A kernel view on manifold sub-sampling based on Karcher variance optimization

Nicolas Courty 1 Thomas Burger 2
1 SEASIDE - SEarch, Analyze, Synthesize and Interact with Data Ecosystems
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, UBS - Université de Bretagne Sud
Abstract : . In the Hilbert space reproducing the Gaussian kernel, projected data points are located on an hypersphere. Following some recent works on geodesic analysis on that particular manifold, we propose a method which purpose is to select a subset of input data by sampling the corresponding hypersphere. The selected data should represent correctly the input data, while also maximizing the diversity. We show how these two opposite objectives can be characterized in terms of Karcher variance optimization. The corresponding algorithms are defined and results are reported on toy datasets. This shows the interest of working on the kernelized festure space instead of the input space.
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https://hal.archives-ouvertes.fr/hal-00849821
Contributor : Thomas Burger <>
Submitted on : Thursday, August 1, 2013 - 10:52:51 AM
Last modification on : Thursday, March 7, 2019 - 4:56:03 PM

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  • HAL Id : hal-00849821, version 1

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Nicolas Courty, Thomas Burger. A kernel view on manifold sub-sampling based on Karcher variance optimization. Geometric sciences of information 2013, 2013, France. ⟨hal-00849821⟩

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