Block GTM: Incorporating prior knowledge of covariance structure in data visualisation

Visualising data for exploratory analysis is a big challenge in scientific and engineering domains where there is a need to gain insight into the structure and distribution of the data. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are used, but it is difficult to incorporate prior knowledge about structure of the data into the analysis. In this technical report we discuss a complementary approach based on an extension of a well known non-linear probabilistic model, the Generative Topographic Mapping. We show that by including prior information of the covariance structure into the model, we are able to improve both the data visualisation and the model fit.

The factors affecting the optimal performance of eddy-current machines

This thesis presents an examination of the factors which influence the performance of eddy-current machines and the way in which they affect optimality of those machines. After a brief introduction to the types of eddy-current machine considered, the applications to which these machines are put are examined. A list of parameters by which to assess their performance is obtained by considering the machine as part of a system. in this way an idea of what constitutes an optimal machine is obtained. The third chapter then identifies the factors which affects the performance and makes a quantitative evaluation of the effect. Here the various alternative configurations and components are compared with regard to their influence on the mechanical, electromagnetic, and thermal performance criteria of the machine. Chapter four contains a brief review of the methods of controlling eddy-current machines by electronic methods using thyristors or transistors as the final control element. Where necessary, the results of previous workers in the field of electrical machines have been extended or adapted to increase the usefulness of this thesis.

Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.