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The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an L-q,L-p-Sobolev inequality (2
We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...
The main challenge of new information technologies is to retrieve intelligible information from the large volume of digital data gathered every day. Among the variety of existing data sources, the satellites continuously observing the surface of the Earth ...
We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(p) -type data terms in the manifold case. These algorithms are ba ...
Aligning data distributions that underwent spectral distortions related to acquisition conditions is a key issue to improve the performance of classifiers applied to multi-temporal and multi-angular images. In this paper, we propose a feature extraction me ...
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics th ...
We complete the picture of sharp eigenvalue estimates for the -Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator when the Ricci curvature is bounded from below by a negative constant. We ...
In this paper, we propose a novel algorithm for dimensionality reduction that uses as a criterion the mutual information (MI) between the transformed data and their cor- responding class labels. The MI is a powerful criterion that can be used as a proxy to ...
Institute of Electrical and Electronics Engineers2015
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represent manifold data accurately while preserving the manifold's structure. For this purpo ...
In this paper we consider some practical applications of model reduction methods in unstable gas turbine and rocket combustion. We explore a set of promising methods for reducing computational burden in large scale LES calculations of unsteady turbulent co ...
