Efficient clustering on Riemannian manifolds: A kernelised random projection approach

Zhao, Kun, Alavi, Azadeh, Wiliem, Arnold and Lovell, Brian C. (2015) Efficient clustering on Riemannian manifolds: A kernelised random projection approach. Pattern Recognition, 51 333-345. doi:10.1016/j.patcog.2015.09.017

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Author Zhao, Kun
Alavi, Azadeh
Wiliem, Arnold
Lovell, Brian C.
Title Efficient clustering on Riemannian manifolds: A kernelised random projection approach
Journal name Pattern Recognition   Check publisher's open access policy
ISSN 0031-3203
1873-5142
Publication date 2015-10-28
Year available 2015
Sub-type Article (original research)
DOI 10.1016/j.patcog.2015.09.017
Open Access Status File (Author Post-print)
Volume 51
Start page 333
End page 345
Total pages 13
Place of publication Amsterdam, The Netherlands
Publisher Elsevier
Language eng
Subject 1712 Software
1711 Signal Processing
1707 Computer Vision and Pattern Recognition
1702 Artificial Intelligence
Abstract Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space embedded in a higher dimensional space. However, since these manifolds belong to non-Euclidean topological spaces, exploiting their structures is computationally expensive, especially when one considers the clustering analysis of massive amounts of data. To this end, we propose an efficient framework to address the clustering problem on Riemannian manifolds. This framework implements random projections for manifold points via kernel space, which can preserve the geometric structure of the original space, but is computationally efficient. Here, we introduce three methods that follow our framework. We then validate our framework on several computer vision applications by comparing against popular clustering methods on Riemannian manifolds. Experimental results demonstrate that our framework maintains the performance of the clustering whilst massively reducing computational complexity by over two orders of magnitude in some cases.
Formatted abstract
Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space embedded in a higher dimensional space. However, since these manifolds belong to non-Euclidean topological spaces, exploiting their structures is computationally expensive, especially when one considers the clustering analysis of massive amounts of data. To this end, we propose an efficient framework to address the clustering problem on Riemannian manifolds. This framework implements random projections for manifold points via kernel space, which can preserve the geometric structure of the original space, but is computationally efficient. Here, we introduce three methods that follow our framework. We then validate our framework on several computer vision applications by comparing against popular clustering methods on Riemannian manifolds. Experimental results demonstrate that our framework maintains the performance of the clustering whilst massively reducing computational complexity by over two orders of magnitude in some cases.
Keyword Riemannian manifolds
Random projection
Clustering
Q-Index Code C1
Q-Index Status Confirmed Code
Grant ID LP130100230
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2016 Collection
School of Information Technology and Electrical Engineering Publications
 
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Created: Thu, 29 Oct 2015, 21:41:08 EST by Arnold Wiliem on behalf of School of Information Technol and Elec Engineering