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Proceedings of the 46th IEEE Conference on Decision and Control, Pages 3678-4134

作者： Matthew M. Peet Antonis Papachristodoulou Department of Engineering Science University of Oxford Oxford UK INRIA-Rocquencourt France

ISBN: (纸本)9781424414970;1424414970

The purpose of this paper is to provide further results on a method of constructing Lyapunov functionals for infinite-dimensional systems using semidefinite programming. Specifically, we give a necessary and sufficient condition for positivity of a positive integral operator described by a polynomial kernel. We then show how to combine this result with multiplier operators in order to obtain positive composite Lyapunov functionals. These types of functionals are used to prove stability of linear time-delay systems.

关键词： kernel functions FUNCTIONALS linear time-delay system Communication Research Operators

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Inductive Regularized Learning of kernel functions 10

Inductive Regularized Learning of Kernel Functions

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Annual Conference on Neural Information Processing Systems

作者： Prateek Jain Brian Kulis Inderjit Dhillon Microsoft Research Bangalore Bangalore India UC Berkeley EECS and ICSI Berkeley CA USA UT Austin Dept. of Computer Sciences Austin TX USA

ISBN: (纸本)9781617823800

In this paper we consider the problem of semi-supervised kernel function learning. We first propose a general regularized framework for learning a kernel matrix, and then demonstrate an equivalence between our proposed kernel matrix learning framework and a general linear transformation learning problem. Our result shows that the learned kernel matrices parameterize a linear transformation kernel function and can be applied inductively to new data points. Furthermore, our result gives a constructive method for kernelizing most existing Mahalanobis metric learning formulations. To make our results practical for large-scale data, we modify our framework to limit the number of parameters in the optimization process. We also consider the problem of kemelized inductive dimensionality reduction in the semi-supervised setting. To this end, we introduce a novel method for this problem by considering a special case of our general kernel learning framework where we select the trace norm function as the regularizer. We empirically demonstrate that our framework learns useful kernel functions, improving the k-NN classification accuracy significantly in a variety of domains. Furthermore, our kernel-ized dimensionality reduction technique significantly reduces the dimensionality of the feature space while achieving competitive classification accuracies.

关键词： Optimization Procedure Eigenvector kernel functions Learning kernel dimensionality reduction Frameworks linear transformations

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Polyhedral conic kernel-like functions for SVMs

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TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES 2019年第2期27卷 1172-1180页

作者： Ozturk, Gurkan Cimen, Emre Eskisehir Tech Univ Engn Fac Dept Ind Engn Eskisehir Turkey Eskisehir Tech Univ Engn Fac Computat Intelligence & Optimizat Lab Eskisehir Turkey

In this study, we propose a new approach that can be used as a kernel-like function for support vector machines (SVMs) in order to get nonlinear classification surfaces. We combined polyhedral conic functions (PCFs) with the SVM method. To get nonlinear classification surfaces, kernel functions are used with SVMs. However, the parameter selection of the kernel function affects the classification accuracy. Generally, in order to get successful classifiers which can predict unknown data accurately, best parameters are explored with the grid search method which is computationally expensive. We solved this problem with the proposed method. There is no need to optimize any parameter in the proposed method. We tested the proposed method on three publicly available datasets. Next, the classification accuracies of the proposed method were compared with the linear, radial basis function (RBF), Pearson universal kernel (PUK), and polynomial kernel SVMs. The results are competitive with those of the other methods.

