Piecewise affine and support vector models for robust and low complex regression

Function representation defined with a relatively small number of parameters in the relationship between input and output of the system provides a way of data reduction and compression. One of the main contributions of the thesis is to develop the function representation and optimization methods applied to be a given finite set of input-output sample data. At the beginning, an adequate theoretical background and also a guide for the study of function representations in the literature are described for reader. Next, novel studies on function representation are presented. First of all, a robust and low complex regression models by introducing new loss functions for rejecting outliers and noises, and l_p with p?1 norms for model parameters in order to reduce model complexity in support vector regression are developed. After that, to ignore the small errors less than a predetermined number (epsilon), the ? insensitive least squares support vector nonlinear regression is proposed and their associated solutions are compared with standard least square regression and support vector regression in a qualitative way. Another contribution of this thesis is the new type of kernel which is called piecewise linear kernel where feature space is explicitly given with a piece-wise linear mapping from the input space. The support vector regression is formulated by using the new kernel. Finally, for piecewise affine representation, input-output clustering method is proposed and applied to the real ECG data.