| Locality preserving projection on SPD matrix Lie group: algorithm and analysis | |
Li, Yangyang1,2; Lu, Ruqian1
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| 2018-09-01 | |
| Source Publication | SCIENCE CHINA-INFORMATION SCIENCES
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| ISSN | 1674-733X |
| Volume | 61Issue:9Pages:15 |
| Abstract | 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. |
| Keyword | manifold learning SPD matrix Lie group locally preserving projection Laplace operator Log Euclidean metric |
| DOI | 10.1007/s11432-017-9233-4 |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science ; Engineering |
| WOS Subject | Computer Science, Information Systems ; Engineering, Electrical & Electronic |
| WOS ID | WOS:000436194500004 |
| Publisher | SCIENCE PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/30587 |
| Collection | 数学所 |
| Corresponding Author | Li, Yangyang |
| Affiliation | 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 |
| 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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