Discrete Laplace operator

Applied sciences
Information engineering
Artificial intelligence
Computer vision

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Graph-based structures in data science : fundamental limits and applications to machine learning

Nathanaël Perraudin

State-of-the-art data analysis tools have to deal with high-dimensional data. Fortunately, the inherent dimensionality of data is often much smaller, as it has an internal structure limiting its degrees of freedom. In most cases, this structure can be appr ...

EPFL2017

On sums of eigenvalues of elliptic operators on manifolds

Joachim Stubbe

We use the averaged variational principle introduced in a recent article on graph spectra [10] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kroger's bound ...

European Mathematical Soc2017

Discreteness of interior transmission eigenvalues revisited

Hoài-Minh Nguyên, Quoc Hung Nguyen

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the ...

Springer Verlag2017

When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

Dimitri Nestor Alice Van De Ville, Maria Giulia Preti, Robin Jonathan Demesmaeker

The study of complex systems greatly benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smalles ...

IEEE Institute of Electrical and Electronics Engineers2017

Sparse Gradient Optimization and its Applications in Image Processing

Nikolaos Arvanitopoulos Darginis

Millions of digital images are captured by imaging devices on a daily basis. The way imaging devices operate follows an integral process from which the information of the original scene needs to be estimated. The estimation is done by inverting the integra ...

EPFL2017

Compressive Spectral Clustering

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy, Nicolas Tremblay

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a fea ...

2016

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