22. M. Aladjem, (1998) "Nonparametric discriminant
analysis via recursive optimization of PatrickFisher distance", IEEE
Trans. on Syst. ,Man, Cybern, vol. 28B, No 2, pp. 292299.
23. M. Aladjem, (1998) "Supervised learning of a neural network for classification via successive modification of the training data  an experimental study " in A.P. del Pobil, J.Mira and M.Ali (eds.), Lecture Notes in Artificial Intelligence11th Int. Conf. on Industrial & Engineering Applications of the Artificial Intelligence & Expert Systems (IEA/AIE98), Vol. II, Benicassim, Castellon (Spain), June 14, 1998, Springer, 593602. 24. M. Aladjem, (1998) "Training of an ML neural
network for classification via recursive reduction of the class separation",
14th
Int. Conf. on Pattern Recognition, Brisbane, Queensland, Australia,
August 1720, 1998, IEEE Computer Society Press, (in press).
25. M. Aladjem, (1998) "Linear discriminant analysis
for two classes via recursive neural network reduction of the class separation
",
in A.Amin and P.Pudil (eds.), Lecture Notes in Computer Science
2nd Int. Workshop on Statistical Techniques in Pattern Recognition,
Sydney, Australia, August 1113, 1998, Springer, (in press).

In conference paper [25] we discuss discriminant analysis
of two classes which is carried out by a linear mapping, which maximizes
the PatrickFisher (PF) distance. The PF distance is a highly nonlinear
function with respect to the mapping, and has more than one maximum.
In [22] we proposed a recursive method which searches for several large
local maxima of the PF distance via successive “reduction of the class
separation”. In this work we generalize this method. We propose a neural
network (NN) implementation of the procedure for “reduction of the class
separation”, which increases its efficacy. We use an autoassociative multilayer
network having nonlinear activation functions instead of a linear transformation
performed in our previous work [22]. This increases the computational complexity,
which is the price we pay in order to gain the following advantages:
1. The NN implementation improves the preservation of
the training data: Our method, proposed in [22], exactly preserves
the data in the subspace orthogonal to the vector which is the object of
the reduction of the class separation. The NN implementation, by performing
highly nonlinear data transformation, increases the range of data preservation,
which is demonstrated by the experiments explained in the conference paper
[25].
2. The NN implementation can be applied for reduction
of the class separation of the nonlinear classification functions:
Actually, by using the autoassociative network, we overcome the use of
an orthonormal linear transformation . This makes it possible to apply
NN implementation for the nonlinear classification functions. Using this
feature of the NN implementation, we proposed a method for recursive training
of a multilayer (ML) neural network for classification (conference
papers [23,24]). We have compared our method and conventional training
with random initialization of the weights using a synthetic data set and
the data set of an OCR problem for discrimination the uppercase handwritten
letters “M” and the lowercase handwritten letters “m”. The results obtained
confirm the efficacy of our method which finds solutions with lower misclassification
errors than does conventional training.
