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Relevant bibliographies by topics / Reproducing Kernel Hilbert Space (RKHS)

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Academic literature on the topic 'Reproducing Kernel Hilbert Space (RKHS)'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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Journal articles on the topic "Reproducing Kernel Hilbert Space (RKHS)"

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Xu, Lixiang, Bin Luo, Yuanyan Tang, and Xiaohua Ma. "An efficient multiple kernel learning in reproducing kernel Hilbert spaces (RKHS)." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 02 (2015): 1550008. http://dx.doi.org/10.1142/s0219691315500083.

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The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel with a Hilbert space of functions. Recently, reproducing kernel Hilbert space (RKHS) has come wildly alive in the pattern recognition and machine learning community. In this paper, we propose a novel method named multiple kernel learning with reproducing property (MKLRP) to achieve some classification tasks. The MKLRP consists of two major steps. First, we find the basic solution of a generalized differential operator by delta function, and prove this basic solution

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LI, BING-ZHAO, and QING-HUA JI. "Sampling analysis in the complex reproducing kernel Hilbert space." European Journal of Applied Mathematics 26, no. 1 (2014): 109–20. http://dx.doi.org/10.1017/s0956792514000357.

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We consider and analyse sampling theories in the reproducing kernel Hilbert space (RKHS) in this paper. The reconstruction of a function in an RKHS from a given set of sampling points and the reproducing kernel of the RKHS is discussed. Firstly, we analyse and give the optimal approximation of any function belonging to the RKHS in detail. Then, a necessary and sufficient condition to perfectly reconstruct the function in the corresponding RKHS of complex-valued functions is investigated. Based on the derived results, another proof of the sampling theorem in the linear canonical transform (LCT)

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Prasad, Srijanani Anurag. "Reproducing Kernel Hilbert Space and Coalescence Hidden-variable Fractal Interpolation Functions." Demonstratio Mathematica 52, no. 1 (2019): 467–74. http://dx.doi.org/10.1515/dema-2019-0027.

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AbstractReproducing Kernel Hilbert Spaces (RKHS) and their kernel are important tools which have been found to be incredibly useful in many areas like machine learning, complex analysis, probability theory, group representation theory and the theory of integral operator. In the present paper, the space of Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is demonstrated to be an RKHS and its associated kernel is derived. This extends the possibility of using this new kernel function, which is partly self-affine and partly non-self-affine, in diverse fields wherein the struct

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Paiva, António R. C., Il Park, and José C. Príncipe. "A Reproducing Kernel Hilbert Space Framework for Spike Train Signal Processing." Neural Computation 21, no. 2 (2009): 424–49. http://dx.doi.org/10.1162/neco.2008.09-07-614.

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This letter presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a f

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Andelić, E., M. Schafföner, M. Katz, S. E. Krüger, and A. Wendemuth. "Kernel Least-Squares Models Using Updates of the Pseudoinverse." Neural Computation 18, no. 12 (2006): 2928–35. http://dx.doi.org/10.1162/neco.2006.18.12.2928.

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Sparse nonlinear classification and regression models in reproducing kernel Hilbert spaces (RKHSs) are considered. The use of Mercer kernels and the square loss function gives rise to an overdetermined linear least-squares problem in the corresponding RKHS. When we apply a greedy forward selection scheme, the least-squares problem may be solved by an order-recursive update of the pseudoinverse in each iteration step. The computational time is linear with respect to the number of the selected training samples.

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Alvandi, Azizallah, and Mahmoud Paripour. "The Combined Reproducing Kernel Method and Taylor Series for Solving Weakly Singular Fredholm Integral Equations." International Journal of Advances in Applied Sciences 5, no. 3 (2016): 109. http://dx.doi.org/10.11591/ijaas.v5.i3.pp109-117.

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<p>In this paper, a numerical method is proposed for solving weakly singular Fredholm integral equations in Hilbert reproducing kernel space (RKHS). The Taylor series is used to remove singularity and reproducing kernel function are used as a basis. The effectiveness and stability of the numerical scheme is illustrated through two numerical examples.</p>

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Yao, Lingqing, Roussos Dimitrakopoulos, and Michel Gamache. "High-Order Sequential Simulation via Statistical Learning in Reproducing Kernel Hilbert Space." Mathematical Geosciences 52, no. 5 (2019): 693–723. http://dx.doi.org/10.1007/s11004-019-09843-3.

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AbstractThe present work proposes a new high-order simulation framework based on statistical learning. The training data consist of the sample data together with a training image, and the learning target is the underlying random field model of spatial attributes of interest. The learning process attempts to find a model with expected high-order spatial statistics that coincide with those observed in the available data, while the learning problem is approached within the statistical learning framework in a reproducing kernel Hilbert space (RKHS). More specifically, the required RKHS is construc

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Saldır, Onur, Mehmet Giyas Sakar, and Fevzi Erdogan. "Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method." Fractal and Fractional 4, no. 2 (2020): 27. http://dx.doi.org/10.3390/fractalfract4020027.

