Ph.D. THESIS PROPOSAL

TITLE: From spatio-temporal data to functional weighted networks: methods and 
applications in climate science, neuroscience and ecology.

Ilias Fountalis
School of Computer Science
College of Computing
Georgia Institute of Technology

Date: Wednesday, December 3, 2014
Time: 11:00 AM - 1:00 PM
Location: KACB 3100

Committee:
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Prof. Constantine Dovrolis, School of Computer Science, GeorgiaTech 
(Advisor)
Prof. Mostafa H. Ammar, School of Computer Science, GeorgiaTech
Prof. Annalisa Bracco, Earth and Atmospheric Sciences Department, 
GeorgiaTech
Assistant Prof. Bistra Dilkina,  School of Computational Science and 
Engineering, GeorgiaTech
Associate Prof. Shella Keilholz, Wallace H. Coulter Department of 
Biomedical Engineering, GeorgiaTech and Emory University School of Medicine
Prof. Athanasios Nenes, Earth and Atmospheric Sciences Department, 
GeorgiaTech

Abstract:
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There is an abundance of spatio-temporal data today from diverse complex 
systems such as the Earth's climate, the human brain, or the mobility 
patterns of migratory species. By analyzing such data, scientists are 
able to discover the key modules of the corresponding system, and to 
investigate their dynamics and inter-dependencies.

Spatio-temporal data are typically embedded in a two- or 
three-dimensional grid, and the dynamics of each grid cell are 
represented by a time-series. Common computational analysis methods for 
such data include standard time series analysis, spatial clustering, and 
principal/independent component analysis. These techniques, although 
valuable in specific contexts, are not able to directly identify the 
latent functional components of the system and how these components 
interact with each other. This objective can be met more naturally with 
a framework that is based on network analysis.

The emerging field of network analysis incorporates a broad range of 
models, metrics and algorithms to study complex nonlinear dynamical 
systems; its main premise is that the underlying topology or network 
structure of a system has a strong impact on its dynamics and evolution.

We propose a novel network-based analysis framework for the study of 
spatio-temporal data. First, we cluster grid-cells into "areas", defined 
as spatially coherent regions that are highly homogeneous in terms of 
dynamics. The proposed algorithm identifies a parsimonious set of latent 
functional components, and it relies on a single parameter that is set 
based on a target statistical significance level. In a second step, we 
identify edges between areas. The strength of the edge between two areas 
is given by the covariance of their cumulative anomaly time series. Each 
edge is also characterized by the lag at which the cross-correlation 
between the two areas is maximum, in absolute sense.

The proposed framework has been applied successfully in Climate Science 
to evaluate state-of-the-art climate models and to assess their 
performance. Further, we have investigated future projections of these 
models' trajectories under increased greenhouse gas emission scenarios. 
We are going to also apply the proposed method on functional MRI data to 
construct dynamic functional brain networks. Finally, we will apply the 
proposed framework in the context of Ecology, to investigate bird 
migration patterns.