PhD project
Asymmetric classification methods

In supervised classification the task is to classify observations in a 
supervised way, i.e., based on training data with known classification, into 
a certain number of prespecified classes. 

Most methods of supervised classification treat all classes formally in the 
same way (for example by making the same model assumptions for all classes). 
However, in many applications there are essential differences between the 
classes. For example, in some diagnostic classification problems in medicine,
in credit scoring, fraud detection, or generally in situations where a 
homogeneous class should be distinguished from another potentially 
heterogeneous class containing "everything else" (including possible
outliers) without the possibility to specify precisely what can be expected 
there, it may be advantageous to treat the classes in an asymmetric way.

One approach is to declare one class as "the homogeneous class" and fit it 
with a standard parametric model (such as the normal distribution) whereas
the other class is characterised by a nonparametric approach. 

The project is about exploring whether, and in which way, a classifier 
can be defined in such a situation that takes into account the 
"interpretatory" differences between the classes. Such a method could be 
based on the asymmetric visualisation and dimension reduction methods 
introduced in Hennig (2004).
This could be compared to the "one-class support vector machine"
(Schoelkopf et al., 2001), discriminant analysis using class-asymmetric
loss functions and more general nonparametric classifiers.

C. Hennig:  Asymmetric linear dimension reduction for classification. 
Journal of Computational and Graphical Statistics 13 (2004), 930-945.

B.Schoelkopf, J. C. Platt, J. C. Shawe-Taylor, A. J. Smola,
and R. C. Williamson: Estimating the support of a highdimensional
distribution. Neural Computation, 13 (2001), 1443-1471.