iccv iccv2013 iccv2013-295 iccv2013-295-reference knowledge-graph by maker-knowledge-mining
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Author: Stefanos Zafeiriou, Irene Kotsia
Abstract: Kernels have been a common tool of machine learning and computer vision applications for modeling nonlinearities and/or the design of robust1 similarity measures between objects. Arguably, the class of positive semidefinite (psd) kernels, widely known as Mercer’s Kernels, constitutes one of the most well-studied cases. For every psd kernel there exists an associated feature map to an arbitrary dimensional Hilbert space H, the so-called feature space. Tdihme mnsaiionn reason ebreth sipnadc ep s Hd ,ke threne slos’-c c aplolpedul aferiattyu rise the fact that classification/regression techniques (such as Support Vector Machines (SVMs)) and component analysis algorithms (such as Kernel Principal Component Analysis (KPCA)) can be devised in H, without an explicit defisnisiti (oKnP of t)h)e c feature map, only by using athne xkperlniceitl (dtehfeso-called kernel trick). Recently, due to the development of very efficient solutions for large scale linear SVMs and for incremental linear component analysis, the research to- wards finding feature map approximations for classes of kernels has attracted significant interest. In this paper, we attempt the derivation of explicit feature maps of a recently proposed class of kernels, the so-called one-shot similarity kernels. We show that for this class of kernels either there exists an explicit representation in feature space or the kernel can be expressed in such a form that allows for exact incremental learning. We theoretically explore the properties of these kernels and show how these kernels can be used for the development of robust visual tracking, recognition and deformable fitting algorithms. 1Robustness may refer to either the presence of outliers and noise the robustness to a class of transformations (e.g., translation). or to ∗ Irene Kotsia ,†,? ∗Electronics Laboratory, Department of Physics, University of Patras, Greece ?School of Science and Technology, Middlesex University, London i .kot s i @mdx . ac .uk a
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