Discriminant analysis using wavelet derived features
This thesis examines the ability of the wavelet transform to form features which may be used successfully in a discriminant analysis. We apply our methods to two different data sets and consider the problem of selecting the 'best' features for discrimination. In the first data set, our interest is in automatically recognising the variety of a carrot from an image. After necessary image preprocessing we examine the usefulness of shape descriptors and texture features for discrimination. We show that it is better to use the different 'types' of features separately, and that the wavelet coefficients of the outline coordinates are more useful. In the second data set we consider the task of automatically identifying individual haddock from the sounds they produce. We use the smoothing property of wavelets to automatically isolate individual haddock sounds, and use the stationary wavelet transform to overcome the shift dependence of the standard wavelet transform. Again we calculate different 'types' of wavelet features and compare their usefulness in classification and show that including information on the source of the previous sound can substantially increase the correct classification rate. We also apply our techniques to recognise different species of fish which is also highly successful. In each analysis, we explore different allocation rules via regularised discriminant analysis and show that the highest classification rates obtained are only slightly better than linear discriminant analysis. We also consider the problem of selecting the best subset of features for discrimination. We propose two new measures for selecting good subsets and using a genetic algorithm we search for the 'best' subsets. We investigate the relationship between out measures and classification rates showing that our method is better than selection based on F-ratios and we also discover that our two measures are closely related.