Diffusion filtering of graph signals and its use in recommendation systems

Ma, Jie; Huang, Wen; Segarra, Santiago; Ribeiro, Alejandro

doi:10.1109/icassp.2016.7472541

Cited by 31 publications

(32 citation statements)

References 31 publications

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“…There are also several variants of the graph Laplacian [73] such as the symmetric normalized graph Laplacian L sym = D −1/2 LD −1/2 that factors out differences in degree and is thus only reflecting relative connectivity, or the random-walk normalized graph Laplacian: L rw = D −1 L. Generalizations of the graph Laplacian also exist for graphs with negative weights [45], [74].…”

Section: A Graph Fourier Transformmentioning

confidence: 99%

A Graph Signal Processing Perspective on Functional Brain Imaging

et al. 2018

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Modern neuroimaging techniques provide us with unique views on brain structure and function; i.e., how the brain is wired, and where and when activity takes place. Data acquired using these techniques can be analyzed in terms of its network structure to reveal organizing principles at the systems level. Graph representations are versatile models where nodes are associated to brain regions and edges to structural or functional connections. Structural graphs model neural pathways in white matter that are the anatomical backbone between regions. Functional graphs are built based on functional connectivity, which is a pairwise measure of statistical interdependency between activity traces of regions. Therefore, most research to date has focused on analyzing these graphs reflecting structure or function.Graph signal processing (GSP) is an emerging area of research where signals recorded at the nodes of the graph are studied atop the underlying graph structure. An increasing number of fundamental operations have been generalized to the graph setting, allowing to analyze the signals from a new viewpoint. Here, we review GSP for brain imaging data and discuss their potential to integrate brain structure, contained in the graph itself, with brain function, residing in the graph signals. We review how brain activity can be meaningfully filtered based on concepts of spectral modes derived from brain structure. We also derive other operations such as surrogate data generation or decompositions informed by cognitive systems. In sum, GSP offers a novel framework for the analysis of brain imaging data.

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Section: A Graph Fourier Transformmentioning

confidence: 99%

A Graph Signal Processing Perspective on Functional Brain Imaging

et al. 2018

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“…The benefits of incorporating network information into signal analysis has been demonstrated in multiple domains. Notable examples of applications include video compression [9], rating predictions in recommendation systems [10], and breast cancer diagnostics [11], and semi-supervised learning [12].…”

Section: Introductionmentioning

confidence: 99%

Graph Frequency Analysis of Brain Signals

Huang

Goldsberry

Wymbs

et al. 2016

IEEE J. Sel. Top. Signal Process.

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This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains, and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations. We relate graph frequency with principal component analysis when the networks of interest denote functional connectivity. The methods are utilized to analyze brain networks and signals as subjects master a simple motor skill. We observe that brain signals corresponding to different graph frequencies exhibit different levels of adaptability throughout learning. Further, we notice a strong association between graph spectral properties of brain networks and the level of exposure to tasks performed, and recognize the most contributing and important frequency signatures at different levels of task familiarity.

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“…GSP merges algebraic and spectral graph theory with computational harmonic analysis to process such signals on graphs. GSP has resulted in advanced solutions to manifold applications, such as computational science [5], image analysis [6] and recommendation system [7,8]. Moreover, GSP can be used to extend convolutional neural networks (CNNs) to graph data, which is called graph convolutional networks (GCNs) [9].…”

Section: Introductionmentioning

confidence: 99%

“…Similar to classical frequency-domain filtering, GFs manipulate the signal by selectively amplifying or attenuating its graph frequency domain components. GFs have been adopted in applications such as signal analysis [16,17], classification [8,18], reconstruction [10,19], denoising [20,21], clustering [22] and topology identification [23].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Graph Filters: Design and Implementation

Qiu

Feng

2021

Electronics

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Existing graph filters, polynomial or rational, are mainly of integer order forms. However, there are some frequency responses which are not easily achieved by integer order approximation. It will substantially increase the flexibility of the filters if we relax the integer order to fractional ones. Motivated by fractional order models, we introduce the fractional order graph filters (FOGF), and propose to design the filter coefficients by genetic algorithm. In order to implement distributed computation on a graph, an FOGF can be approximated by the continued fraction expansion and transformed to an infinite impulse response graph filter.

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Diffusion filtering of graph signals and its use in recommendation systems

Cited by 31 publications

References 31 publications

A Graph Signal Processing Perspective on Functional Brain Imaging

A Graph Signal Processing Perspective on Functional Brain Imaging

Graph Frequency Analysis of Brain Signals

Fractional Order Graph Filters: Design and Implementation

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