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In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. The convergence of this approach and its error estimates are given. The numerical algorithm of the method is presented. Furthermore, numerical outcomes are shown with tables and graphics for some examples. These outcomes demonstrate that the proposed method is convenient and effective

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Al-Humedi, Hameeda Oda. "The Reproducing Kernel Hilbert Space Method for Solving System of Linear Weakly Singular Volterra Integral Equations." JOURNAL OF ADVANCES IN MATHEMATICS 15 (November 14, 2018): 8070–80. http://dx.doi.org/10.24297/jam.v15i0.7869.

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The exact solutions of a system of linear weakly singular Volterra integral equations (VIE) have been a difficult to find. The aim of this paper is to apply reproducing kernel Hilbert space (RKHS) method to find the approximate solutions to this type of systems. At first, we used Taylor's expansion to omit the singularity. From an expansion the given system of linear weakly singular VIE is transform into a system of linear ordinary differential equations (LODEs). The approximate solutions are represent in the form of series in the reproducing kernel space . By comparing with the exact solution

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Gumah, Ghaleb, Khaled Moaddy, Mohammed Al-Smadi, and Ishak Hashim. "Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method." Journal of Function Spaces 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/2920463.

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We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert spaceW21a,bin order to formulate the analytical solutions in a rapidly convergent series form in terms of theirα-cut representation. The approximation solution is expressed byn-term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreeme

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Dissertations / Theses on the topic "Reproducing Kernel Hilbert Space (RKHS)"

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Bhujwalla, Yusuf. "Nonlinear System Identification with Kernels : Applications of Derivatives in Reproducing Kernel Hilbert Spaces." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0315/document.

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Cette thèse se concentrera exclusivement sur l’application de méthodes non paramétriques basées sur le noyau à des problèmes d’identification non-linéaires. Comme pour les autres méthodes non-linéaires, deux questions clés dans l’identification basée sur le noyau sont les questions de comment définir un modèle non-linéaire (sélection du noyau) et comment ajuster la complexité du modèle (régularisation). La contribution principale de cette thèse est la présentation et l’étude de deux critères d’optimisation (un existant dans la littérature et une nouvelle proposition) pou

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Pan, Yue. "Currents- and varifolds-based registration of lung vessels and lung surfaces." Thesis, University of Iowa, 2016. https://ir.uiowa.edu/etd/2257.

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This thesis compares and contrasts currents- and varifolds-based diffeomorphic image registration approaches for registering tree-like structures in the lung and surface of the lung. In these approaches, curve-like structures in the lung—for example, the skeletons of vessels and airways segmentation—and surface of the lung are represented by currents or varifolds in the dual space of a Reproducing Kernel Hilbert Space (RKHS). Currents and varifolds representations are discretized and are parameterized via of a collection of momenta. A momenta corresponds to a line segment via the coordinates o

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Ren, Haobo. "Functional inverse regression and reproducing kernel Hilbert space." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/4203.

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The basic philosophy of Functional Data Analysis (FDA) is to think of the observed data functions as elements of a possibly infinite-dimensional function space. Most of the current research topics on FDA focus on advancing theoretical tools and extending existing multivariate techniques to accommodate the infinite-dimensional nature of data. This dissertation reports contributions on both fronts, where a unifying inverse regression theory for both the multivariate setting (Li 1991) and functional data from a Reproducing Kernel Hilbert Space (RKHS) prospective is developed. We proposed a functi

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Ammanouil, Rita. "Contributions au démélange non-supervisé et non-linéaire de données hyperspectrales." Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4079/document.

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Le démélange spectral est l’un des problèmes centraux pour l’exploitation des images hyperspectrales. En raison de la faible résolution spatiale des imageurs hyperspectraux en télédetection, la surface représentée par un pixel peut contenir plusieurs matériaux. Dans ce contexte, le démélange consiste à estimer les spectres purs (les end members) ainsi que leurs fractions (les abondances) pour chaque pixel de l’image. Le but de cette thèse estde proposer de nouveaux algorithmes de démélange qui visent à améliorer l’estimation des spectres purs et des abondances. En particulier, les algorithmes

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Sabree, Aqeeb A. "Positive definite kernels, harmonic analysis, and boundary spaces: Drury-Arveson theory, and related." Diss., University of Iowa, 2019. https://ir.uiowa.edu/etd/7023.

