Local hybrid approximation for scattered data fitting with bivariate splines

We suggest a local hybrid approximation scheme based on polynomials and radial basis functions, and use it to improve the scattered data fitting algorithm of (Davydov, O., Zeilfelder, F., 2004. Scattered data fitting by direct extension of local polynomials to bivariate splines. Adv. Comp. Math. 21, 223–271). Similar to that algorithm, the new method has linear computational complexity and is therefore suitable for large real world data. Numerical examples suggest that it can produce high quality artifact-free approximations that are more accurate than those given by the original method where pure polynomial local approximations are used.     

Calculating with box splines

Box splines are multivariate splines over regular grids. Two recursion formulas for box splines are developed: (1) a Mansfield-de Boor-like expression of box splines as linear combinations of box splines of lower degree and (2) a deBoor-like reduction of the net of box spline control points. The ideas follow those from the paper by deBoor in 1972. The proofs are geometrical and simple.     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

Stochastic approximation learning for mixtures of multivariate elliptical distributions

Most of the current approaches to mixture modeling consider mixture components from a few families of probability distributions, in particular from the Gaussian family. The reasons of these preferences can be traced to their training algorithms, typically versions of the Expectation-Maximization (EM) method. The re-estimation equations needed by this method become very complex as the mixture components depart from the simplest cases. Here we propose to use a stochastic approximation method for probabilistic mixture learning. Under this method it is straightforward to train mixtures composed by a wide range of mixture components from different families. Hence, it is a flexible alternative for mixture learning. Experimental results are presented to show the probability density and missing value estimation capabilities of our proposal.     

Fitting Triangular B-Splines to Functional Scattered Data

Scattered data is, by definition, irregularly spaced. Uniform surface schemes are not well adapted to the locally varying nature of such data. Conversely, Triangular B-Spline surfaces 2 are more flexible in that they can be built over arbitrary triangulations and thus can be adapted to the scattered data. This paper discusses the use of DMS spline surfaces for approximation of scattered data. A method is provided for automatically triangulating the domain containing the points and generating basis functions over this triangulation. A surface approximating the data is then found by a combination of least squares and bending energy minimization. This combination serves both to generate a smooth surface and to accommodate for gaps in the data. Examples are presented which demonstrate the eftectiveness of the technique for mathematical, geographical and other data sets.     

Application of integrated recurrent neural network with multivariate adaptive regression splines on SPC-EPC process

The integration of statistical process control and engineering process control has been reported as an effective way to monitor and control the autocorrelated process. However, because engineering process control compensates for the effects of underlying disturbances, the disturbance patterns become very hard to recognize, especially when various abnormal control chart patterns are mixed and co-existed in the engineering process. In this study, a new control chart pattern recognition model which integrates multivariate adaptive regression splines and recurrent neural network is proposed to not only address the problem of feature selection (i.e., lagged process measurements) but also improve the pattern recognition accuracy. The performance of the proposed method is evaluated by comparing the recognition results of multivariate adaptive regression splines and recurrent neural network with the results of four competing approaches (multivariate adaptive regression splines-extreme learning machine, multivariate adaptive regression splines-random forest, single recurrent neural network, and single random forest) on the simulated individual process data. The experimental study shows that the proposed multivariate adaptive regression splines and recurrent neural network approach can not only solve the problem of variable selection but also outperform other competing models. Moreover, according to the lagged process measurements selected by the proposed approach, lagged observations that exerted significant impact on the construction of the control chart pattern recognition model can be identified successfully. This study has significant implications for research and practice in production management and provides a valuable reference for manufacturing process managers to better understand and develop strategies for control chart pattern recognition.     

A two-stage hybrid credit scoring model using artificial neural networks and multivariate adaptive regression splines

The objective of the proposed study is to explore the performance of credit scoring using a two-stage hybrid modeling procedure with artificial neural networks and multivariate adaptive regression splines (MARS). The rationale under the analyses is firstly to use MARS in building the credit scoring model, the obtained significant variables are then served as the input nodes of the neural networks model. To demonstrate the effectiveness and feasibility of the proposed modeling procedure, credit scoring tasks are performed on one bank housing loan dataset using cross-validation approach. As the results reveal, the proposed hybrid approach outperforms the results using discriminant analysis, logistic regression, artificial neural networks and MARS and hence provides an alternative in handling credit scoring tasks.     

Numerical integration on multivariate scattered data by Lobachevsky splines

In this paper, we investigate the numerical integration problem of a real valued function generally known only on multivariate scattered points using Lobachevsky splines, a pioneering version of cardinal B-splines. Starting from their interpolation properties, we focus on the construction of new integration formulas, which are quite flexible requiring no special distribution of nodes. Numerical results using Lobachevsky splines turn out to be interesting and promising for both accuracy and simplicity in computation. Finally, a comparison with integration by radial basis functions confirms the validity of the proposed approach.     

Recursive identification for multivariate errors-in-variables systems

The recursive algorithm is given for estimating matrix coefficients of the multivariate errors-in-variables (EIV) systems. It is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the Yule-Walker equation satisfied by the true coefficients of the system. The sufficient conditions guaranteeing the uniqueness of the solution to the Yule-Walker equation are given. In this case the estimate provided by the recursive algorithm is strongly consistent.     

