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Asian Conference on Computer Vision

ACCV 2016: Computer Vision – ACCV 2016 pp 400–415Cite as

Clustering Symmetric Positive Definite Matrices on the Riemannian Manifolds

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10111))

Abstract

Using structured features such as symmetric positive definite (SPD) matrices to encode visual information has been found to be effective in computer vision. Traditional pattern recognition methods developed in the Euclidean space are not suitable for directly processing SPD matrices because they lie in Riemannian manifolds of negative curvature. The main contribution of this paper is the development of a novel framework, termed Riemannian Competitive Learning (RCL), for SPD matrices clustering. In this framework, we introduce a conscious competition mechanism and develop a robust algorithm termed Riemannian Frequency Sensitive Competitive Learning (rFSCL). Compared with existing methods, rFSCL has three distinctive advantages. Firstly, rFSCL inherits the online nature of competitive learning making it capable of handling very large data sets. Secondly, rFSCL inherits the advantage of conscious competitive learning which means that it is less sensitive to the initial values of the cluster centers and that all clusters are fully utilized without the “dead unit” problem associated with many clustering algorithms. Thirdly, as an intrinsic Riemannian clustering method, rFSCL operates along the geodesic on the manifold and the algorithms is completely independent of the choice of local coordinate systems. Extensive experiments show its superior performance compared with other state of the art SPD matrices clustering methods.

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Notes

  1. 1.

    Please note that an equivalent form of affine-invariant Riemannian metric (AIRM) is given in [19]. Affine-invariant Riemannian metric was first used to calculate the geodesic distance of two SPD matrices in [26] and Pennec et al. promoted AIRM as a computing framework in [18].

  2. 2.

    The experiments are conducted on the simulated dataset.

  3. 3.

    The code is downloaded from http://www.robots.ox.ac.uk/~sadeep/.

  4. 4.

    The code is downloaded from http://www.cise.ufl.edu/~salehian/Softwares.html.

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Acknowledgement

Part of this paper is supported by NSFC (61332012, 61300205), Shenzhen R&D Program (JCYJ20160328144421330, GJHZ20140418191518323).

Author information

Authors and Affiliations

  1. Guangzhou University, Guangzhou, China

    Ligang Zheng

  2. University of Nottingham, Nottingham, UK

    Guoping Qiu

  3. Shenzhen University, Shenzhen, China

    Jiwu Huang

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  1. Ligang Zheng
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  2. Guoping Qiu
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  3. Jiwu Huang
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Corresponding author

Correspondence to Ligang Zheng .

Editor information

Editors and Affiliations

  1. National Tsing Hua University, Hsinchu, Taiwan

    Shang-Hong Lai

  2. Graz University of Technology, Graz, Austria

    Vincent Lepetit

  3. Drexel University, Philadelphia, Pennsylvania, USA

    Ko Nishino

  4. The University of Tokyo, Tokyo, Japan

    Yoichi Sato

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Zheng, L., Qiu, G., Huang, J. (2017). Clustering Symmetric Positive Definite Matrices on the Riemannian Manifolds. In: Lai, SH., Lepetit, V., Nishino, K., Sato, Y. (eds) Computer Vision – ACCV 2016. ACCV 2016. Lecture Notes in Computer Science(), vol 10111. Springer, Cham. https://doi.org/10.1007/978-3-319-54181-5_26

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  • DOI: https://doi.org/10.1007/978-3-319-54181-5_26

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