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A reproducing kernel Hilbert space (RKHS) is a Hilbert space $\mathscr{H}$ of functions with the property that the values $f(x)$ for $f \in \mathscr{H}$ are reproduced from the inner product in $\mathscr{H}$. Recent applications are found in stochastic processes (Ito Calculus), harmonic analysis, complex analysis, learning theory, and machine learning algorithms. This research began with the study of RKHSs to areas such as learning theory, sampling theory, and harmonic analysis. From the Moore-Aronszajn theorem, we have an explicit correspondence between reproducing kernel Hilbert spaces (RKHS

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Agrawal, Devanshu. "The Complete Structure of Linear and Nonlinear Deformations of Frames on a Hilbert Space." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/3003.

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A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show that

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Jordão, Thaís. "Diferenciabilidade em espaços de Hilbert de reprodução sobre a esfera." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-29032012-103159/.

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Um espaço de Hilbert de reprodução (EHR) é um espaço de Hilbert de funções construído de maneira específica e única a partir de um núcleo positivo definido. As funções do EHR tem a seguinte peculiaridade: seus valores podem ser reproduzidos através de uma operação elementar envolvendo a própria função, o núcleo gerador e o produto interno do espaço. Neste trabalho, consideramos EHR gerados por núcleos positivos definidos sobre a esfera unitária m-dimensional usual. Analisamos quais propriedades são herdadas pelos elementos do espaço, quando o núcleo gerador possui alguma hipótese de diferencia

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Wang, Roy Chih Chung. "Adaptive Kernel Functions and Optimization Over a Space of Rank-One Decompositions." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36975.

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The representer theorem from the reproducing kernel Hilbert space theory is the origin of many kernel-based machine learning and signal modelling techniques that are popular today. Most kernel functions used in practical applications behave in a homogeneous manner across the domain of the signal of interest, and they are called stationary kernels. One open problem in the literature is the specification of a non-stationary kernel that is computationally tractable. Some recent works solve large-scale optimization problems to obtain such kernels, and they often suffer from non-identifiability iss

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Shin, Hyejin. "Infinite dimensional discrimination and classification." Texas A&M University, 2003. http://hdl.handle.net/1969.1/5832.

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Modern data collection methods are now frequently returning observations that should be viewed as the result of digitized recording or sampling from stochastic processes rather than vectors of finite length. In spite of great demands, only a few classification methodologies for such data have been suggested and supporting theory is quite limited. The focus of this dissertation is on discrimination and classification in this infinite dimensional setting. The methodology and theory we develop are based on the abstract canonical correlation concept of Eubank and Hsing (2005), and motivated by the

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Ke, Chenlu. "A NEW INDEPENDENCE MEASURE AND ITS APPLICATIONS IN HIGH DIMENSIONAL DATA ANALYSIS." UKnowledge, 2019. https://uknowledge.uky.edu/statistics_etds/41.

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This dissertation has three consecutive topics. First, we propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. The index is also applicable when both variables are continuous. Second, we develop a sufficient variable selection procedure based on the new measure in a large p small

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Books on the topic "Reproducing Kernel Hilbert Space (RKHS)"

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Christine, Thomas-Agnan, ed. Reproducing kernel Hilbert spaces in probability and statistics. Kluwer Academic, 2004.

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Dym, H. J contractive matrix functions, reproducing kernel Hilbert spaces and interpolation. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1989.

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Introduction to the Theory of Reproducing Kernel Hilbert Spaces. Cambridge University Press, 2016.

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Minggen, Cui, and Lin Yingzhen, eds. Nonlinear numerical analysis in the reproducing Kernel space. Nova Science Publishers, 2008.

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Berlinet, Alain, and Christine Thomas-Agnan. Reproducing Kernel Hilbert Spaces in Probability and Statistics. Springer, 2003.

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Berlinet, Alain, and Christine Thomas-Agnan. Reproducing Kernel Hilbert Spaces in Probability and Statistics. Springer, 2011.

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(Translator), Stephen S. Wilson, ed. The Schur Algorithm, Reproducing Kernel Spaces and System Theory. American Mathematical Society, 2001.

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Baillo, Amparo, Antonio Cuevas, and Ricardo Fraiman. Classification methods for functional data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.10.

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This article reviews the literature concerning supervised and unsupervised classification of functional data. It first explains the meaning of unsupervised classification vs. supervised classification before discussing the supervised classification problem in the infinite-dimensional case, showing that its formal statement generally coincides with that of discriminant analysis in the classical multivariate case. It then considers the optimal classifier and plug-in rules, empirical risk and empirical minimization rules, linear discrimination rules, the k nearest neighbor (k-NN) method, and kern

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Book chapters on the topic "Reproducing Kernel Hilbert Space (RKHS)"

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Berlinet, Alain, and Christine Thomas-Agnan. "RKHS and Stochastic Processes." In Reproducing Kernel Hilbert Spaces in Probability and Statistics. Springer US, 2004. http://dx.doi.org/10.1007/978-1-4419-9096-9_2.

