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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

Geometric deep learning: going beyond Euclidean data

Pierre Vandergheynst, Michael Bronstein

Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of ...

2017

A Multiscale Pyramid Transform for Graph Signals

Pierre Vandergheynst, David Shuman, Mohammadjavad Faraji

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic topology of the graph data ...

Institute of Electrical and Electronics Engineers2016

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

Multilinear Low-Rank Tensors on Graphs & Applications

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

2016

Approximation algorithms for geometric dispersion

Alfonso Bolívar Cevallos Manzano

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...

EPFL2016

Space lower bounds for low-stretch greedy embeddings

Christos Kalaitzis

Greedy (geometric) routing is an important paradigm for routing in communication networks. It uses an embedding of the nodes of a network into points of a space (e.g., R-d) equipped with a distance function (e.g., the Euclidean distance l(2)) and uses as a ...

Elsevier Science Bv2016

Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks

Pierre Vandergheynst, Michael Bronstein

In this paper, we propose a generalization of convolutional neural networks (CNN) to non-Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform ...

Wiley-Blackwell2015

Euclidean domain

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On sums of eigenvalues of elliptic operators on manifolds

Geometric deep learning: going beyond Euclidean data

Small subset sums

A Multiscale Pyramid Transform for Graph Signals

Inhomogeneous minima of mixed signature lattices

Multilinear Low-Rank Tensors on Graphs & Applications

Approximation algorithms for geometric dispersion

Space lower bounds for low-stretch greedy embeddings

Obstacles For Splitting Multidimensional Necklaces

Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks

Small subset sums

Geometric deep learning: going beyond Euclidean data

Space lower bounds for low-stretch greedy embeddings

On sums of eigenvalues of elliptic operators on manifolds

A Multiscale Pyramid Transform for Graph Signals

Approximation algorithms for geometric dispersion

Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks

Inhomogeneous minima of mixed signature lattices

Obstacles For Splitting Multidimensional Necklaces

Multilinear Low-Rank Tensors on Graphs & Applications