Theme III: High-Dimensional Data Analysis on Graphs and Networks
Participants:
- CS - P. Devanbu, I. Tagkopoulos
- ECE - C.-N. Chuah, Z. Ding
- Math - R. Chaudhuri, N. Saito
- Stat - A. Aue, K. Balasubramanian, S. Chen, T. Lee, C. Le, X. Li, D. Paul, J. Sharpnack
Graphs and networks play a crucial role in modern data analysis as they help study the interaction and relationship between various objects represented as the nodes in a graph. We can easily observe such problems in truly diverse fields: biology and medicine (analyzing data measured on neuronal networks); computer science (analyzing friendship relations in social networks); electrical engineering (monitoring and controlling sensor networks); geology (measuring stream flows in a ramified river network); and civil engineering (monitoring traffic flow on a road network), to name just a few.
Our research aims to study the impact of spatial and time information to networks. For example, in a sensor network scenario (e.g., a network of electrodes placed along the scalp in the EEG setting to record electrical activity of the brain), one measures and records time series of interest at each sensor node, and analyze them as a whole and make important prediction and diagnostics. Moreover, each measured time series almost always consists of multicomponent signals, i.e., signals that result from a combination of events originated from different sources/causes. In many such scenarios, we need to address the spatial distribution of measurement locations (i.e., the 'x'-axis) and the time series themselves measured in time (i.e., the 't'-axis) separately. Often the former is irregularly sampled while data in the latter domain always contain transient events and are non-stationary although they may be regularly sampled with the sampling rate Δt. These represents serious mathematical, computational, and statistical challenges.
The collective expertise and work of the UCD4IDS Data Analysis on Graphs & Networks team are truly impressive and ideal to tackle those modern graph data analysis by developing new and fundamental tools and investigating important problems, particularly in biological and medical applications.
Our research projects in this theme include:
- Hypergraphs and tensors
- Collective computation in distributed neural systems
- High-volume neural data analysis
- Anomaly and change detections over networks
- Random matrix theory for network applications
- Network adaptation for machine learning