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Bee Dagum, Estela, and Silvia Bianconcini. "A Unified View of Trend-Cycle Predictors in Reproducing Kernel Hilbert Spaces (RKHS)." In Seasonal Adjustment Methods and Real Time Trend-Cycle Estimation. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31822-6_9.

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Higgins, J. R. "Sampling in Reproducing Kernel Hilbert Space." In New Perspectives on Approximation and Sampling Theory. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08801-3_2.

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Mboup, Mamadou. "On the Structure of Self-similar Systems: A Hilbert Space Approach." In Reproducing Kernel Spaces and Applications. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8077-0_9.

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Xu, Jianwu, Robert Jenssen, Antonio Paiva, and Il Park. "A Reproducing Kernel Hilbert Space Framework for ITL." In Information Theoretic Learning. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-1570-2_9.

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Gualtierotti, Antonio F. "The Functions of a Reproducing Kernel Hilbert Space." In Detection of Random Signals in Dependent Gaussian Noise. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22315-5_2.

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Zou, Dongfang. "Local Subspace Classifier in Reproducing Kernel Hilbert Space." In Advances in Multimodal Interfaces — ICMI 2000. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-40063-x_57.

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Szafraniec, Franciszek Hugon. "Multipliers in the Reproducing Kernel Hilbert Space, Subnormality and Noncommutative Complex Analysis." In Reproducing Kernel Spaces and Applications. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8077-0_11.

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Szafraniec, Franciszek Hugon. "The reproducing kernel Hilbert space and its multiplication operators." In Complex Analysis and Related Topics. Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8698-7_17.

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Taqqu, Murad S., and Claudia Czado. "Reproducing kernel Hilbert space for some non-Gaussian processes." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074948.

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Conference papers on the topic "Reproducing Kernel Hilbert Space (RKHS)"

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Guo, Jia, Sai Tej Paruchuri, and Andrew J. Kurdila. "Approximations of the Reproducing Kernel Hilbert Space (RKHS) Embedding Method over Manifolds." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9304331.

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Li, Xuelong, Jian Yang, and Qi Wang. "Nonrigid Points Alignment with Soft-weighted Selection." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/111.

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Point set registration (PSR) is a crucial problem in computer vision and pattern recognition. Existing PSR methods cannot align point sets robustly due to degradations, such as deformation, noise, occlusion, outlier, and multi-view changes. In this paper, we present a self-selected regularized Gaussian fields criterion for nonrigid point matching. Unlike most existing methods, we formulate the registration problem as a sparse approximation task with low rank constraint in reproducing kernel Hilbert space (RKHS). A self-selected mechanism is used to dynamically assign real-valued label for each

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Guo, Jia, Sai Tej Paruchuri, and Andrew J. Kurdila. "Persistence of Excitation in Uniformly Embedded Reproducing Kernel Hilbert (RKH) Spaces." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147851.

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Lu, Kou, Jiajing Zhao, Jianming Zhang, and Cheng Qin. "Multiple Kernel Learning via Ensemble Artifice in Reproducing Kernel Hilbert Space." In 2020 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC). IEEE, 2020. http://dx.doi.org/10.1109/cyberc49757.2020.00049.

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Lauer, Fabien, and Gerard Bloch. "Piecewise smooth system identification in reproducing kernel Hilbert space." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7040408.

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Deng, Cai-Xia, Shuai Li, and Zuo-Xian Fu. "The reproducing kernel Hilbert space based on wavelet transform." In 2010 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR). IEEE, 2010. http://dx.doi.org/10.1109/icwapr.2010.5576389.

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Akgül, A., and M. Giyas Sakar. "A new application of reproducing kernel Hilbert space method." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044176.

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Peifer, Maria, Luiz F. O. Chamon, Santiago Paternain, and Alejandro Ribeiro. "Sparse Learning of Parsimonious Reproducing Kernel Hilbert Space Models." In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2019. http://dx.doi.org/10.1109/icassp.2019.8682173.

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Gauci, Oliver, Carl J. Debono, and Paul Micallef. "A reproducing kernel Hilbert space approach for speech enhancement." In 2008 3rd International Symposium on Communications, Control and Signal Processing (ISCCSP). IEEE, 2008. http://dx.doi.org/10.1109/isccsp.2008.4537338.

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Washizawa, Y., and Y. Yamashita. "Non-linear Wiener filter in reproducing kernel Hilbert space." In 18th International Conference on Pattern Recognition (ICPR'06). IEEE, 2006. http://dx.doi.org/10.1109/icpr.2006.861.

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