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Functional analytic aspects of non-commutative harmonic analysis

E.G.F. Thomas
2005 Indagationes mathematicae  
EMBEDDED HILBERT SPACES, REPRODUCING KERNELS AND OPERATORS Hilbert subspaces. Let E be a locally convex space over R or C, for simplicity C.  ...  It generalizes the classical reproducing kernels K(x,y) of Hilbert subspaces of the space of continuous functions on X.  ... 
doi:10.1016/s0019-3577(05)80046-1 fatcat:3vlsyhfz6nc67ea76sfibkgbn4

Multi-lead ECG signal analysis for myocardial infarction detection and localization through the mapping of Grassmannian and Euclidean features into a common Hilbert space

Panagiotis Barmpoutis, Kosmas Dimitropoulos, Anestis Apostolidis, Nikos Grammalidis
2020 Zenodo  
In this paper we propose a novel approach for the automatic detection and localization of myocardial infarction from multi-lead electrocardiogram signals.  ...  The most serious outcome of coronary heart disease is the myocardial infarction, i.e. the rapid and irreversible damage of cardiac muscles, which, if not diagnosed and treated in time, continues to damage  ...  subspaces and are extracted from either shallow or deep classifiers is required. and Euclidean features in a Reproducing Kernel Hilbert Space, provides excellent results in both cases, i.e., detection  ... 
doi:10.5281/zenodo.3678671 fatcat:im7jcztsfzd4lbqbdts2ktsp74

Gabor Kernels for Textured Image Representation and Classification [chapter]

Hugo Hidalgo-Silva
2006 Lecture Notes in Computer Science  
Instead of the ordinary filter bank, a reproducing kernel representation is constructed consisting of a sum of several local reproducing kernels.  ...  The feature vectors are used to construct a kernel for a support vector classifier. Results are presented for a set of oriented texture images.  ...  In this work, we are interested in the construction of a reproducing kernel Hilbert space (RKHS) for images with a kernel derived of the Gabor elementary functions.  ... 
doi:10.1007/11892755_96 fatcat:k775gzie7nf5fdmr35dap3o7nu

Composite Kernel Local Angular Discriminant Analysis for Multi-Sensor Geospatial Image Analysis [article]

Saurabh Prasad, Minshan Cui, Lifeng Yan
2016 arXiv   pre-print
Kernel Hilbert Space (RKHS).  ...  In recent work, we proposed and developed an angle-based discriminant analysis approach that projected data onto subspaces with maximal "angular" separability in the input (raw) feature space and Reproducible  ...  Several of these methods are implemented in both the input (raw) feature space and the Reproducible Kernel Hilbert Space (RKHS) for data that are nonlinearly separable.  ... 
arXiv:1607.04939v1 fatcat:f4zslal3nnbezhc5r33asvbgji

When VLAD Met Hilbert

Mehrtash Harandi, Mathieu Salzmann, Fatih Porikli
2016 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
In this paper, we address two fundamental limitations of VLAD: its requirement for the local descriptors to have vector form and its restriction to linear classifiers due to its high-dimensionality.  ...  Our results also evidence the benefits of our nonlinear VLAD descriptors against the linear ones in Euclidean space using several standard benchmark datasets.  ...  In particular, we first derive a kernelized version of VLAD that relies on mapping each local descriptor to a Reproducing Kernel Hilbert Space (RKHS).  ... 
doi:10.1109/cvpr.2016.560 dblp:conf/cvpr/HarandiSP16 fatcat:yhhhwhrs3vgz7aahmii2jyomfq

Mixed Region Covariance Discriminative Learning for Image Classification on Riemannian Manifolds

Xi Liu, Zhengming Ma, Guo Niu
2019 Mathematical Problems in Engineering  
Kernel Hilbert Space (RKHS) and then project it onto a subspace of the RKHS.  ...  In this paper, we propose a subspace projection framework for the classification task on Riemannian manifolds and give the mathematical derivation for it.  ...  Kernelbased methods embed the manifold into a high-dimensional Reproducing Kernel Hilbert Spaces (RKHS) and further project the elements in RKHS onto Euclidean space by an explicit mapping.  ... 
doi:10.1155/2019/1261398 fatcat:s6sn5wypsnb2hoedthukh7v4na

Page 1810 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
The classical concept of Berezin transform, usually associated with Hilbert spaces of holomorphic functions of Bergman type, is considered in a general setting of reproducing kernel Hilbert spaces H C  ...  The reproducing kernel K of H gives rise to a bounded “diagonalization operator” M:H @H — L?  ... 

