Concept Of Kernel Research Articles

Using mixed kernel support vector machine to improve the predictive accuracy of genome selection1

The advantages of genome selection (GS) in animal and plant breeding are self-evident. Traditional parametric models have disadvantage in better fit the increasingly large sequencing data and capture complex effects accurately. Machine learning models have demonstrated remarkable potential in addressing these challenges. In this study, we introduced the concept of mixed kernel functions to explore the performance of support vector machine regression (SVR) in GS. Six single kernel functions (SVR_L, SVR_C, SVR_G, SVR_P, SVR_S, SVR_L) and four mixed kernel functions (SVR_GS, SVR_GP, SVR_LS, SVR_LP) were used to predict genome breeding values. The prediction accuracy, mean squared error (MSE) and mean absolute error (MAE) were used as evaluation indicators to compare with two traditional parametric models (GBLUP, BayesB) and two popular machine learning models (RF, KcRR). The results indicate that in most cases, the performance of the mixed kernel function model significantly outperforms that of GBLUP, BayesB and single kernel function. For instance, for T1 in the pig dataset, the predictive accuracy of SVR_GS is improved by 10% compared to GBLUP, and by approximately 4.4 and 18.6% compared to SVR_G and SVR_S respectively. For E1 in the wheat dataset, SVR_GS achieves 13.3% higher prediction accuracy than GBLUP. Among single kernel functions, the Laplacian and Gaussian kernel functions yield similar results, with the Gaussian kernel function performing better. The mixed kernel function notably reduces the MSE and MAE when compared to all single kernel functions. Furthermore, regarding runtime, SVR_GS and SVR_GP mixed kernel functions run approximately three times faster than GBLUP in the pig dataset, with only a slight increase in runtime compared to the single kernel function model. In summary, the mixed kernel function model of SVR demonstrates speed and accuracy competitiveness, and the model such as SVR_GS has important application potential for GS.

Kernel estimates as general concept for the measuring of pedestrian density

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 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.

Numerical Solution of the Atmospheric Perturbations Triggered by Persistent Lithospheric Vibrations

Recently, atmospheric perturbations residing over around epicenters of forthcoming earthquakes were remotely sensed by the multiple instruments of the MVP-LAI (Monitoring of Vibrations and Perturbations in Lithosphere, Atmosphere and Ionosphere) system. In this study, we found another way and proposed a theory for the evolution of the perturbations in the atmosphere from the aspect of numerical simulation. We started from the fundamental hydromechanics equations for the perturbations based on the atmospheric dynamics in the cylindrical symmetric coordinate to solve their analytical solution. The solution shows that a persistent vibration at the bottom of the cylindrical symmetric coordinate tends to decay exponentially with along altitude. In other words, a persistent ground vibration in a wide area can rapidly evolve into small-scale perturbations in the atmosphere. The preliminary theoretical model in this study shows the kernel concept for the coupling of geospheres.

Reproducing kernel Hilbert spaces in the mean field limit

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of kernels and function spaces generated by kernels, so–called reproducing kernel Hilbert spaces. Motivated by recent developments of learning approaches in the context of interacting particle systems, we investigate kernel methods acting on data with many measurement variables. We show the rigorous mean field limit of kernels and provide a detailed analysis of the limiting reproducing kernel Hilbert space. Furthermore, several examples of kernels, that allow a rigorous mean field limit, are presented.

Self-representative kernel concept factorization

Kernel concept factorization (KCF) has successfully utilized kernel trick to conduct matrix factorization in the kernel space. However, conventional KCF methods usually define kernel in advance, which limits their ability to exploit the power of kernel. This paper proposes a semi-supervised self-representative kernel concept factorization (S3RKCF) method to integrate adaptive kernel learning and low-dimensional data representation learning into a unified model. Technically, an adaptive local geometric structure is acquired in the KCF-induced self-representation space, and then it facilitates data representation learning simultaneously. Furthermore, to enhance the discriminability of data representation, limited supervisory information is imposed in the formulated optimization problem as constraints. In this way, our model can learn kernel and discriminative low-dimensional representation adaptively and iteratively. To solve the optimization problem, an alternating iterative algorithm is designed with convergence guarantee. The performance of our proposed S3RKCF is evaluated through clustering and classification tasks, and the experimental results on eight real-world data sets demonstrate its effectiveness compared to state-of-the-art methods.

