The module descriptor for the project is here.

Please see me or send me mail at R.M.Everson@exeter.ac.uk if you would like more details or want to talk about a completely different project.

• Clustering non-stationary data
• Bayesian Generative Topographic Mapping
• Curvature in high dimensional spaces
• Pattern Recognition in Python
• Combining decision trees
• Particle Swarm Optimisation

Clustering non-stationary data

Clustering is an important unsupervised method for visualising, modelling and understanding data. There is a wide variety of methods for obtaining clusters from data, though many of them are very ad hoc. When the data themselves change with time the problem is harder as clusters may move, split and merge. This project aims to produce principled methods of clustering non-stationary data, probably using particle filter methods. Particular application areas include clustering neuronal spike trains and segmentation of image sequences.

The project would suit someone who is comfortable with mathematical manipulations.

Bayesian Generative Topographic Mapping

GTM is a principled alternative to Self Organising Maps useful for modelling and visualising high-dimensional data. The parameters of the GTM model are conventionally learned using the Expectation-Maxisation algorithm to find maximum likelihood solution.

This project would develop a Bayesian Markov Chain Monte Carlo method for the GTM model, bringing the benefits of automatic model selection, robustness and confidence intervals. Although useful for visualisation, the main application is to nonlinear Independent Component Analysis. This project provides the opportunity of learning and applying Bayesian MCMC methods to deal with nonlinear problems. The project would suit someone who is comfortable with mathematical manipulations.

Curvature in high dimensional spaces

It is often important to visualise high-dimensional data and a number of tools, such as the Generative Topographic Mapping, Self Organising Maps, Locally Linear Embedding and Isomap have been developed to map manifolds in high dimensions down into a few dimensions. Additionally one would often like to know the curvature of the manifold as it provides information on how rapidly quantities vary.

This project is to investigate and develop methods of quantifying the curvature of manifolds specified only by data points in a high dimensional space. It provides an opportunity to learn about and apply various visualisation methods and to investigate ideas about curvature on manifolds.

Pattern Recognition in Python

Python is a relatively new, free, object-oriented scripting language. It has the ability to easily components from other languages and is developing a wide base of users. Building on the numerical capabilities of Python, this project would build a suite of Pattern Recognition tools for use in research. The objected-oriented, modular nature of Python should permit a very powerful toolbox. I anticipate that the project would include analogues of the routines in Netlab together with some more advanced methods.

Combining decision trees

Decision trees are a widely used as classifiers that are easily implemented, rapidly trained and allow some insight to be gained into the way in which a classification is reached.

Classifiers can be combined to give an average answer by voting or by some method that gives each classifier a vote proportional to how reliable the classifier thinks it is. This project would explore ways of combining decision trees using the Bayesian evidence.

Particle Swarm Optimisation

Swarm intelligence (SI) is an artificial intelligence technique involving the study of collective behaviour in decentralised systems. Such systems are made up by a population of simple agents interacting locally with one other and with their environment. Swarm-like algorithms, such as particle swarm optimisation (PSO), have already been applied successfully to solve real-world optimisation problems, and has many features in common with evolutionary algorithms (EA).

The PSO heuristic has traditionally been applied to optimisation of single objective problems, however in 2002 a number of papers introduced extensions to the general model to allow search in multi-objective domains. Due to this transition however it is obvious that there is no longer a single "best" solution for the particles to fly towards, but rather a set representing a curve or surface. Current work in the field is greatly concerned with ensuring coverage of this set and investigating the most efficient way to alter a particle's trajectory in order to promote rapid convergence to the "best" solutions. This project aims to investigate the area of multi-objective PSO, by investigating a number current points of concern: Should a particle fly toward fit areas in objective space that are close in decision space or further away, or combination of the two? Should they be concerned with flying away from unfit regions of decision space as well as flying towards fit regions? How does the search progress with different swarm sizes in relation to convergence speed?

This project would be in conjunction with Jonathan Fieldsend.