关键词： Support vector machines polyhedral conic functions kernel functions classification mathematical programming

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An Efficient Hyperbolic kernel Function Yielding the Best Known Iteration Bounds for Linear Programming

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Acta Mathematicae Applicatae Sinica 2025年第1期41卷 133-151页

作者： Imene TOUIL Wided CHIKOUCHE Djamel BENTERKI Amina ZERARI LMPA Mohammed Seddik Ben Yahia UniversityPO Box 98Ouled Aissa18000 JijelAlgeria LMFN Ferhat Abbas UniversitySetif 19000Algeria

Interior-point methods(IPMs) for linear programming(LP) are generally based on the logarithmic barrier function. Peng et al.(J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions(KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their ***, Bai et al.(SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche(Filomat. 34(12):3957–3969, 2020;Acta Math. Sin.(Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite program(ming(SD)P). They( establishe)d that the iteration complexities of algorithms based on their proposed KFs are O(n2/3log(n/ε) and O(n3/4log(n/ε)) for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is O(√n log n log(n/ε)) iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of *** algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results.

关键词： linear programming primal-dual interior-point methods kernel functions complexity analysis large and small-update methods

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Higher-order memory enriched thermoelastic behavior under the presence of heat source in an initially stressed orthotropic medium

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JOURNAL OF THERMAL STRESSES 2025年

作者： Karmakar, Subhadip Pal Sarkar, Smita Indian Inst Engn Sci & Technol Dept Math Howrah 711103 India

The primary objective of this article is to study the memory effect for thermoelastic interaction within a two-dimensional, homogeneous, initially stressed orthotropic medium. The interaction is caused by an instantaneous heat source. This study integrates the utilization of higher-order memory-dependent derivative within the dual phase lag model of thermoelasticity theory. The problem is addressed by formulating a system of ordinary differential equations in vector-matrix form, utilizing Laplace-Fourier integral transforms. The eigenvalue approach is utilized for obtaining solutions in the transformed domain. Subsequently, suitable numerical methodologies have been put to use to estimate thermophysical quantities across the space-time domain. Solutions are presented graphically, with and without initial stress, to understand its influence. A comparative analysis is conducted between the solutions derived from the dual phase lag model and the Lord-Shulman model, aiming to evaluate the efficacy of the dual phase lag model. The article graphically illustrates the impact of three kernel functions, considering the role of the memory-dependent derivative. Furthermore, results without the memory-dependent derivative are shown to assess its efficacy, and outcomes related to the higher-order memory-dependent derivative are graphically depicted.

关键词： Dual phase lag Fourier and Laplace transform higher-order memory-dependent derivative instantaneous heat source kernel functions orthotropic medium thermoelasticity

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kernel estimates as general concept for the measuring of pedestrian density

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2025年第1期21卷 303-328页

作者： Vackova, Jana Bukacek, Marek Czech Tech Univ Fac Nucl Sci & Phys Engn Prague Czech Republic

The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a general framework based on various kernels that bring desired properties of density estimates (e.g. continuity) and incorporate ordinarily used methods. The developed kernel concept considers each pedestrian as a source of density distribution, parametrised by the kernel type (e.g. Gauss, cone) and kernel size. The quantitative parametric study performed on experimental data illustrates that parametrisation brings desired features, for instance, a conic kernel with a base radius in (0.7, 1.2) m produces smooth values that retain trend features. The correspondence between kernel and non-kernel methods (namely Voronoi diagram and customised inverse distance to the nearest pedestrian) is achievable for a wide range of kernel parameter. Thereby the generality of the concept is supported.

关键词： Pedestrian dynamics density kernel functions minimum distance density Voronoi diagram

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A Bayesian Lasso based sparse learning model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2025年第4期54卷 1108-1124页

作者： Helgoy, Ingvild M. Li, Yushu Univ Bergen Dept Math Bergen Norway

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main difference from the original Bayesian Lasso lies in the estimation procedure;the BLS uses a learning algorithm based on the type-II maximum likelihood procedure. Opposed to the Bayesian Lasso, the BLS provides sparse estimates of the regression parameters. The BLS is also derived for nonlinear supervised learning problems by introducing kernel functions. We compare the BLS model to the well known Relevance Vector Machine, the Fast Laplace, the Bayesian Lasso, and the Lasso, on both simulated and real data. The numerical results show that the BLS is sparse and precise, especially when dealing with noisy and irregular dataset.

