Orthogonal forward selection for constructing the radial basis function network with tunable nodes

An orthogonal forward selection (OFS) algorithm based on the leave-one-out (LOO) criterion is proposed for the construction of radial basis function (RBF) networks with tunable nodes. This OFS-LOO algorithm is computationally efficient and is capable of identifying parsimonious RBF networks that generalise well. Moreover, the proposed algorithm is fully automatic and the user does not need to specify a termination criterion for the construction process.

Fully complex-valued radial basis function networks: orthogonal least squares regression and classification

We consider a fully complex-valued radial basis function (RBF) network for regression and classification applications. For regression problems, the locally regularised orthogonal least squares (LROLS) algorithm aided with the D-optimality experimental design, originally derived for constructing parsimonious real-valued RBF models, is extended to the fully complex-valued RBF (CVRBF) network. Like its real-valued counterpart, the proposed algorithm aims to achieve maximised model robustness and sparsity by combining two effective and complementary approaches. The LROLS algorithm alone is capable of producing a very parsimonious model with excellent generalisation performance while the D-optimality design criterion further enhances the model efficiency and robustness. By specifying an appropriate weighting for the D-optimality cost in the combined model selecting criterion, the entire model construction procedure becomes automatic. An example of identifying a complex-valued nonlinear channel is used to illustrate the regression application of the proposed fully CVRBF network. The proposed fully CVRBF network is also applied to four-class classification problems that are typically encountered in communication systems. A complex-valued orthogonal forward selection algorithm based on the multi-class Fisher ratio of class separability measure is derived for constructing sparse CVRBF classifiers that generalise well. The effectiveness of the proposed algorithm is demonstrated using the example of nonlinear beamforming for multiple-antenna aided communication systems that employ complex-valued quadrature phase shift keying modulation scheme. (C) 2007 Elsevier B.V. All rights reserved.

Construction of tunable radial basis function networks using orthogonal forward selection

An orthogonal forward selection (OFS) algorithm based on leave-one-out (LOO) criteria is proposed for the construction of radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines an RBF node, namely, its center vector and diagonal covariance matrix, by minimizing the LOO statistics. For regression application, the LOO criterion is chosen to be the LOO mean-square error, while the LOO misclassification rate is adopted in two-class classification application. This OFS-LOO algorithm is computationally efficient, and it is capable of constructing parsimonious RBF networks that generalize well. Moreover, the proposed algorithm is fully automatic, and the user does not need to specify a termination criterion for the construction process. The effectiveness of the proposed RBF network construction procedure is demonstrated using examples taken from both regression and classification applications.

Cooled infrared filters and dichroics for the James Webb Space Telescope Mid-Infrared Instrument

The cooled infrared filters and dichroic beam splitters manufactured for the Mid-Infrared Instrument are key optical components for the selection and isolation of wavelengths in the study of astrophysical properties of stars, galaxies, and other planetary objects. We describe the spectral design and manufacture of the precision cooled filter coatings for the spectrometer (7 K) and imager (9 K). Details of the design methods used to achieve the spectral requirements, selection of thin film materials, deposition technique, and testing are presented together with the optical layout of the instrument. (C) 2008 Optical Society of America.

A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

Modified radial basis function neural network using output transformation

A modified radial basis function (RBF) neural network and its identification algorithm based on observational data with heterogeneous noise are introduced. The transformed system output of Box-Cox is represented by the RBF neural network. To identify the model from observational data, the singular value decomposition of the full regression matrix consisting of basis functions formed by system input data is initially carried out and a new fast identification method is then developed using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator (MLE) for a model base spanned by the largest eigenvectors. Finally, the Box-Cox transformation-based RBF neural network, with good generalisation and sparsity, is identified based on the derived optimal Box-Cox transformation and an orthogonal forward regression algorithm using a pseudo-PRESS statistic to select a sparse RBF model with good generalisation. The proposed algorithm and its efficacy are demonstrated with numerical examples.

