SVM with Quadratic Polynomial Kernel Function Based Nonlinear Model One-step-ahead Predictive Control

A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.

Landslide prediction based on improved principal component analysis and mixed kernel function least squares support vector regression model

Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a curse of dimensionality and thus lead to reduce prediction accuracy.Then the generalization ability of the model will also decline sharply when there are only small samples.To reduce the dimension of calculation and balance the model’s generalization and learning ability,this study proposed a landslide prediction method based on improved principal component analysis(PCA)and mixed kernel function least squares support vector regression(LSSVR)model.First,the traditional PCA was introduced with the idea of linear discrimination,and the dimensions of initial influencing factors were reduced from 8 to 3.The improved PCA can not only weight variables but also extract the original feature.Furthermore,combined with global and local kernel function,the mixed kernel function LSSVR model was framed to improve the generalization ability.Whale optimization algorithm(WOA)was used to optimize the parameters.Moreover,Root Mean Square Error(RMSE),the sum of squared errors(SSE),Mean Absolute Error(MAE),Mean Absolute Precentage Error(MAPE),and reliability were employed to verify the performance of the model.Compared with radial basis function(RBF)LSSVR model,Elman neural network model,and fuzzy decision model,the proposed method has a smaller deviation.Finally,the landslide warning level obtained from the landslide probability can also provide references for relevant decision-making departments in emergency response.

An algorithm for moving target detection in IR image based on grayscale distribution and kernel function

A fast algorithm based on the grayscale distribution of infrared target and the weighted kernel function was proposed for the moving target detection(MTD) in dynamic scene of image series. This algorithm is used to deal with issues like the large computational complexity, the fluctuation of grayscale, and the noise in infrared images. Four characteristic points were selected by analyzing the grayscale distribution in infrared image, of which the series was quickly matched with an affine transformation model. The image was then divided into 32×32 squares and the gray-weighted kernel(GWK) for each square was calculated. At last, the MTD was carried out according to the variation of the four GWKs. The results indicate that the MTD can be achieved in real time using the algorithm with the fluctuations of grayscale and noise can be effectively suppressed. The detection probability is greater than 90% with the false alarm rate lower than 5% when the calculation time is less than 40 ms.

Interior-point algorithm based on general kernel function for monotone linear complementarity problem

A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.

AN ASYMPTOTIC EXPANSION FORMULA OF KERNEL FUNCTION FOR QUASI FOURIER-LEGENDRE SERIES AND ITS APPLICATION

Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.

Multi-output Gaussian Process Regression Model with Combined Kernel Function for Polyester Esterification Processes

In polyester fiber industrial processes,the prediction of key performance indicators is vital for product quality.The esterification process is an indispensable step in the polyester polymerization process.It has the characteristics of strong coupling,nonlinearity and complex mechanism.To solve these problems,we put forward a multi-output Gaussian process regression(MGPR)model based on the combined kernel function for the polyester esterification process.Since the seasonal and trend decomposition using loess(STL)can extract the periodic and trend characteristics of time series,a combined kernel function based on the STL and the kernel function analysis is constructed for the MGPR.The effectiveness of the proposed model is verified by the actual polyester esterification process data collected from fiber production.

Protein-Protein Interaction Extraction Based on Convex Combination Kernel Function

Owing to the effect of classified models was different in Protein-Protein Interaction(PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the optimal classified model to extract PPI, this paper presents a strategy to find the optimal kernel function from a kernel function set. The strategy is that in the kernel function set which consists of different single kernel functions, endlessly finding the last two kernel functions on the performance in PPI extraction, using their optimal kernel function to replace them, until there is only one kernel function and it’s the final optimal kernel function. Finally, extracting PPI using the classified model made by this kernel function. This paper conducted the PPI extraction experiment on AIMed corpus, the experimental result shows that the optimal convex combination kernel function this paper presents can effectively improve the extraction performance than single kernel function, and it gets the best precision which reaches 65.0 among the similar PPI extraction systems.

A Modified Full-NT-Step Infeasible Interior-Point Algorithm for SDP Based on a Specific Kernel Function

This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.

A New Full-NT-Step Infeasible Interior-Point Algorithm for SDP Based on a Specific Kernel Function

In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.

