Publications associées à Higher-order singular value decomposition

Fourier dimensionality reduction of radio-interferometric data

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Vijay Kartik

Next-generation radio-interferometers face a computing challenge with respect to the imaging techniques that can be applied in the big data setting in which they are designed. Dimensionality reduction can thus provide essential savings of computing resourc ...

2017

A Fourier dimensionality reduction model for big data interferometric imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Vijay Kartik

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging method ...

Oxford Univ Press2017

MATHICSE Technical Report : Perturbation of higher-order singular values

Daniel Kressner, André Uschmajew

The higher-order singular values for a tensor of order d are defined as the singular values of the d different matricizations associated with the multilinear rank. When d≥3, the singular values are generally different for different matricizations but not c ...

MATHICSE2016

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

Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

Daniel Kressner, Jonas Ballani

We propose a novel combination of the reduced basis method with low-rank tensor techniques for the efficient solution of parameter-dependent linear systems in the case of several parameters. This combination, called rbTensor, consists of three ingredients. ...

Siam Publications2016

MATHICSE Technical Report : Multigrid methods combined with low-rank approximation for tensor structured Markov chains

Daniel Kressner, Francisco Santos Paredes Quartin de Macedo

Markov chains that describe interacting subsystems suffer, on the one hand, from state space explosion but lead, on the other hand, to highly structured matrices. In this work, we propose a novel tensor-based algorithm to address such tensor structured Mar ...

MATHICSE2016

Tensor low-rank and sparse light field photography

Pierre Vandergheynst, Mahdad Hosseini Kamal

High-quality light field photography has been one of the most difficult challenges in computational photography. Conventional methods either sacrifice resolution, use multiple devices, or require multiple images to be captured. Combining coded image acquis ...

Elsevier2016

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

Daniel Kressner, Jonas Ballani

MATHICSE2015

Low-Rank Tensor Methods for Communicating Markov Processes

Daniel Kressner, Francisco Santos Paredes Quartin de Macedo

Stochastic models that describe interacting processes, such as stochastic automata networks, feature a dimensionality that grows exponentially with the number of processes. This state space explosion severely impairs the use of standard methods for the num ...

Springer-Verlag Berlin2014

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Higher-order singular value decomposition

Fourier dimensionality reduction of radio-interferometric data

A Fourier dimensionality reduction model for big data interferometric imaging

MATHICSE Technical Report : Perturbation of higher-order singular values

Multilinear Low-Rank Tensors on Graphs & Applications

Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

MATHICSE Technical Report : Multigrid methods combined with low-rank approximation for tensor structured Markov chains

Tensor low-rank and sparse light field photography

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

Structure Modeling of High Dimensional Data

Low-Rank Tensor Methods for Communicating Markov Processes

Graph Chatbot

Chattez avec Graph Search

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

A Fourier dimensionality reduction model for big data interferometric imaging

MATHICSE Technical Report : Perturbation of higher-order singular values

Fourier dimensionality reduction of radio-interferometric data

Tensor low-rank and sparse light field photography

MATHICSE Technical Report : Multigrid methods combined with low-rank approximation for tensor structured Markov chains

Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

Structure Modeling of High Dimensional Data

Low-Rank Tensor Methods for Communicating Markov Processes

Multilinear Low-Rank Tensors on Graphs & Applications