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Incidences Between Planes Over Finite Fields

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Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

Pierre Vandergheynst, Xavier Bresson, Michaël Defferrard

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or wor ...

2016

Double-Normal Pairs In Space

János Pach

A double-normal pair of a finite set S of points that spans R-d is a pair of points {p, q} from S such that S lies in the closed strip bounded by the hyperplanes through p and q perpendicular to pq. A double-normal pair {p, q} is strict if S \ {p,q} lies i ...

London Mathematical Society, Cambridge2015

Graph-based Image Inpainting

Michaël Defferrard

The project goal was to explore the applications of spectral graph theory to address the inpainting problem of large missing chunks. We used a non-local patch graph representation of the image and proposed a structure detector which leverages the graph rep ...

2014

Ramsey-type results for semi-algebraic relations

János Pach

A k-ary semi-algebraic relation E on R^d is a subset of R^{kd}, the set of k-tuples of points in R^d, which is determined by a finite number of polynomial equations and inequalities in kd real variables. The description complexity of such a relation is at ...

2013

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most

d

d ...

2012

Wavelets on graphs via spectral graph theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral deco ...

Elsevier2011

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagati ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

A bipartite strengthening of the Crossing Lemma

János Pach

Let G = (V, E) be a graph with n vertices and m >= 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Omega(m(3)/n(2)) pairs of crossing edges; or equivalently, there is an edge that crosses Omega(m(2)/n(2)) other edges. ...

2010

Wavelets on Graphs via Spectral Graph Theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite graph. We define a notion of scaling using the graph analogue of the Fourier domain, namely the space of eigenfunctions forming the sp ...

2008

Polarity of chordal graphs

Dominique de Werra, Tinaz Ekim

Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NP-complete to decide for general graphs. It has been recently proved that for cographs, th ...

2008

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagati ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most

d

d ...

2012