Statistical classification procedures for analyisng functional data
Thesis (MCom)--Stellenbosch University, 2016.
ENGLISH SUMMARY : Functional data are obtained through the measurement of one or more variables at a set of discrete evaluation points over a continuum such as time, wavelength or values of a spatial variable. Functional extensions of traditional statistical methods are considered in the analyses of such data sets, which are typically comprised of a sample of functions. Linear discriminant analysis for functional data and functional support vector machines are investigated in this thesis as binary functional classification procedures. To address the high correlations which typically exist amongst the input features of a functional data set, the fused lasso, which selects contiguous intervals of variables, is discussed. In addition, a sparse equivalent of partial least squares (SPLS), which achieves simultaneous variable selection and dimension reduction, is considered in a functional context. An infrared spectroscopy data set is considered for practical implementation of the fore mentioned functional data analysis techniques. The procedures are compared in terms of classification accuracy and variable selection properties, reported in the results of an empirical study.
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