Fábio L. Dias

Wavelet-based visualization of time-varying data on graphs

Visualizing time-varying data defined on the nodes of a graph is a challenging problem that has been faced with different approaches. Although techniques based on aggregation, topology, and topic modeling have proven their usefulness, the visual analysis of smooth and/or abrupt data variations as well as the evolution of such variations over time are aspects not properly tackled by existing methods. In this work we propose a novel visualization methodology that relies on graph wavelet theory and stacked graph metaphor to enable the visual analysis of time-varying data defined on the nodes of a graph. The proposed method is able to identify regions where data presents abrupt and mild spacial and/or temporal variation while still been able to show how such changes evolve over time, making the identification of events an easier task. The usefulness of our approach is shown through a set of results using synthetic as well as a real data set involving taxi trips in downtown Manhattan. The methodology was able to reveal interesting phenomena and events such as the identification of specific locations with abrupt variation in the number of taxi pickups.

Topological Analysis of Inertial Dynamics

Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N-body systems both in 2D and 3D.

The 2009 earthquake, magnitude mb 4.8, in the Pantanal Wetlands, west-central Brazil

The main goal of this paper is to characterize the Coxim earthquake occurred in June 15th, 2009 in the Pantanal Basin and to discuss the relationship between its faulting mechanism with the Transbrasiliano Lineament. The earthquake had maximum intensity MM V causing damage in farm houses and was felt in several cities located around, including Campo Grande and Goiânia. The event had an mb 4.8 magnitude and depth was 6 km, i.e., it occurred in the upper crust, within the basement and 5 km below the Cenozoic sedimentary cover. The mechanism, a thrust fault mechanism with lateral motion, was obtained by P-wave first-motion polarities and confirmed by regional waveform modelling. The two nodal planes have orientations (strike/dip) of 300°/55° and 180°/55° and the orientation of the P-axis is approximately NE-SW. The results are similar to the Pantanal earthquake of 1964 with mb 5.4 and NE-SW compressional axis. Both events show that Pantanal Basin is a seismically active area, under compressional stress. The focal mechanism of the 1964 and 2009 events have no nodal plane that could be directly associated with the main SW-NE trending Transbrasiliano system indicating that a direct link of the Transbrasiliano with the seismicity in the Pantanal Basin is improbable.

A Hierarchical Network Simplification via Non-Negative Matrix Factorization

Visualization tools play an important part in assisting analysts in the understanding of networks and underlying phenomena. However these tasks can be hindered by visual clutter. Simplification/decimation schemes have been a main alternative in this context. Nevertheless, network simplification methods have not been properly evaluated w.r.t. their effectiveness in reducing complexity while reserving relevant structures and content. Moreover, most simplification techniques only consider information extracted from the topology of the network, altogether disregarding additional content. In this work we propose a novel methodology to network simplification that leverages topological information and additional content associated with network elements. The proposed methodology relies on non-negative matrix factorization (NMF) and graph matching, combined to generate a hierarchical representation of the network, grouping the most similar elements in each level of the hierarchy. Moreover, the matrix factorization is only performed at the beginning of the process, reducing the computational cost without compromising the quality of the simplification. The effectiveness of the proposed methodology is assessed through a comprehensive set of quantitative evaluations and comparisons, which shows that our approach outperforms existing simplification methods.