Scale-Space Clustering on a Unit Hypersphere

  • Yuta Hirano
  • Atsushi ImiyaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9256)


We present an algorithm for the scale-space clustering of a point cloud on a hypersphere in a higher-imensional Euclidean space. Our method achieves clustering by estimating the density distribution of the points in the linear scale space on the sphere. The algorithm regards the union of observed point sets as an image defined by the delta functions located at the positions of the points on the sphere. As numerical examples, we illustrate clustering on the 3-sphere \(\mathbb {S}^3\) in four-dimensional Euclidean space.


Point Cloud Heat Kernel Scale Space Dimensional Euclidean Space Unit Hypersphere 
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.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Integrated SciencesChiba UniversityChibaJapan
  2. 2.Institute of Management and Information TechnologiesChiba UniversityInage-kuJapan

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