Partial differences as tools for filtering data on graphs

doi:10.1016/j.patrec.2010.03.022

Partial differences as tools for filtering data on graphs

2010-10-01

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DOI：10.1016/j.patrec.2010.03.022

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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. (C) 2010 Elsevier B.V. All rights reserved.

Keyword:

Partial difference equations

Weighted graphs

Mathematical morphology

Anisotropic and isotropic discrete regularization

Partial differences as tools for filtering data on graphs

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