Multi-graph learning of spectral graph dictionaries

Thanou, Dorina; Frossard, Pascal

doi:10.1109/icassp.2015.7178601

Cited by 13 publications

(9 citation statements)

References 21 publications

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“…The studies in [49,50,51] employ graph Fourier bases in solving multiview 3D shape analysis or clustering problems. The methods in [52,53,54] propose to use sparse signal representations on graphs via localized graph dictionaries, however in an unsupervised setting where the purpose is to reconstruct and approximate graph signals. Our preliminary study in [55], which proposes to represent label functions over graph Fourier bases, is a first attempt towards using graph signal processing techniques in domain adaptation problems.…”

Section: Related Workmentioning

confidence: 99%

Graph Domain Adaptation with Localized Graph Signal Representations

Pilavci¹,

Güneyi²,

Cengiz³

et al. 2019

Preprint

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In this paper we propose a domain adaptation algorithm designed for graph domains. Given a source graph with many labeled nodes and a target graph with few or no labeled nodes, we aim to estimate the target labels by making use of the similarity between the characteristics of the variation of the label functions on the two graphs. Our assumption about the source and the target domains is that the local behaviour of the label function, such as its spread and speed of variation on the graph, bears resemblance between the two graphs. We estimate the unknown target labels by solving an optimization problem where the label information is transferred from the source graph to the target graph based on the prior that the projections of the label functions onto localized graph bases be similar between the source and the target graphs. In order to efficiently capture the local variation of the label functions on the graphs, spectral graph wavelets are used as the graph bases. Experimentation on various data sets shows that the proposed method yields quite satisfactory classification accuracy compared to reference domain adaptation methods.

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Section: Related Workmentioning

confidence: 99%

Graph Domain Adaptation with Localized Graph Signal Representations

Pilavci¹,

Güneyi²,

Cengiz³

et al. 2019

Preprint

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“…We therefore propose to use here a spectral graph dictionary learned on a set of training images. We form the dictionary as a concatenation of subdictionaries that are polynomials of the Laplacian L of the graph G, as defined in [14], [15]. As the atoms are constructed on a polynomial kernel, they are well localized on the graph, which permits to effectively represent the local characteristics of the target images.…”

Section: Graph-based Interpolation Problemmentioning

confidence: 99%

“…We chose n = 10 for patch size, K = 5 for the degree of polynomial functions and S = 4 for the number of subdictionaries. We fix the sparsity constraint to 10% of the signal dimension in the dictionary learning algorithm [15] and we use a total of 2880 training signals on different graphs.…”

Section: A Experimental Settingsmentioning

confidence: 99%

Graph-based interpolation for zooming in 3D scenes

Akyazi

Frossard

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In multiview systems, color plus depth format builds 3D representations of scenes within which the users can freely navigate by changing their viewpoints. In this paper we present a framework for view synthesis when the user requests an arbitrary viewpoint that is closer to the 3D scene than the reference image. On the target image plane, the requested view obtained via depth-image-based-rendering (DIBR) is irregularly structured and has missing information due to the expansion of objects. We propose a novel framework that adopts a graph-based representation of the target view in order to interpolate the missing image pixels under sparsity priors. More specifically, we impose that the target image is reconstructed with a few atoms of a graph-based dictionary. Experimental results show that the reconstructed views have better PSNR and MSSIM quality than the ones generated within the same framework with analytical dictionaries, and are comparable to the ones reconstructed with TV regularization and linear interpolation on graphs. Visual results, however, show that our method better preserves the details and results in fewer disturbing artifacts than the other interpolation methods.

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“…Thus, much attention has been given to generalizing fundamental signal processing operations to the graph setting [1]- [3]. In particular, many proposals relate to extending multi-resolution transforms, filter bank designs and dictionary constructions for signals on graphs [4]- [27]. These studies fall essentially within two regimes: spatial (vertex) and spectral (frequency) designs.…”

mentioning

confidence: 99%

“…To this aim, Thanou et al [26], [27] have pursued a structured, numerical dictionary learning approach in which wavelet dictionaries are learnt based on a set of training signals. Since the graph structure is incorporated into the learning process, the learned kernels are indirectly adapted to the graph Laplacian spectrum as well as to the training data.…”

mentioning

confidence: 99%

Signal-Adapted Tight Frames on Graphs

Behjat

Richter

Ville

et al. 2016

IEEE Trans. Signal Process.

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Abstract-The analysis of signals on complex topologies modeled by graphs is a topic of increasing importance. Decompositions play a crucial role in the representation and processing of such information. Here, we propose a new tight frame design that is adapted to a class of signals on a graph. The construction starts from a prototype Meyer-type system of kernels with uniform subbands. The ensemble energy spectral density is then defined for a given set of signals defined on the graph. The prototype design is then warped such that the resulting subbands capture the same amount of energy for the signal class. This approach accounts at the same time for graph topology and signal features. The proposed frames are constructed for three different graph signal sets and are compared with non-signal-adapted frames. Vertex localization of a set of resulting atoms is studied. The frames are then used to decompose a set of real graph signals and are also used in a setting of signal denoising. The results illustrate the superiority of the designed signal-adapted frames, over frames blind to signal characteristics, in representing data and in denoising.

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Multi-graph learning of spectral graph dictionaries

Cited by 13 publications

References 21 publications

Graph Domain Adaptation with Localized Graph Signal Representations

Graph Domain Adaptation with Localized Graph Signal Representations

Graph-based interpolation for zooming in 3D scenes

Signal-Adapted Tight Frames on Graphs

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