Semi-supervised adaptive kernel concept factorization

Kernelized concept factorization (KCF) has shown its advantage on handling data with nonlinear structures; however, the kernels involved in the existing KCF-based methods are empirically predefined, which may compromise the performance. In this paper, we propose semi-supervised adaptive kernel concept factorization (SAKCF), which integrates the data representation and kernel learning into a unified model to make the two learning processes adapt to each other. SAKCF extends traditional KCF in a semi-supervised manner, which encourages the high-dimensional representation to be consistent with both the limited supervisory and local geometric information. Besides, an alternating iterative algorithm is proposed to solve the resulting constrained optimization problem. Experimental results on six real-world data sets verify the effectiveness and advantages of our SAKCF over state-of-the-art methods when applied on the clustering task.

ANALYSIS OF PIECEWISE COVID-19 MODEL WITH ASYMPTOMATIC AND SYMPTOMATIC POPULATIONS WITH WANING IMMUNITY UNDER SINGULAR AND NONSINGULAR KERNELS

The COVID-19 pandemic touched about 200 countries of the globe. A strategy is given in this paper by considering a seven-compartment mathematical model with the inclusion of asymptomatic and symptomatic populations with waning immunity under the piecewise derivative concept of singular and nonsingular kernels, respectively. We investigate the dynamics of COVID-19 with the new framework of piecewise fractional derivative in the sense of Caputo and Atangana–Baleanu–Caputo fractional operators. The said analysis includes at least one solution and unique solution analysis with piecewise derivative in two subintervals. The proposed model is carried out by the approximate solution of piecewise numerical iterative technique of Newton polynomial. Each equation is written separately for the algorithm of numerical technique. Graphical representation for the proposed piecewise derivable model has been simulated with the available data at various global orders lying between 0 and 1 for both the subintervals. Such type of analysis will be very good and helpful for all those global problems where sudden or abrupt variation occurs.

Stein Variational Gradient Descent on Infinite-Dimensional Space and Applications to Statistical Inverse Problems

In this paper, we propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The method can generate approximate samples from posteriors efficiently. Based on the concepts of operator-valued kernels and vector-valued reproducing kernel Hilbert spaces, a rigorous definition is given for the infinite-dimensional objects, e.g., the Stein operator, which are proved to be the limit of finite-dimensional ones. Moreover, a more efficient iSVGD with preconditioning operators is constructed by generalizing the change of variables formula and introducing a regularity parameter. The proposed algorithms are applied to an inverse problem of the steady state Darcy flow equation. Numerical results confirm our theoretical findings and demonstrate the potential applications of the proposed approach in the posterior sampling of large-scale nonlinear statistical inverse problems.

Phraseology and Style in Subgenres of the Novel: A Synthesis of Corpus and Literary Perspectives

Phraseology and Style in Subgenres of the Novel: A Synthesis of Corpus and Literary Perspectives

On condensed set in ideal topological spaces

The main pillar of the research is the definition of a new type of operator ϵ* : p(k) → p(k), and to study its relationship with density in ideal spaces. The second path depends on the definition of the topological compatibility with the ideal and its relationship to this operator. Finally we defined the new concept of kernel by using this operator.

A Survey on Formal Verification of Separation Kernels

Introduction: In developing safety and security critical systems, separation kernel acts as a primary foundation, which provides spatial as well as temporal separation. Separation kernel offers highly assured partitions to the applications hosted on the fundamentally critical systems and can also control the flow of information between them. The industries, as well as academia, have developed several separation kernels that have been broadly applied in critical systems like military/defense secured applications, avionics/aerospace intelligent systems, healthcare units that deal with human lives and in many more areas. The increasing popularity of separation kernels demands the formal verification that assures the correctness of the functionalities in it. Further, formal verification of separation kernels has become mandatory by the security/safety certification authorities. Conclusion: This paper first presents the concept of separation kernel, and then it discusses the functionalities, design, and properties of it. The classification and analysis of the formal languages are being presented in this paper that has been used for writing the specifications of separation kernel and verifying it. The paper is an attempt towards the classification of formal languages being used for the verification of several separation kernels.