Experimental design and model construction algorithms for radial basis function networks

New construction algorithms for radial basis function (RBF) network modelling are introduced based on the A-optimality and D-optimality experimental design criteria respectively. We utilize new cost functions, based on experimental design criteria, for model selection that simultaneously optimizes model approximation, parameter variance (A-optimality) or model robustness (D-optimality). The proposed approaches are based on the forward orthogonal least-squares (OLS) algorithm, such that the new A-optimality- and D-optimality-based cost functions are constructed on the basis of an orthogonalization process that gains computational advantages and hence maintains the inherent computational efficiency associated with the conventional forward OLS approach. The proposed approach enhances the very popular forward OLS-algorithm-based RBF model construction method since the resultant RBF models are constructed in a manner that the system dynamics approximation capability, model adequacy and robustness are optimized simultaneously. The numerical examples provided show significant improvement based on the D-optimality design criterion, demonstrating that there is significant room for improvement in modelling via the popular RBF neural network.

Search space pruning and global optimisation of Multiple Gravity Assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.

Determining information requirements for e-business Systems - from activity space to information space

The study of information requirements for e-business systems reveals that the level of detail, granularity, format of presentation, and a broad range of information types are required for the applications. The provision of relevant information affects how e-business systems can efficiently support the business goals and processes. This paper presents an approach for determining information requirements for e-business systems (DIRES) which will allow the user to describe the core business processes, whose specification maps onto a business activity space. It further aids a configuration of information requirements into an information space. A case study of a logistics company in China demonstrates the use of DIRES techniques and assesses the validity of the research.

Orthogonal space-time block codes for free-space IM/DD optical links

Use of orthogonal space-time block codes (STBCs) with multiple transmitters and receivers can improve signal quality. However, in optical intensity modulated signals, output of the transmitter is non-negative and hence standard orthogonal STBC schemes need to be modified. A generalised framework for applying orthogonal STBCs for free-space IM/DD optical links is presented.

PIC detector for distributed space-time block coding under imperfect synchronisation

A parallel interference cancellation (PIC) detection scheme is proposed to suppress the impact of imperfect synchronisation. By treating as interference the extra components in the received signal caused by timing misalignment, the PIC detector not only offers much improved performance but also retains a low structural and computational complexity.

Near-optimum detection for distributed space-time block coding under imperfect synchronization

Significant performance gain can potentially be achieved by employing distributed space-time block coding (D-STBC) in ad hoc or mesh networks. So far, however, most research on D-STBC has assumed that cooperative relay nodes are perfectly synchronized. Considering the difficulty in meeting such an assumption in many practical systems, this paper proposes a simple and near-optimum detection scheme for the case of two relay nodes, which proves to be able to handle far greater timing misalignment than the conventional STBC detector.

Signal detection for distributed space-time block coding: 4 relay nodes under quasi-synchronisation

Most research on Distributed Space-Time Block Coding (D-STBC) has so far focused on the case of 2 relay nodes and assumed that the relay nodes are perfectly synchronised at the symbol level. This paper applies STBC to 4-relaynode systems under quasi-synchronisation and derives a new detector based on parallel interference cancellation, which proves to be very effective in suppressing the impact of imperfect synchronisation.

Radial basis function classifier construction using particle swarm optimisation aided orthogonal forward regression

We develop a particle swarm optimisation (PSO) aided orthogonal forward regression (OFR) approach for constructing radial basis function (RBF) classifiers with tunable nodes. At each stage of the OFR construction process, the centre vector and diagonal covariance matrix of one RBF node is determined efficiently by minimising the leave-one-out (LOO) misclassification rate (MR) using a PSO algorithm. Compared with the state-of-the-art regularisation assisted orthogonal least square algorithm based on the LOO MR for selecting fixednode RBF classifiers, the proposed PSO aided OFR algorithm for constructing tunable-node RBF classifiers offers significant advantages in terms of better generalisation performance and smaller model size as well as imposes lower computational complexity in classifier construction process. Moreover, the proposed algorithm does not have any hyperparameter that requires costly tuning based on cross validation.

Prediction of Parkinson’s disease tremor onset using radial basis function neural networks

The possibility of using a radial basis function neural network (RBFNN) to accurately recognise and predict the onset of Parkinson’s disease tremors in human subjects is discussed in this paper. The data for training the RBFNN are obtained by means of deep brain electrodes implanted in a Parkinson disease patient’s brain. The effectiveness of a RBFNN is initially demonstrated by a real case study.