The Performance of Statistical Pattern Recognition Methods in High Dimensional Settings

We report on an extensive simulation study comparing eight statistical classiication methods, focusing on problems where the number of observations is less than the number of variables. Using a wide range of artiicial and real data, two types of classiiers were contrasted; methods that classify using all variables, and methods that rst reduce the number of dimensions to two or three. The full feature space methods include linear, quadratic and regularized discriminant analysis, and the nearest neighbour method. The four dimensionality reducing classiiers are characterized by the transform they implement. The four transforms compared are the Fisher discriminant plane, the Fisher-Fukunaga-Koonz, the Fisher-radius, and the Fisher-variance transforms. The Fisher-Fukunaga and the Fisher-radius transform based classiiers have recently been proposed for two class classiication problems. We also present an extension to these transforms such that they can be applied to classiication problems with arbitrary numbers of classes. The simulations identiied reg-ularized discriminant analysis as the overall clearly most powerful classiier. The results show that in most cases, a reduction of the dimensionality to two or three dimensions prior to classiication decreases the probability of correctly allocating test observations.