Potential Graduate Research Projects

The following projects are indicative of my own research interests, which broadly covers signal processing, information theory, computational intelligence and control. All research students who work under my supervision are expected to go through a process whereby the scope and plan for their own research projects are defined. Projects are not limited to the ones listed here.

** Enquires from potential graduate students are welcome.

Tensor Decomposition: Applications to Signal Processing

Engineers are generally familiar with vectors and matrices. In order to compactly represent and logically comprehend the data contained in these structures, they are often decomposed into fundamental elements. Various decomposition techniques such as linear transformations, matrix factorization, principal/independent component analysis have been developed. These techniques have been used for blind source separation, dimensionality reduction, feature extraction, clustering, classification, and visualization.

The more common use of multi-sensor technology generates data that are not only multi-dimensional but also of different variety (images, time series, discrete data). Tensors are multi-dimensional generalizations of matrices which provide a natural vehicle to provide "multi-way" analysis of such data. Tensor decompositions have previously been applied to audio, image and video processing, machine learning and computational neuroscience applications.

While standard tensor models and relatively efficient computational algorithms are relatively well established, there remains a number of important analytical and computational challenges to be tackled.

Development of a Non-Stochastic Network Information Theory

Network control systems consist of spatially separated elements (actuators, sensors, controllers) which communicate with each other through a wired or wireless network. The analysis of such systems therefore require us to combine the two different disciplines of communication and control. It is natural to see how Shannon's information theory can be applied to study the limits of network control systems.

The performance of communication systems is measured in an average sense. In contrast, for control systems, performance must be guaranteed all the time, not just on average. Hence it is a bit tricky to apply the standard information theory which models variables as random variables with a probability distribution, directly to network control, which need to treat uncertainties as bounded unknown without a need for a statistical structure.

There has recently been some work towards a non-stochastic information theory that is useful for point-to-point analysis. This project aims to extend it to a communication network setting.

Autonomous Collective Robotics

Swarm or collective robotics is the study of the control and emergent behaviour of a large number of relatively simple autonomous robots which interacts with other similar robots in their near vicinity and with their environment. It has been demonstrated that relatively simple interaction rules can produce a number of complex swarm behaviour (e.g. flocking). This is similar to the similar behaviour observed in nature.

Unfortunately, the underlying mathematical theory for this kind of behaviour is not well established. This project aims to study how the theory of coupled oscillators can be used as the foundation of such a mathematical theory so that such swarm behaviour could be predicted.