Wavelet-Based Visual Analysis of Dynamic Networks

Abstract

Dynamic networks naturally appear in a multitude of applications from different fields. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. In this work, we propose a novel visual analytics methodology for dynamic networks, which relies on the spectral graph wavelet theory. We enable the automatic analysis of a signal defined on the nodes of the network, making viable the robust detection of network properties. Specifically, we use a fast approximation of a graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The coefficients naturally encode the spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This methodology allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using usage scenarios and comparisons involving real dynamic networks.

On the Use of Vertex-Frequency Analysis for Anomaly Detection in Graph Signals

“…In [19], the authors applied GFT and high-pass filtering for detecting anomalies in the whole network, but without providing any clue about where is the corrupted measurement. In [20] a graph-filtering-based method is developed to identify anomalies in wireless sensor networks, and in [21] the SGWT is used to identify patterns in dynamic networks. Centrality measures of graphs, such as node degree, shortest path distance, and entries of u N , have also been used as extracted features to feed anomaly detectors [22].…”

Visualizing demographic evolution using geographically inconsistent census data

“…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].…”

“…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.…”

“…Using data clustering, we can represent the region's cluster instead of all the its variables [2], [20], [22]. While this simplifies the geographic portion of the visualization, it introduces the problem of how to summarize the contents of each cluster.…”

Processamento de sinal em grafos: Teoria de amostragem e sua aplicação no aprendizado semi-supervisionado ativo

“…Existe um grande número de aplicações que podem beneficiar-se da teoria de processamento de sinais em grafos, tais como a análise de redes sociais (HAND, 2010), rede de sensores (ZHU; RABBAT, 2012), processamento de imagens (NARANG; CHAO; ORTEGA, 2012), sistemas de recomendação (NARANG; GADDE; ORTEGA, 2013), detecção de comunidades ( agrupamento em grafos) (TREMBLAY; BORGNAT, 2014;DONG et al, 2014), aprendizado semi-supervisionado (GADDE; ANIS; ORTEGA, 2014), visualização de grafos dinâmicos (VALDIVIA et al, 2015;COL et al, 2018) e reconstrução do sinal de grafo (CHEN et al, 2014;.…”