Fully complex-valued radial basis function networks for orthogonal least squares regression

We consider a fully complex-valued radial basis function (RBF) network for regression application. The locally regularised orthogonal least squares (LROLS) algorithm with the D-optimality experimental design, originally derived for constructing parsimonious real-valued RBF network models, is extended to the fully complex-valued RBF 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 complex-valued RBF network.

Sparse multioutput radial basis function network construction using combined locally regularised orthogonal least square and D-optimality experimental design

A construction algorithm for multioutput radial basis function (RBF) network modelling is introduced by combining a locally regularised orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximised model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious RBF network model with excellent generalisation performance. The D-optimality design criterion enhances the model efficiency and robustness. A further advantage of the combined approach is that the user only needs to specify a weighting for the D-optimality cost in the combined RBF model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

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.

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.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Evaluation of reach and grasp robot-assisted therapy suggests similar functional recovery patterns on proximal and distal arm segments in sub-acute hemiplegia

This paper provides some additional evidence in support of the hypothesis that robot therapies are clinically beneficial in neurorehabilitation. Although only 4 subjects were included in the study, the design of the intervention and the measures were done so as to minimise bias. The results are presented as single case studies, and can only be interpreted as such due to the study size. The intensity of intervention was 16 hours and the therapy philosophy (based on Carr and Shepherd) was that coordinated movements are preferable to joint based therapies, and that coordinating distal movements (in this case grasps) helps not only to recover function in these areas, but has greater value since the results are immediately transferable to daily skills such as reach and grasp movements.

Interactions between cocoa flavanols and inorganic nitrate: additive effects on endothelial function at achievable dietary amounts

Dietary intervention studies have shown that flavanols and inorganic nitrate can improve vascular function, suggesting that these two bioactives may be responsible for beneficial health effects of diets rich in fruits and vegetables. We aimed to study interactions between cocoa flavanols (CF) and nitrate, focusing on absorption, bioavailability, excretion, and efficacy to increase endothelial function. In a double-blind randomized, dose-response crossover study, flow-mediated dilation (FMD) was measured in 15 healthy subjects before and at 1, 2, 3, and 4 h after consumption of CF (1.4-10.9 mg/kg bw) or nitrate (0.1-10 mg/kg bw). To study flavanol-nitrate interactions, an additional intervention trial was performed with nitrate and CF taken in sequence at low and high amounts. FMD was measured before (0 h) and at 1h after ingestion of nitrate (3 or 8.5 mg/kg bw) or water. Then subjects received a CF drink (2.7 or 10.9 mg/kg bw) or a micro- and macronutrient-matched CF-free drink. FMD was measured at 1, 2, and 4 h thereafter. Blood and urine samples were collected and assessed for CF and nitric oxide (NO) metabolites with HPLC and gas-phase reductive chemiluminescence. Finally, intragastric formation of NO after CF and nitrate consumption was investigated. Both CF and nitrate induced similar intake-dependent increases in FMD. Maximal values were achieved at 1 h postingestion and gradually decreased to reach baseline values at 4 h. These effects were additive at low intake levels, whereas CF did not further increase FMD after high nitrate intake. Nitrate did not affect flavanol absorption, bioavailability, or excretion, but CF enhanced nitrate-related gastric NO formation and attenuated the increase in plasma nitrite after nitrate intake. Both flavanols and inorganic nitrate can improve endothelial function in healthy subjects at intake amounts that are achievable with a normal diet. Even low dietary intake of these bioactives may exert relevant effects on endothelial function when ingested together.