Simultaneous upscaling of two properties of reservoirs in one dimension using adaptive bandwidth in kernel function method

Upscaling of primary geological models with huge cells, especially in porous media, is the first step in fluid flow simulation. Numerical methods are often used to solve the models. The upscaling method must preserve the important properties of the spatial distribution of the reservoir properties. An grid upscaling method based on adaptive bandwidth in kernel function is proposed according to the spatial distribution of property. This type of upscaling reduces the number of cells, while preserves the main heterogeneity features of the original fine model. The key point of the paper is upscaling two reservoir properties simultaneously. For each reservoir feature, the amount of bandwidth or optimal threshold is calculated and the results of the upscaling are obtained. Then two approaches are used to upscaling two properties simultaneously based on maximum bandwidth and minimum bandwidth. In fact, we now have a finalized upscaled model for both reservoir properties for each approach in which not only the number of their cells, but also the locations of the cells are equal. The upscaling error of the minimum bandwidth approach is less than that of the maximum bandwidth approach.

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.

Bergman kernel function on Hua Construction of the second type

In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.

A Large-update Interior-point Algorithm for Convex Quadratic Semi-definite Optimization Based on a New Kernel Function

In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O（√n（logn）2 log e/n）. This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and in optimization fields. Some computational results recent kernel functions introduced by some authors have been provided.

Bergman kernel function on the third Hua Construction

The Bergman kernel function for Hua Construction of the third type is given in an explicit formula.

Interior-Point Algorithm for Linear Optimization Based on a New Kernel Function

In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.

Zero Problems of the Bergman Kernel Function on the First Type of Cartan-Hartogs Domain

The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros.If the Bergman kernel function of this type of domain has zeros,the zero set is composed of several path-connected branches,and there exists a continuous curve to connect any two points in the non-zero set.

Complexity Analysis of an Interior Point Algorithm for the Semidefinite Optimization Based on a Kernel Function with a Double Barrier Term

In this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization（SDO） problems. The proposed algorithm is based on a new kernel function which differs from the existing kernel functions in which it has a double barrier term. With this function we define a new search direction and also a new proximity function for analyzing its complexity. We show that if q1 〉 q2 〉 1, the algorithm has O（（q1 ＋ 1） nq1＋1/2（q1-q2）logn/ε）and O（（q1 ＋ 1）2（q1-q2）^3q1-2q2＋1√n logn/c） complexity results for large- and small-update methods, respectively.

A Full-Newton Step Feasible IPM for Semidefinite Optimization Based on a Kernel Function with Linear Growth Term

In this paper,we propose and analyze a full-Newton step feasible interior-point algorithm for semidefinite optimization based on a kernel function with linear growth term.The kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center for the algorithm.By developing a new norm-based proximity measure and some technical results,we derive the iteration bound that coincides with the currently best known iteration bound for the algorithm with small-update method.In our knowledge,this result is the first instance of full-Newton step feasible interior-point method for SDO which involving the kernel function.

Extremal optimization for optimizing kernel function and its parameters in support vector regression

The performance of the support vector regression (SVR) model is sensitive to the kernel type and its parameters.The determination of an appropriate kernel type and the associated parameters for SVR is a challenging research topic in the field of support vector learning.In this study,we present a novel method for simultaneous optimization of the SVR kernel function and its parameters,formulated as a mixed integer optimization problem and solved using the recently proposed heuristic 'extremal optimization (EO)'.We present the problem formulation for the optimization of the SVR kernel and parameters,the EO-SVR algorithm,and experimental tests with five benchmark regression problems.The results of comparison with other traditional approaches show that the proposed EO-SVR method provides better generalization performance by successfully identifying the optimal SVR kernel function and its parameters.

A Primal-dual Large-update Interior-point Algorithm for P_*(κ)-LCP Based on a New Class of Kernel Functions

In this paper, we propose a large-update primal-dual interior point algorithm for P_＊（κ）-linear complementarity problem. The method is based on a new class of kernel functions which is neither classical logarithmic function nor self-regular functions. It is determines both search directions and the proximity measure between the iterate and the center path. We show that if a strictly feasible starting point is available, then the new algorithm has O（1 ＋ 2κ）p√n（1/plog n ＋ 1）^2 lognε iteration complexity which becomes O（（1 ＋ 2κ）√nlog n logn/ε）with special choice of the parameter p. It is matches the currently best known iteration bound for P＊（κ）-linear complementarity problem. Some computational results have been provided.