关键词： Bayesian lasso Hierarchical models kernel functions Relevance vector machine Sparse Bayesian learning Type-II maximum likelihood

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Lithium-Ion Battery Capacity Prediction Method Based on Improved Extreme Learning Machine

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JOURNAL OF ELECTROCHEMICAL ENERGY CONVERSION AND STORAGE 2025年第1期22卷 011002页

作者： Liu, Zhengyu Huang, Zaijun Tang, Liandong Wang, Hao Hefei Univ Technol Dept Mech Engn Hefei 230009 Peoples R China

Currently, research and applications in the field of capacity prediction mainly focus on the use and recycling of batteries, encompassing topics such as SOH estimation, RUL prediction, and echelon use. However, there is scant research and application based on capacity prediction in the battery manufacturing process. Measuring capacity in the grading process is an important step in battery production. The traditional capacity acquisition method consumes considerable time and energy. To address the above issues, this study establishes an improved extreme learning machine (ELM) model for predicting battery capacity in the manufacturing process, which can save approximately 45% of energy and time in the grading process. The study involves the extraction of features from the battery charge-discharge curve that can reflect battery capacity performance and subsequent calculation of the grey correlation between these features and capacity. The feature set comprises features with a high correlation with capacity, which are used as inputs for the ELM model. kernel functions are used to adjust the ELM model, and Bayesian optimization methods are employed to automatically optimize the hyperparameters to improve the capacity prediction performance of the model. The study uses lithium-ion battery data from an actual manufacturing process to test the predictive effect of the model. The mean absolute percentage error of the capacity prediction results is less than 0.2%, and the root-mean-square error is less than 0.3 Ah.

关键词： Bayesian optimization method capacity ELM grading kernel functions batteries

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Bilinear Generating functions in kernel Sparse Modeling and Learning Towards the kernel engineering

Bilinear Generating Functions in Kernel Sparse Modeling and ...

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IEEE Symposium Series on Computational Intelligence (IEEE SSCI)

作者： Lu, Zhao Yan, Wen Wu, Qi Tuskegee Univ Dept Elect Engn Tuskegee AL 36088 USA Tuskegee Univ Dept Math Tuskegee AL 36088 USA Zhejiang Univ State Key Lab CAD&CG Hangzhou Zhejiang Peoples R China

ISBN: (纸本)9781538627266

As the cornerstone of nonlinear kernel learning algorithms, the kernel functions play a major role in sparse modeling via learning from data, as it largely determines the performance of a learning algorithm. In the literature, almost all kernels used are either dot product functions or distance functions. However, the highly challenging and complex learning tasks encountered in the real world necessitate innovative kernel functions with the capability of overcoming the fundamental limitations of conventional kernels. In this paper, the conexus between kernel functions in machine learning and generating functions of special functions is explored, by which the special functions of mathematical physics come into the picture of kernel-based machine learning, and in particular, a new trail to construct kernel function via bilinear generating function of special functions is blazed. To our best knowledge, it is the first study to investigate the use of bilinear generating functions of some special functions in constructing innovative kernel functions for linear programming support vector learning and sparse modeling.

关键词： Laguerre polynomials modified Bessel functions kernel functions linear programming support vector learning

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Different Objective functions in Fuzzy c-Means Algorithms and kernel-Based Clustering

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2011年第2期13卷 89-97页

作者： Miyamoto, Sadaaki Univ Tsukuba Dept Risk Engn Tsukuba Ibaraki 3058573 Japan

An overview of fuzzy c-means clustering algorithms is given where we focus on different objective functions: they use regularized dissimilarity, entropy-based function, and function for possibilistic clustering. Classification functions for the objective functions and their properties are studied. Fuzzy c-means algorithms using kernel functions is also discussed with kernelized cluster validity measures and numerical experiments. New kernel functions derived from the classification functions are moreover studied.

关键词： cluster validity measure fuzzy c-means clustering kernel functions possibilistic clustering

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