Comparing RBF‐FD approximations based on stabilized Gaussians and on polyharmonic splines with polynomials

In this work, we are concerned with radial basis function–generated finite difference (RBF‐FD) approximations. Numerical error estimates are presented for stabilized flat Gaussians (RBF(SGA)‐FD) and polyharmonic splines with supplementary polynomials (RBF(PHS)‐FD) using some analytical solutions of the Poisson equation in a square domain. Both structured and unstructured point clouds are employed for evaluating the influence of cloud refinement, size of local supports, and maximal permissible degree of the polynomials in RBF(PHS)‐FD. High order of accuracy was attained with both RBF(SGA)‐FD and RBF(PHS)‐FD especially for unstructured clouds. Absolute errors in the first and second derivatives were also estimated at all points of the domain using one of the analytical solutions. For RBF(SGA)‐FD, this test showed the occurrence of improprieties of some decentered supports localized on boundary neighborhoods. This phenomenon was not observed with RBF(PHS)‐FD.     

高维部分线性模型中的变量选择

研究了高维部分线性模型中的变量选择,结合样条方法和Dantzig或Lasso变量选择方法,同时进行变量选择和未知参数估计,证明了估计误差的非渐近界.模拟结果说明,该方法在参数维数较高时优于已有方法.     

Optimizing at the end-points the Akima's interpolation method of smooth curve fitting

In this paper we propose an optimized version, at the end-points, of the Akima's interpolation method for experimental data fitting. Comparing with the Akima's procedure, the error estimate, in terms of the modulus of continuity, is improved. Similarly, we optimize at the end points the Catmull–Rom's cubic spline. The properties of the obtained splines are illustrated on a numerical experiment.     

Differential constraints for bounded recursive identification with multivariate splines

The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model-based control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able to perform online model identification and bounded model extrapolation in the framework of a model-based control system. A new type of linear constraints, the differential constraints, are used as differential boundary conditions within the recursive estimator which limit polynomial divergence when extrapolating data. The differential constraints are derived with a new, one-step matrix form of the de Casteljau algorithm, which reduces their formulation into a single matrix multiplication. The recursive estimator is demonstrated on a bivariate dataset, where it is shown to provide a speedup of two orders of magnitude over an ordinary least squares batch method. Additionally, it is demonstrated that inclusion of differential constraints in the least squares optimization scheme can prevent polynomial divergence close to edges of the model domain where local data coverage may be insufficient, a situation often encountered with global recursive data approximation.     

A data mining application to deposit pricing: Main determinants and prediction models

This study provides unique empirical evidence regarding the determinants of deposit pricing by employing data mining methods and making use of proprietary data provided by a commercial bank. Results highlight the importance of taking into account customer- and account-specific characteristics in the determination of deposit rates. Contrary to existing evidence obtained from macro-level bank data, the customer-level data used in this study suggest that depositors with a multi-faceted and long-term relationship with the same bank seem to benefit from higher deposit rates as a reward for being a core depositor. The location of the customer is also shown to have a limited effect on the deposit rates.     

Spline approximation with interpolation constraints for numerical integration

By using a Walsh-type theorem, we impose a finite number of interpolation constraints to a polynomial spline approximation operator. These constrained approximating splines reproduce polynomials and give orders of convergence identical to those of the unconstrained ones. We give an application in numerical integration by using the constrained splines for evaluation of Cauchy principal value integrals.     

A hybrid fuzzy regression model and its application in hydrology engineering

The goal of this paper is to handle the large variation issues in fuzzy data by constructing a variable spread multivariate adaptive regression splines (MARS) fuzzy regression model with crisp parameters estimation and fuzzy error terms. It deals with imprecise measurement of response variable and crisp measurement of explanatory variables. The proposed method is a two-phase procedure which applies the MARS technique at phase one and an optimization problem at phase two to estimate the center and fuzziness of the response variable. The proposed method, therefore, handles two problems simultaneously: the problem of large variation issue and the problem of variation spreads in fuzzy observations. A realistic application of the proposed method is also presented, by which the suspended load is modeled using discharge in a hydrology engineering problem. Empirical results demonstrate that the proposed approach is more efficient and more realistic than some well-known least-squares fuzzy regression models.     

Control of Nonlinear Systems Using a Self-Organising Neural Network

Two applications of Self Organising Map (SOM) networks in the context of nonlinear control are introduced, one in approximate feedback linearisation and the second in optimal control. It is shown that a modified SOM can be used to approximately Input/Output (I/O) linearise and to control nonlinear systems using a combination of the SOM learning algorithm, and a biologically inspired optimisation algorithm known as chemotaxis. A proof to guarantee the stability of the closed loop during the training of the network and the operation of the whole system is included. The results are illustrated with simulations of a single link manipulator.