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Locality preserving projection on SPD matrix Lie group: algorithm and analysis
Li, Yangyang1,2; Lu, Ruqian1
AbstractSymmetric 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.
Keywordmanifold learning SPD matrix Lie group locally preserving projection Laplace operator Log Euclidean metric
Funding ProjectNational 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 Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000436194500004
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Document Type期刊论文
Corresponding AuthorLi, Yangyang
Affiliation1.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
Recommended Citation
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.
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