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Generalized Learning Riemannian Space Quantization: A Case Study on Riemannian Manifold of SPD Matrices
Tang FZ(唐凤珍)1,2,3; Fan ML(范孟灵)1,2,3; Tino, Peter4
Department机器人学研究室
Source PublicationIEEE Transactions on Neural Networks and Learning Systems
ISSN2162-237X
2021
Volume32Issue:1Pages:281-292
Indexed ByEI
EI Accession number20210309770169
Contribution Rank1
Funding OrganizationNational Natural Science Foundation of China under Grant 61803369 ; CAS Pioneer Hundred Talents Program under Grant Y8A1220104 ; Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61821005 ; Frontier Science Research Project of the Chinese Academy of Sciences under Grant QYZDY-SSW-JSC005 ; European Commission Horizon 2020 Innovative Training Network SUNDAIL under Project 721463.
KeywordGeneralized learning vector quantization (GLVQ) learning vector quantization (LVQ) Riemannian geodesic distances Riemannian manifold
Abstract

Learning vector quantization (LVQ) is a simple and efficient classification method, enjoying great popularity. However, in many classification scenarios, such as electroencephalogram (EEG) classification, the input features are represented by symmetric positive-definite (SPD) matrices that live in a curved manifold rather than vectors that live in the flat Euclidean space. In this article, we propose a new classification method for data points that live in the curved Riemannian manifolds in the framework of LVQ. The proposed method alters generalized LVQ (GLVQ) with the Euclidean distance to the one operating under the appropriate Riemannian metric. We instantiate the proposed method for the Riemannian manifold of SPD matrices equipped with the Riemannian natural metric. Empirical investigations on synthetic data and real-world motor imagery EEG data demonstrate that the performance of the proposed generalized learning Riemannian space quantization can significantly outperform the Euclidean GLVQ, generalized relevance LVQ (GRLVQ), and generalized matrix LVQ (GMLVQ). The proposed method also shows competitive performance to the state-of-the-art methods on the EEG classification of motor imagery tasks.

Language英语
Document Type期刊论文
Identifierhttp://ir.sia.cn/handle/173321/28159
Collection机器人学研究室
Corresponding AuthorTang FZ(唐凤珍)
Affiliation1.State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
2.Institute for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, China
3.School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
4.School of Computer Science, University of irmingham, Birmingham, United Kingdom
Recommended Citation
GB/T 7714
Tang FZ,Fan ML,Tino, Peter. Generalized Learning Riemannian Space Quantization: A Case Study on Riemannian Manifold of SPD Matrices[J]. IEEE Transactions on Neural Networks and Learning Systems,2021,32(1):281-292.
APA Tang FZ,Fan ML,&Tino, Peter.(2021).Generalized Learning Riemannian Space Quantization: A Case Study on Riemannian Manifold of SPD Matrices.IEEE Transactions on Neural Networks and Learning Systems,32(1),281-292.
MLA Tang FZ,et al."Generalized Learning Riemannian Space Quantization: A Case Study on Riemannian Manifold of SPD Matrices".IEEE Transactions on Neural Networks and Learning Systems 32.1(2021):281-292.
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