带形状参数的三次三角Hermite插值样条曲线

给出了一种带形状参数的三次三角Hermite插值样条曲线,具有标准三次Hermite插值样条曲线完全相同的性质。给定插值条件时,样条曲线的形状可通过改变形状参数的取值进行调控。在适当条件下,该样条曲线对应的Ferguson曲线可精确表示椭圆、抛物线等工程曲线。通过选择合适的形状参数,该插值样条曲线能达到[C2]连续,而且其整体逼近效果要好于标准三次Hermite插值样条曲线。     

Reexamining the impact of information technology investment on productivity using regression tree and multivariate adaptive regression splines (MARS)

As health care costs increased significantly in the 1990s, investments in information technology (IT) in the health care industry have also increased continuously in order to improve the quality of patient care and to respond to government pressure to reduce costs. Several studies have investigated the impact of IT on productivity with mixed conclusions. In this paper, we revisit this issue and re-examine the impact of investments in IT on hospital productivity using two data mining techniques, which allowed us to explore interactions between the input variables as well as conditional impacts. The results of our study indicated that the relationship between IT investment and productivity is very complex. We found that the impact of IT investment is not uniform and the rate of IT impact varies contingent on the amounts invested in the IT Stock, Non-IT Labor, Non-IT Capital, and possibly time.     

Maximum likelihood-based recursive least-squares estimation for multivariable systems using the data filtering technique

For multivariable equation-error systems with an autoregressive moving average noise, this paper applies the decomposition technique to transform a multivariable model into several identification sub-models based on the number of the system outputs, and derives a data filtering and maximum likelihood-based recursive least-squares algorithm to reduce the computation complexity and improve the parameter estimation accuracy. A multivariable recursive generalised extended least-squares method and a filtering-based recursive extended least-squares method are presented to show the effectiveness of the proposed algorithm. The simulation results indicate that the proposed method is effective and can produce more accurate parameter estimates than the compared methods.     

An algorithm for multivariate function estimation based on hierarchically refined sparse grids

An adaptive function estimation approach is presented to recover an unknown, multivariate functional relation from noisy data. Using a sparse grid combination approach, both discretization and Tikhonov regularization need to be selected appropriately to resolve functional details whilst suppressing measurement noise. An initially coarse, multivariate grid is adaptively refined using sensitivity analysis, creating a sequence of hierarchically refined grids. The problem of choosing a multi-dimensional discretization level is thus transformed to the identification of a suitable refinement step, giving rise to a nested approach for the selection of both discretization and Tikhonov regularization. Validation on multivariate test functions shows good approximation results.     

KNN-kernel density-based clustering for high-dimensional multivariate data

Density-based clustering algorithms for multivariate data often have difficulties with high-dimensional data and clusters of very different densities. A new density-based clustering algorithm, called KNNCLUST, is presented in this paper that is able to tackle these situations. It is based on the combination of nonparametric k-nearest-neighbor (KNN) and kernel (KNN-kernel) density estimation. The KNN-kernel density estimation technique makes it possible to model clusters of different densities in high-dimensional data sets. Moreover, the number of clusters is identified automatically by the algorithm. KNNCLUST is tested using simulated data and applied to a multispectral compact airborne spectrographic imager (CASI)_image of a floodplain in the Netherlands to illustrate the characteristics of the method.     

Joint order and parameter estimation of multivariate autoregressive models using multi-model partitioning theory

In this paper the multi-model partitioning theory is used for simultaneous order and parameter estimation of multivariate autoregressive models. Simulation experiments show that the proposed method successfully selects the correct model order and estimates the parameters accurately, in very few steps, even with a small sample size. They also show that the proposed method performs equally well when the complexity of the model is increased. The results are compared to those obtained using well-established order selection criteria. Finally, it is shown that the method is also successful in tracking model order changes, in real time.     

Parameter identification for models with bounded errors in all variables

In this paper, the problem of parameter identification for models with bounded measurement errors both on the input and on the output is addressed and some corrections to previously published results are presented. In particular, it is shown that only parameter overbounds can in general be computed for systems of the form y = (φ + δφ)θ + δy when the bounded measurement errors δφ and δy are correlated. Since ARMAX and bilinear systems can be represented in this form, it turns out that tight parameter bounds are in general not available for these systems. Finally, we show that it is possible to check a posteriori whether the obtained bounds are tight or not.     

Strong consistence of recursive identification for Wiener systems

The paper concerns identification of the Wiener system consisting of a linear subsystem followed by a static nonlinearity f(·) with no invertibility and structure assumption. Recursive estimates are given for coefficients of the linear subsystem and for the value f(v) at any fixed v. The main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values. This probably is the first strong consistency result for this kind of Wiener systems. A numerical example is given, which justifies the theoretical analysis.     

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.     

Survey of glyph-based visualization techniques for spatial multivariate medical data

In this survey article, we review glyph-based visualization techniques that have been exploited when visualizing spatial multivariate medical data. To classify these techniques, we derive a taxonomy of glyph properties that is based on classification concepts established in information visualization. Considering both the glyph visualization as well as the interaction techniques that are employed to generate or explore the glyph visualization, we are able to classify glyph techniques into two main groups: those supporting pre-attentive and those supporting attentive processing. With respect to this classification, we review glyph-based techniques described in the medical visualization literature. Based on the outcome of the literature review, we propose design guidelines for glyph visualizations in the medical domain.