Περίληψη:
Kernel discriminants are greatly appreciated because 1) they permit to
establish nonlinear boundaries between classes and 2) they offer the
possibility of visualizing graphically the data vectors belonging to
different classes. One such method, called Generalized Discriminant
analysis (GDA) was proposed by Baudat and Anouar (2000). GDA operates on
a kernel matrix of size N x N, (N denotes the sample size) and is for
large N prohibitive. Our aim was to find out how this method works in a
real situation, when dealing with relatively large data. We considered a
set of predictors of erosion risk in the Kefallinia island categorized
into five classes of erosion risk (together N=3422 data items). Direct
evaluation of the discriminants, using entire data, was computationally
demanding. Therefore, we sought for a representative sample. We found it
by a kind of sieve algorithm. It appeared that using the representative
sample, we could greatly speed up the evaluations and obtain
discriminative functions with good generalization properties. We have
worked with Gaussian kernels which need one declared parameter SIGMA
called kernel width. We found that for a large range of parameters the
GDA algorithm gave visualization with a good separation of the
considered risk classes.
Συγγραφείς:
Bartkowiak, Anna
Evelpidou, Niki
Vasilopoulos, Andreas
