Multiple Classifier Systems Incorporating Uncertainty

The inclusion of uncertain class information into multi classifier systems (MCS) is the central theme in this thesis. A multi classifier system relies on multiple base classifiers, each of which is trained on a separate view of the problem at hand. Combining their answers will lead to a more accurate final decision. An example would be emotion recognition, with decisions based on observations of the mouth, the eyes or the pitch of the voice. Traditionally in classification one sample is associated with exactly one class, for example anger. But, in practical applications, such a hard distinction is not warranted; instead a sample should have soft class memberships, thus being associated fuzzily with multiple classes at the same time. The inclusion of this uncertain information into various, but isolated building blocks of a MCS has been tackled by a great many researchers. This thesis places these approaches in the greater MCS context and assesses their utility. Remaining problems are identified and in many cases a solution is proposed. Bayesian probability is the most obvious tool for modelling class uncertainty, but perhaps the Dempster-Shafer theory of evidence, fuzzy logic or fuzzy sets, or even a distribution of opinions are much more viable in a classification context. These formal uncertainty theories, as well as some others, are assessed regarding their aptitude to support the core flavours of uncertainty in MCS, as identified in this work: vagueness, imprecision, and certainty. For the very fitting Dempster-Shafer theory, practical applications are reported. Some base classifiers have been extended to be trained on and answer with uncertain labels: learning vector quantisation, self-organizing maps, and most notably support vector machines (SVMs). The latter are an already very powerful breed of classifiers, and based on the idea of duplication, the underlying optimisation problem could be altered to accept fuzzy labels. Obtaining soft outputs from the binary SVMs is not trivial, but complete solutions are provided for the Onevs-Rest and One-vs-One multiclass decomposition architectures. Experiments do confirm the effectiveness of the fuzzy trained machines over their hard trained