Partial differences as tools for filtering data on graphs

  • Authors:

  • Olivier Lézoray;Vinh-Thong Ta;Abderrahim Elmoataz

  • Affiliations:

  • Université de Caen Basse-Normandie, ENSICAEN, CNRS, 6 Boulevard Maréchal Juin, F-14050 Caen Cedex, France;Université de Caen Basse-Normandie, ENSICAEN, CNRS, 6 Boulevard Maréchal Juin, F-14050 Caen Cedex, France;Université de Caen Basse-Normandie, ENSICAEN, CNRS, 6 Boulevard Maréchal Juin, F-14050 Caen Cedex, France

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2010

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Abstract

High-dimensional feature spaces are often corrupted by noise. This is problematic for the processing of manifolds and data sets since most of reference methods (and especially graph-based ones) are sensitive to noise. This paper presents pre-processing methods for manifold denoising and simplification based on discrete analogues of continuous regularization and mathematical morphology. The proposed filtering methods provide a general discrete framework for the filtering of manifolds and data with p-Laplacian regularization and mathematical morphology. With our proposals, one obtains filters that can operate on any high-dimensional unorganized multivariate data. Experiments will show that the proposed approaches are efficient to denoise manifolds and data, to project initial noisy data onto a submanifold, and to ease dimensionality reduction, clustering and classification.