Wavelet-based visualization of time-varying data on graphs

Valdivia, Paola; Dias, Fabio; Petronetto, Fabiano; Silva, Cláudio T.; Nonato, Luís Gustavo

doi:10.1109/vast.2015.7347624

Cited by 24 publications

(21 citation statements)

References 18 publications

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“…The idea of analyzing the behavior of graph filters with time-varying signals first appeared in [28], showing that graph filters could be analyzed by applying jointly a GFT and a Ztransform and as such they possess a joint frequency response. Since then, we have seen a number of works dealing with time-varying signals on graphs: Authors in [29] propose a method that relies on graph wavelet theory and product graphs to visualize time-varying data defined on the vertices of a graph in order to identify spatial and/or temporal variations. A step towards the graphical model has been carried out by authors in [30].…”

Section: A Related Workmentioning

confidence: 99%

A Time-Vertex Signal Processing Framework: Scalable Processing and Meaningful Representations for Time-Series on Graphs

Grassi

Loukas

Perraudin

et al. 2018

IEEE Trans. Signal Process.

149

148

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Abstract-An emerging way to deal with highdimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work aims to elevate the notion of joint harmonic analysis to a full-fledged framework denoted as Time-Vertex Signal Processing, that links together the time-domain signal processing techniques with the new tools of graph signal processing. This entails three main contributions: (a) We provide a formal motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of simple Partial Differential Equations on graphs. (b) We improve the accuracy of joint filtering operators by up-to two orders of magnitude. (c) Using our joint filters, we construct time-vertex dictionaries analyzing the different scales and the local time-frequency content of a signal. The utility of our tools is illustrated in numerous applications and datasets, such as dynamic mesh denoising and classification, still-video inpainting, and source localization in seismic events. Our results suggest that joint analysis of time-vertex signals can bring benefits to regression and learning.

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Section: A Related Workmentioning

confidence: 99%

A Time-Vertex Signal Processing Framework: Scalable Processing and Meaningful Representations for Time-Series on Graphs

Grassi

Loukas

Perraudin

et al. 2018

IEEE Trans. Signal Process.

149

148

View full text Add to dashboard Cite

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“…Instead of a collection of timeseries, the data is represented as a dynamic graph. Graph based representation of geographic information is fairly well explored in the literature, as a basis for topological methods for event detection [17], leveraging signal processing on graphs [18], [19] to find patterns and outliers [20], [21], [22]. Graphs are well suited to represent trajectories as well [2], [3], [23], allowing the use of graph visualization methods [24], [25].…”

Section: Data Representationmentioning

confidence: 99%

“…Glyphs can also be used [46], [47], but this may lead to cluttering when many small regions are present. A simpler, well adopted, option is to display a map that corresponds to a subset of the temporal information, allowing the user to change the time with an associated control [1], [17], [20], [22]. Small multiples can be used [2], but only when there are few temporal snapshots.…”

Section: Cluster Characterizationmentioning

confidence: 99%

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Visualizing demographic evolution using geographically inconsistent census data

Dias¹,

Silver²

2018

Preprint

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Video Abstract: https://youtu.be/bKeV08Os0uA Census measurements provide reliable demographic data going back centuries. However, their analysis is often hampered by the lack of geographical consistency across time. We propose a visual analytics system that enables the exploration of geographically inconsistent data. Our method also includes incremental developments in the representation, clustering, and visual exploration of census data, allowing an easier understanding of the demographic groups present in a city and their evolution over time. We present the feedback of experts in urban sciences and sociology, along with illustrative scenarios in the USA and Canada.

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“…O processamento de sinal em grafos (Graph Signal Processing -GSP) (SHUMAN et al, 2013) tem como objetivo desenvolver ferramentas para processamento de sinais definidos em grafos. Esta teoria já vem sendo aplicada na área de visualização de informação (COL et al, 2017;VALDIVIA et al, 2015). Primeiro apresentaremos a teoria matemática da transformada de Fourier em grafos (Graph Fourier Transform -GFT) para então descrevermos o processo de filtragem espectral, que é a base da metodologia proposta.…”

Section: Processamento De Sinais Em Grafosunclassified

Simplificação e análise de redes com dados multivariados

Dias¹

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As técnicas de visualização desempenham um papel importante na assistência e compreensão de redes e seus elementos. No entanto, quando enfrentamos redes massivas, a análise tende a ser prejudicada pela confusão visual. Esquemas de simplificação e agrupamento têm sido algumas das principais alternativas neste contexto. No entanto, a maioria das técnicas de simplificação consideram apenas informações extraídas da topologia da rede, desconsiderando conteúdo adicional definido nos nós ou arestas da rede.Neste trabalho, propomos dois estudos. Primeiro uma nova metodologia para simplificação de redes que utiliza tanto a topologia quanto o conteúdo associado aos elementos de rede. A metodologia proposta baseia-se na fatoração de matriz não negativa (NMF) e emparelhamento para realizar a simplificação, combinadas para gerar uma representação hierárquica da rede, agrupando elementos semelhantes em cada nível da hierarquia. Propomos também um estudo da utilização da teoria de processamento de sinal em grafos para filtrar os dados associados aos elementos da rede e o seu efeito no processo de simplificação.Palavras-chave: Redes, Agrupamento, Fatoração de matrizes não negativas, Visualização, Emparelhamento de grafos.ABSTRACT DIAS, M. D. S. S. Simplification and analysis of network with multivariate data. 2018. 81 p. Tese (Doutorado em Ciências -Visualization tools play an important role in assisting and understanding networks and their elements. However, when faced with larger networks, analytical tasks can be hindered by visual clutter. Schemes of simplification and clustering have been a main alternative in this context. Nevertheless, most simplification techniques consider only information extracted from the network topology, disregarding additional content defined in nodes or edges.In this paper, we propose two studies. First, a new methodology for network simplification that uses both topology and content associated with network elements. The proposed methodology is based on non-negative matrix factorization (NMF) and graph matching to perform the simplification, combined to generate a hierarchical representation of the network, grouping the most similar elements at each level of a hierarchy. We also provide a study of the use of the graph signal processing theory to filter data associated to the elements of a network and its effect in the process of simplification.

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Wavelet-based visualization of time-varying data on graphs

Cited by 24 publications

References 18 publications

A Time-Vertex Signal Processing Framework: Scalable Processing and Meaningful Representations for Time-Series on Graphs

A Time-Vertex Signal Processing Framework: Scalable Processing and Meaningful Representations for Time-Series on Graphs

Visualizing demographic evolution using geographically inconsistent census data

Simplificação e análise de redes com dados multivariados

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