Finite-time control of discrete-time semi-Markov jump linear systems: A self-triggered MPC approach

In this paper, a self-triggered model predictive control (MPC) strategy is developed for discrete-time semi-Markov jump linear systems to achieve a desired finite-time performance. To obtain the multi-step predictive states when system mode jumping is subject to the semi-Markov chain, the concept of multi-step semi-Markov kernel is addressed. Meanwhile, a self-triggered scheme is formulated to predict sampling instants automatically and to reduce the computational burden of the on-line solving of MPC. Furthermore, the co-design of the self-triggered scheme and the MPC approach is adjusted to design the control input when keeping the state trajectories within a pre-specified bound over a given time interval. Finally, a numerical example and a population ecological system are introduced to evaluate the effectiveness of the proposed control.

Graph Filtration Kernels

The majority of popular graph kernels is based on the concept of Haussler's R-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering graph filtrations: Using meaningful orders on the set of edges, which allow to construct a sequence of nested graphs, we can consider a graph at multiple granularities. A key concept of our approach is to track graph features over the course of such graph resolutions. Rather than to simply compare frequencies of features in graphs, this allows for their comparison in terms of when and for how long they exist in the sequences. In this work, we propose a family of graph kernels that incorporate these existence intervals of features. While our approach can be applied to arbitrary graph features, we particularly highlight Weisfeiler-Lehman vertex labels, leading to efficient kernels. We show that using Weisfeiler-Lehman labels over certain filtrations strictly increases the expressive power over the ordinary Weisfeiler-Lehman procedure in terms of deciding graph isomorphism. In fact, this result directly yields more powerful graph kernels based on such features and has implications to graph neural networks due to their close relationship to the Weisfeiler-Lehman method. We empirically validate the expressive power of our graph kernels and show significant improvements over state-of-the-art graph kernels in terms of predictive performance on various real-world benchmark datasets.

Using Kernels to Harness the Complexity of Big Data Applications

This paper presents the concept of kernels to address the complexity of solving big-data applications. Their solution strategies often require evaluating domain-dependent subspaces on the big data and selecting the best result. As the data space in these problems is so vast that it is infeasible to scan the data once, we need domain-specific methods for identifying promising and manageable subspaces with a high density of solutions before looking for individual ones. To this end, we introduce kernels to represent some properties of the statistical quality, average density, or probability of solutions in a subspace to prune subspaces with suboptimal kernels. We classify various past approaches based on their analysis methods and illustrate each by an example. Our results confirm that kernels can effectively harness the complexity of solving big-data applications.

Category of Intuitionistic Fuzzy Modules

We study the relationship between the category of R-modules (CR-M) and the category of intuitionistic fuzzy modules (CR−IFM). We construct a category CLat(R−IFM) of complete lattices corresponding to every object in CR−M and then show that, corresponding to each morphism in CR−M, there exists a contravariant functor from CR−IFM to the category CLat (=union of all CLat(R−IFM), corresponding to each object in CR−M) that preserve infima. Then, we show that the category CR−IFM forms a top category over the category CR−M. Finally, we define and discuss the concept of kernel and cokernel in CR−IFM and show that CR−IFM is not an Abelian Category.

A Short Note On The Kernel Subgroup Of Intuitionistic Fuzzy Groups

This paper defines the concept of kernel subgroup of an intuitionistic fuzzy group. Also, it proves that this kernel is a group in the ordinary algebraic meaning as a direct application of the concept of kernel in fuzzy and anti-fuzzy groups. Also, we derive some properties of intuitionistic fuzzy groups.

Texture-Enhanced Light Field Super-Resolution With Spatio-Angular Decomposition Kernels

Despite the recent progress in light field super-resolution (LFSR) achieved by convolutional neural networks, the correlation information of LF images has not been sufficiently studied and exploited due to the complexity of 4-D LF data. To cope with such high-dimensional LF data, most of the existing LFSR methods resorted to decomposing it into lower dimensions and subsequently performing optimization on the decomposed subspaces. However, these methods are inherently limited as they neglected the characteristics of the decomposition operations and only utilized a limited set of LF subspaces ending up failing to sufficiently extract spatio-angular features and leading to a performance bottleneck. To overcome these limitations, in this article, we comprehensively discover the potentials of LF decomposition and propose a novel concept of decomposition kernels. In particular, we systematically unify the decomposition operations of various subspaces into a series of such decomposition kernels, which are incorporated into our proposed decomposition kernel network (DKNet) for comprehensive spatio-angular feature extraction. The proposed DKNet is experimentally verified to achieve considerable improvements compared with state-of-the-art methods. To further improve DKNet in producing more visually pleasing LFSR results, based on the VGG network, we propose a light field VGG (LFVGG) loss to guide the texture-enhanced DKNet (TE-DKNet) to generate rich authentic textures and enhance LF images’ visual quality significantly. We also propose an indirect evaluation metric by taking advantage of LF material recognition to objectively assess the perceptual enhancement brought by the LFVGG loss.

