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Clustering Symmetric Positive Definite Matrices on the Riemannian Manifolds

  • Ligang ZhengEmail author
  • Guoping Qiu
  • Jiwu Huang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Riemannian Manifold Diffusion Tensor Imaging Geodesic Distance Competitive Learning Symmetric Positive Definite Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgement

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

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Guangzhou UniversityGuangzhouChina
  2. 2.University of NottinghamNottinghamUK
  3. 3.Shenzhen UniversityShenzhenChina

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