The classification of incomplete vectors

Hand, David John (1977) The classification of incomplete vectors. University of Southampton, Doctoral Thesis.

Abstract

The thesis begins with a brief introduction to Pattern Recognition followed by a broad survey of the missing data problem in other fields. Possible ways to approach the problem of classifying incomplete vectors are considered. The author argues that substituting estimates for missing components usually leads to a sub-optimal classification, that decision surface methods can be applied in some cases, and that probability density function estimation can provide a general solution.A decision surface method is developed which defines the decision surfaces by point sets selected from. the training set. These point sets are selected by an edited condensed nearest neighbour rule devised by the author; the need to store points more than once is avoided by labelling the points.Two types of pdf estimation methods are defined: local and global. The local method leads to classifications obtained directly from the training set, while the global method v yields decisions via substitution in parametric estimators. The author investigates local nonparametric estimators in detail, explaining their advantages and disadvantages fdr the current application. It is argued that series estimators cannot be usefully applied to the general problem.A general model.suitable for the global method is presented, and different specialisations of it are shown. By deliberately restricting the number of comparisons between these specialisation a greater statistical validity is given to the conclusions. The constrained non-linear optimisation methods used in estimating the parameters of the models are explained, as well as initialisation methods and choice of objective functions. Further particular models suitable for the global methods are also shown.

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