15
摘要Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For high-dimensional SPD matrices, directly using manifold learning algorithms to reduce the dimension of matrix-form data is impossible. The SPD matrix must first be transformed into a long vector, and then the dimension of this vector must be reduced. However, this approach breaks the spatial structure of the SPD matrix space. To overcome this limitation, we propose a new dimension reduction algorithm on SPD matrix space to transform high-dimensional SPD matrices into low-dimensional SPD matrices. Our work is based on the fact that the set of all SPD matrices with the same size has a Lie group structure, and we aim to transform the manifold learning to the SPD matrix Lie group. We use the basic idea of the manifold learning algorithm called locality preserving projection (LPP) to construct the corresponding Laplacian matrix on the SPD matrix Lie group. Thus, we call our approach Lie-LPP to emphasize its Lie group character. We present a detailed algorithm analysis and show through experiments that Lie-LPP achieves effective results on human action recognition and human face recognition.
关键词manifold learning SPD matrix Lie group locally preserving projection Laplace operator Log Euclidean metric
DOI10.1007/s11432-017-9233-4
语种英语
资助项目National Key Research and Development Program of China[2016YFB1000902] ; National Natural Science Foundation of China[61232015] ; National Natural Science Foundation of China[61472412] ; National Natural Science Foundation of China[61621003] ; Beijing Science and Technology Project on-Machine Learning-based Stomatology ; Tsinghua-Tencent-AMSS-Joint Project on WWW Knowledge Structure and its Application
WOS研究方向Computer Science ; Engineering
WOS类目Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号WOS:000436194500004
出版者SCIENCE PRESS
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/30587
专题数学所
通讯作者Li, Yangyang
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Management Decis & Informat Syst, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式
GB/T 7714
Li, Yangyang,Lu, Ruqian. Locality preserving projection on SPD matrix Lie group: algorithm and analysis[J]. SCIENCE CHINA-INFORMATION SCIENCES,2018,61(9):15.
APA Li, Yangyang,&Lu, Ruqian.(2018).Locality preserving projection on SPD matrix Lie group: algorithm and analysis.SCIENCE CHINA-INFORMATION SCIENCES,61(9),15.
MLA Li, Yangyang,et al."Locality preserving projection on SPD matrix Lie group: algorithm and analysis".SCIENCE CHINA-INFORMATION SCIENCES 61.9(2018):15.
条目包含的文件
条目无相关文件。
个性服务
推荐该条目
保存到收藏夹
查看访问统计
导出为Endnote文件
谷歌学术
谷歌学术中相似的文章
[Li, Yangyang]的文章
[Lu, Ruqian]的文章
百度学术
百度学术中相似的文章
[Li, Yangyang]的文章
[Lu, Ruqian]的文章
必应学术
必应学术中相似的文章
[Li, Yangyang]的文章
[Lu, Ruqian]的文章
相关权益政策
暂无数据
收藏/分享
所有评论 (0)
暂无评论
 

除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。