Congruence relations on pseudocomplemented almost distributive lattices

The concept of congruence kernels and congruence cokernels are studied in pseudocomplemented almost distributive lattices. A set of equivalent conditions are derived for a given subset J of a pseudocomplemented ADL L to be a congruence kernel (resp. a congruence cokernel). Moreover, for a given congruence kernel J of L the smallest and the largest *- congruences on L having J as a kernel are given and characterized in various forms.

Modeling and prediction of tool influence function under complex edge in sub-aperture optical polishing.

Edge mis-figures are regarded as one of the most difficult technical issues in optical fabrication. At present, only the near straight-line edge tool influence function (TIF) can be fitted by a polynomial function, but it is difficult to unify a 2-D analytical model suitable for complex edge workpieces and various tools, due to the lack of the scientific understanding of the edge removal behavior. In this paper, a comprehensive mathematical model is proposed to reveal the mechanism of the edge effect and accurately predict the complex edge TIF. The concept of a nonlinear edge kernel is first proposed and verified that the nonlinear pressure can be characterized by convoluting the kernel with the edge contour, which can be easily adapted to complex edge cases; besides, the edge kernel obtaining algorithm is established. The linear pressure part is verified to be constrained by the moment balance formula, which occurs in universal joint tool. Besides, the basic pressure distribution is presented to compensate the pressure distortion caused by the uneven form of the tool pad. The introducing of these three parts makes the complex edge pressure modeled efficiently and matched perfectly with the FEA results. In addition, a series of TIF experiments were carried out on various complex edge workpieces and different tools, which could be well predicted by the proposed model in 2-D view.

Intermittency acceleration of water droplet population dynamics inside the interfacial layer between cloudy and clear air environments

The formation and life-span of clouds as well as the associated unsteady processes concerning the micro-physics of the water phases they may contain are open questions in atmospheric physics.We here use three-dimensional direct numerical simulation to analyse the temporal evolution of a small portion of the top of a cloud. The Eulerian description of the turbulent velocity, temperature and vapor fields is combined with the Lagrangian description of two different ensembles of cloud droplets, that is, with a monodisperse and a polydisperse size distribution. A shear-free turbulent mixing layer is used to model the background air flow of the cloud top. This flow is considered appropriate because clouds cannot stand the presence of shear, which inevitably destroys them quickly. Luke-warm clouds are generally found at an altitude of 1000-2000 meters, live for a few hours or up to 1-2 days, continuously change shape, and have typical dimensions of some hundreds of meters. The global time-scale of these changes is recognized as being of the order of 100 seconds (Shaw (2003), Warhaft (2009)). From the formation phase to the dying out phase, clouds live under a continuous sequence of transients that are slightly different one from the other.In this study, we have tried to reduce the simplification level with respect to the real warm cloud situation as much as possible. We have included the same level of supersaturation of warm clouds, the same amount of liquid water content, and thus, the same numerical number of water droplets, and finally, a typical unstable perturbation of the density stratification and a typical kinetic energy cloud / clear air ratio (order of 10). We have considered an observation duration of the order of a few seconds (about 10 initial turnaround times). During this time, the kinetic energy decays throughout the system by 95%. It should be recalled that the kinetic energy inside the interfacial layer (the shear-free turbulent mixing layer that matches the cloud region to the ambient air region) also decays spatially, by nearly 85%. We observed, with respect to the cloud region, in the interfacial layer, a five times faster achievement of a common value of standard deviation for the probability density of both the monodisperse and poly-disperse populations. This acceleration of the dynamics is remarkable and is somewhat counterintuitive. It is closely correlated with the intermittency of the small scale of the air flow and of the supersaturation fluctuation. We give information on the size distribution of both the positive and negative droplet growth and on the drop size and the corresponding numerical concentration value of the distribution peak as time passes. Finally, we comment on the extension of the concept of the collision kernel for an unstable and inhomogeneous system in which turbulence decays faster than the time scales of the involved aqueous phases.