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.

Statnote 31:analysis of covariance

Analysis of covariance (ANCOVA) is a useful method of ‘error control’, i.e., it can reduce the size of the error variance in an experimental or observational study. An initial measure obtained before the experiment, which is closely related to the final measurement, is used to adjust the final measurements, thus reducing the error variance. When this method is used to reduce the error term, the X variable must not itself be affected by the experimental treatments, because part of the treatment effect would then also be removed. Hence, the method can only be safely used when X is measured before an experiment. A further limitation of the analysis is that only the linear effect of Y on X is being removed and it is possible that Y could be a curvilinear function of X. A question often raised is whether ANCOVA should be used routinely in experiments rather than a randomized blocks or split-plot design, which may also reduce the error variance. The answer to this question depends on the relative precision of the difference methods with reference to each scenario. Considerable judgment is often required to select the best experimental design and statistical help should be sought at an early stage of an investigation.