EFFECTS OF DATA REDUCTION METHODS ON THE PERFORMANCE OF STATISTICAL NEURAL NETWORKS IN MEDICAL APPLICATIONS Gökhan Bilgin Bülent Bolat Tülay Yıldırım e-mail: gokhanb@ce.yildiz.edu.tr 1 e-mail: bbolat@yildiz.edu.tr 2 e-mail: tulay@yildiz.edu.tr 2 Yıldız Technical University, Faculty of Electrical and Electronics, (1) Department of Computer Engineering, (2) Department of Electronics & Communication Engineering, 34349, Besiktas, Istanbul, Turkey Key words: Dimension reduction, statistical neural networks, linear projections, nonlinear kernel methods ABSTRACT Statistical neural networks are good pattern recognition structures. Basic problems of these networks which are known for their high accuracy results in most applications are excessive memory consumption and computational complexity. One way of solving computational complexity problem is to reduce the dimensions of feature vectors. Since developing medical data acquisition tools produce increasing amount of data, interest of scientists has been attached to this problem. In this work success of different types of data reduction methods have been examined and compared. As a result of experiments it is figured out that it is possible to reduce the computational load without lowering accuracy in these networks via data reduction. I. INTRODUCTION Statistical Neural Networks are known as good classifiers. In many applications, these networks can perform better than others. However in these structures, memory requirement and computational complexity are extremely high. By adding new instances to the training set, these problems grow faster. To maintain these weaknesses the training set may be reduced, but a reduced training set may lower the accuracy of the network. Being a solution to that problem, size of the feature vector may be shrunken by some rule, which is called as dimension reduction. In the literature there are many dimension reduction techniques such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Kernel-PCA (KPCA) and Kernel-LDA (KLDA). In this work, the effects of these reduction techniques on statistical neural networks are analyzed. To compare the performances of these methods, three datasets which are taken from UCI MLREP Database [1] (which are New Thyroid, Pima Indian Diabetes and Wisconsin Breast Cancer -WBCD-) are used. Since these datasets are well-known, details of them are not included in this work; but for further information, see [1-7]. Section 2 describes the statistical networks briefly. Dimension reduction methods are introduced in section 3. In sections 4 and 5, details of the applications and results are proposed. II. STATATISTICAL NEURAL NETWORKS Simply, statistical neural networks combine statistical techniques with neural network structures. Radial basis function neural networks (RBF), generalized regression neural networks (GRNN) and probabilistic neural networks (PNN) are main well-known supervised structures which are explained briefly following in subsections RADIAL BASIS FUNCTION N.N. (RBFN) RBF Networks typically have three layers: an input layer, a hidden layer and an output layer. Input and output layers are related to the input vector space and the pattern classes respectively. Hence, the entire structure is degraded to determine the hidden layer’s centers and weights between hidden and output layers. Activation function of j th hidden layer neuron is defined by a center (C i ) and a bandwidth (σ i ). The activation function is a Gaussian curve defined as ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ − − = 2 2 2 exp ) ( j j j C X X σ ϕ (1) Output of the j th output neuron is found by ∑ = + = K i j i ij j b X w X s 1 ) ( ) ( ϕ (2) where ω ij is the weight between the i th hidden neuron and j th output neuron, K is the number of the neurons in the hidden layer [8]. GENERALIZED REGRESSION N.N. (GRNN) GRNN is a special case of RBF where the centers and bandwidths are determined by the training data. Alternatively, learning phase of a GRNN is not iterative. In the GRNN structure, i th training vector x i is the center