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Joint Normalization and Dimensionality Reduction on Grassmannian: A Generalized Perspective
Liu TC(刘天赐)1,2; Shi ZL(史泽林)1,3; Liu YP(刘云鹏)1,3
Department光电信息技术研究室
Source PublicationIEEE Signal Processing Letters
ISSN1070-9908
2018
Volume25Issue:6Pages:858-862
Indexed BySCI ; EI
EI Accession number20181705055201
WOS IDWOS:000432030000001
Contribution Rank1
KeywordImage-set Recognition Grassmann Manifold Dimensionality Reduction Grassmannian Optimization
Abstract

This paper proposes a generalized framework with joint normalization that learns lower-dimensional subspaces with maximum discriminative power by using Riemannian geometry. We model the similarity/dissimilarity between subspaces using various metrics defined on Grassmannian and formulate dimensionality reduction as a non-linear constraint optimization problem considering the orthogonalization. To obtain the linear mapping, we derive the components required to perform Riemannian optimization from the original Grassmannian through an orthonormal projection. We respect the Riemannian geometry of the Grassmann manifold and search for this projection directly from one Grassmann manifold to another face-to-face without any additional transformations. In this natural geometry-aware approach, any metric on the Grassmann manifold can theoretically reside in our model . We combine five metrics with our model, and the learning process is treated as an unconstrained optimization problem on a Grassmann manifold. Experiments on several datasets demonstrate that our approach leads to a significant accuracy gain over state-of-the-art methods.

Language英语
WOS SubjectEngineering, Electrical & Electronic
WOS KeywordRECOGNITION ; MANIFOLDS ; GEOMETRY
WOS Research AreaEngineering
Citation statistics
Document Type期刊论文
Identifierhttp://ir.sia.cn/handle/173321/21874
Collection光电信息技术研究室
Corresponding AuthorLiu TC(刘天赐)
Affiliation1.Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016
2.University of Chinese Academy of Sciences, Beijing 100049
3.Key Laboratory of Opto-Electronic Information Processing, CAS, Shenyang 110016
Recommended Citation
GB/T 7714
Liu TC,Shi ZL,Liu YP. Joint Normalization and Dimensionality Reduction on Grassmannian: A Generalized Perspective[J]. IEEE Signal Processing Letters,2018,25(6):858-862.
APA Liu TC,Shi ZL,&Liu YP.(2018).Joint Normalization and Dimensionality Reduction on Grassmannian: A Generalized Perspective.IEEE Signal Processing Letters,25(6),858-862.
MLA Liu TC,et al."Joint Normalization and Dimensionality Reduction on Grassmannian: A Generalized Perspective".IEEE Signal Processing Letters 25.6(2018):858-862.
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