Piecewise smooth system identification in reproducing kernel Hilbert space

Fabien Lauer, Gerard Bloch
2014 53rd IEEE Conference on Decision and Control  
This is tackled by simultaneously learning a collection of local models from a reproducing kernel Hilbert space via the minimization of a convex functional, for which we prove a representer theorem that  ...  In this approach, the problem is cast as the minimization of a convex cost function implementing a trade-off between the fit to the data and a sparsity prior on the number of pieces.  ...  A Hilbert space of real-valued functions which possesses a reproducing kernel is called a reproducing kernel Hilbert space (RKHS).  ... 
doi:10.1109/cdc.2014.7040408 dblp:conf/cdc/LauerB14 fatcat:77x7qzcux5foxdilxgyznw3lqm

An Introduction to Hilbert Module Approach to Multivariable Operator Theory [article]

Jaydeb Sarkar
2014 arXiv   pre-print
., T_n} be a set of n commuting bounded linear operators on a Hilbert space H.  ...  More developments in the study of Hilbert module approach to operator theory can be found in a companion paper, "Applications of Hilbert Module Approach to Multivariable Operator Theory".  ...  Therefore, H is a reproducing kernel Hilbert space with reproducing kernel K(z, w) = ev z • ev * w ∈ B(E).  ... 
arXiv:1308.6103v3 fatcat:zzvibelf3zddbcgr2os4vqzhva

Maximal margin classification for metric spaces

Matthias Hein, Olivier Bousquet, Bernhard Schölkopf
2005 Journal of computer and system sciences (Print)  
In order to apply the maximum margin method in arbitrary metric spaces, we suggest to embed the metric space into a Banach or Hilbert space and to perform linear classification in this space.  ...  We propose several embeddings and recall that an isometric embedding in a Banach space is always possible while an isometric embedding in a Hilbert space is only possible for certain metric spaces.  ...  Then for every point x 0 ∈ X there exists a reproducing kernel Hilbert space H k and a map : X → H k given by , y) , Proposition 2.  ... 
doi:10.1016/j.jcss.2004.10.013 fatcat:mlls7h5zybat3mt7272tgxgcpm

When VLAD met Hilbert [article]

Mehrtash Harandi, Mathieu Salzmann, Fatih Porikli
2015 arXiv   pre-print
In this paper, we address two fundamental limitations of VLAD: its requirement for the local descriptors to have vector form and its restriction to linear classifiers due to its high-dimensionality.  ...  Our results also evidence the benefits of our nonlinear VLAD descriptors against the linear ones in Euclidean space using several standard benchmark datasets.  ...  In particular, we first introduce a kernelized version of VLAD that relies on mapping of each local descriptor to a Reproducing Kernel Hilbert Space (RKHS).  ... 
arXiv:1507.08373v1 fatcat:4q5cgbzr5jdfpk2g22ofa36c7u

Page 7103 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
Summary: “In this paper, a _ tensor product space W}[a,b]@W3[c,d] which has a_ reproducing kernel is constructed.  ...  46E22 46N40 Zhong, Tan Yi (PRC-HRST; Harbin); Deng, Zhong Xing (PRC-HRST; Harbin) On the best Hermite interpolation operator in the reproducing kernel space W}[a, b]®W7}[c, d}.  ... 

Reproducing Kernel Hilbert Space Associated with a Unitary Representation of a Groupoid

Monika Drewnik, Tomasz Miller, Zbigniew Pasternak-Winiarski
2021 Complex Analysis and Operator Theory  
AbstractThe aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid.  ...  The kernel constructed from the group(oid) representation is inspired by the kernel defined in terms of the convolution of functions on a locally compact group.  ...  If the latter is a Hilbert space, we call H a reproducing kernel Hilbert space (RKHS).  ... 
doi:10.1007/s11785-021-01137-z fatcat:tph5wzogxzhzjirreclordu7ye

Subspace Learning in Krein Spaces: Complete Kernel Fisher Discriminant Analysis with Indefinite Kernels [chapter]

Stefanos Zafeiriou
2012 Lecture Notes in Computer Science  
Recently, classifiers such as Support Vector Machines (SVMs) with npd kernels, Indefinite Kernel Fisher Discriminant Analysis (IKFDA) and Indefinite Kernel Quadratic Analysis (IKQA) were proposed.  ...  In this paper we propose feature extraction methods using indefinite kernels. In particular, first we propose an Indefinite Kernel Principal Component Analysis (IKPCA).  ...  Kernel-based subspace learning algorithms perform an implicit mapping of the input data into a high-dimensional Hilbert space (also referred to as feature space) and use the reproducing properties of pd  ... 
doi:10.1007/978-3-642-33765-9_35 fatcat:llkq4srexbgk5m3pgcec67xkaq

Hilbert–Schmidt Independence Criterion Subspace Learning on Hybrid Region Covariance Descriptor for Image Classification

Xi Liu, Peng Yang, Zengrong Zhan, Zhengming Ma, Muhammad Haroon Yousaf
2021 Mathematical Problems in Engineering  
This algorithm is a kernel function that embeds SPD matrices into the reproducing kernel Hilbert space and further maps them to a linear space.  ...  To address the non-Euclidean properties of SPD manifolds, this study also proposes an algorithm called the Hilbert-Schmidt independence criterion subspace learning (HSIC-SL) for SPD manifolds.  ...  , such as a high-dimensional reproducing kernel Hilbert space (RKHS) [24] and another low-dimensional SPD manifold [25] .  ... 
doi:10.1155/2021/6663710 fatcat:ove6gjdomfd2bcfelqw75uqd3m
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