Abstract-The geometric framework for the support vector machine (SVM) classification problem provides an intuitive ground for the understanding and the application of geometric optimization algorithms, leading to practical solutions of real world classification problems. In this work, the notion of "reduced convex hull" is employed and supported by a set of new theoretical results. These results allow existing geometric algorithms to be directly and practically applied to solve not only separable, but also nonseparable classification problems both accurately and efficiently. As a practical application of the new theoretical results, a known geometric algorithm has been employed and transformed accordingly to solve nonseparable problems successfully.
Abstract-Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex Reproducing Kernel Hilbert Spaces, developed a suitable Wirtinger-like Calculus for general Hilbert Spaces. In this short paper, the extended Wirtinger's calculus is adopted to derive complex kernel-based widely-linear estimation filters. Furthermore, we illuminate several important characteristics of the widely linear filters. We show that, although in many cases the gains from adopting widely linear estimation filters, as alternatives to ordinary linear ones, are rudimentary, for the case of kernel based widely linear filters significant performance improvements can be obtained.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.