Reproducing kernel hilbert space methods for cad tools - Chumachenko, S. V.; Khawar, Parvez; Gowher, Malik (EWDTW, 2004)
The review of known RKHS-methods for analysis of current state in science investigations is represented. The place of Series Summation Method in Reproducing Kernel Hilbert Space (RKHS) is determined. The new results obtained by this method are discussed. Reproducing Kernel Hilbert Space (RKHS) methods are interesting both pure theoretically and applied. RKHS theory has been a well studied topic, stemming from the original works of [1] to more recent studies on their application by [2, 3, 8-11]. Mathematical models based on RKHS and causal operators are presented in [3]. They are used at Pattern Recognition [4], Digital Data Processing [5], Image Compression [6], Computer Graphics [7]. Mentioned directions are described by mathematical tool – theory of wavelets [4]. RKHS methods are base tool in exact incremental learning [8], in statistical learning theory [2, 9]. The general theory of reproducing kernels which is combined with linear mappings in the framework of Hilbert spaces is considered in [2]. A framework for discussing the generalization ability of a trained network in the original function space using tools of functional analysis based on RKHS is introduced in [8]. Special kind of kernel based approximation scheme is also closely linked to regularization theory [10] and Support Vector Machines based approximation schemes [11] (Fig.).
Keywords: Reproducing Kernel Hilbert Space; RKHS; RKHS-methods; Series Summation Method