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.

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.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

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.

The influence of organic acids in relation to acid deposition in controlling the acidity of soil and stream waters on a seasonal basis

Much uncertainty still exists regarding the relative importance of organic acids in relation to acid deposition in controlling the acidity of soil and surface waters. This paper contributes to this debate by presenting analysis of seasonal variations in atmospheric deposition, soil solution and stream water chemistry for two UK headwater catchments with contrasting soils. Acid neutralising capacity (ANC), dissolved organic carbon (DOC) concentrations and the Na:Cl ratio of soil and stream waters displayed strong seasonal patterns with little seasonal variation observed in soil water pH. These patterns, plus the strong relationships between ANC, Cl and DOC, suggest that cation exchange and seasonal changes in the production of DOC and seasalt deposition are driving a shift in the proportion of acidity attributable to strong acid anions, from atmospheric deposition, during winter to predominantly organic acids in summer.

Scenarios as the basis for assessment of mitigation and adaptation

The possibilities and need for adaptation and mitigation depends on uncertain future developments with respect to socio-economic factors and the climate system. Scenarios are used to explore the impacts of different strategies under uncertainty. In this chapter, some scenarios are presented that are used in the ADAM project for this purpose. One scenario explores developments with no mitigation, and thus with high temperature increase and high reliance on adaptation (leading to 4oC increase by 2100 compared to pre-industrial levels). A second scenario explores an ambitious mitigation strategy (leading to 2oC increase by 2100 compared to pre-industrial levels). In the latter scenario, stringent mitigation strategies effectively reduces the risks of climate change, but based on uncertainties in the climate system a temperature increase of 3oC or more cannot be excluded. The analysis shows that, in many cases, adaptation and mitigation are not trade-offs but supplements. For example, the number of people exposed to increased water resource stress due to climate change can be substantially reduced in the mitigation scenario, but even then adaptation will be required for the remaining large numbers of people exposed to increased stress. Another example is sea level rise, for which adaptation is more cost-effective than mitigation, but mitigation can help reduce damages and the cost of adaptation. For agriculture, finally, only the scenario based on a combination of adaptation and mitigation is able to avoid serious climate change impacts.

A structural basis for the inhibition of collagen-stimulated platelet function by quercetin and structurally related flavonoids

Background and purpose: Molecular mechanisms underlying the links between dietary intake of flavonoids and reduced cardiovascular disease risk are only partially understood. Key events in the pathogenesis of cardiovascular disease, particularly thrombosis, are inhibited by these polyphenolic compounds via mechanisms such as inhibition of platelet activation and associated signal transduction, attenuation of generation of reactive oxygen species, enhancement of nitric oxide production and binding to thromboxane A2 receptors. In vivo, effects of flavonoids are mediated by their metabolites, but the effects and modes of action of these compounds are not well-characterized. A good understanding of flavonoid structure–activity relationships with regard to platelet function is also lacking. Experimental approach: Inhibitory potencies of structurally distinct flavonoids (quercetin, apigenin and catechin) and plasma metabolites (tamarixetin, quercetin-3′-sulphate and quercetin-3-glucuronide) for collagen-stimulated platelet aggregation and 5-hydroxytryptamine secretion were measured in human platelets. Tyrosine phosphorylation of total protein, Syk and PLCγ2 (immunoprecipitation and Western blot analyses), and Fyn kinase activity were also measured in platelets. Internalization of flavonoids and metabolites in a megakaryocytic cell line (MEG-01 cells) was studied by fluorescence confocal microscopy. Key results: The inhibitory mechanisms of these compounds included blocking Fyn kinase activity and the tyrosine phosphorylation of Syk and PLCγ2 following internalization. Principal functional groups attributed to potent inhibition were a planar, C-4 carbonyl substituted and C-3 hydroxylated C ring in addition to a B ring catechol moiety. Conclusions and implications: The structure–activity relationship for flavonoids on platelet function presented here may be exploited to design selective inhibitors of cell signalling.

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.

Prediction of Parkinson’s Disease tremor onset using a radial basis function neural network based on particle swarm optimization

Deep Brain Stimulation (DBS) has been successfully used throughout the world for the treatment of Parkinson's disease symptoms. To control abnormal spontaneous electrical activity in target brain areas DBS utilizes a continuous stimulation signal. This continuous power draw means that its implanted battery power source needs to be replaced every 18–24 months. To prolong the life span of the battery, a technique to accurately recognize and predict the onset of the Parkinson's disease tremors in human subjects and thus implement an on-demand stimulator is discussed here. The approach is to use a radial basis function neural network (RBFNN) based on particle swarm optimization (PSO) and principal component analysis (PCA) with Local Field Potential (LFP) data recorded via the stimulation electrodes to predict activity related to tremor onset. To test this approach, LFPs from the subthalamic nucleus (STN) obtained through deep brain electrodes implanted in a Parkinson patient are used to train the network. To validate the network's performance, electromyographic (EMG) signals from the patient's forearm are recorded in parallel with the LFPs to accurately determine occurrences of tremor, and these are compared to the performance of the network. It has been found that detection accuracies of up to 89% are possible. Performance comparisons have also been made between a conventional RBFNN and an RBFNN based on PSO which show a marginal decrease in performance but with notable reduction in computational overhead.

Knowing who likes who: The early developmental basis of coalition understanding

Group biases based on broad category membership appear early in human development. However, like many other primates humans inhabit social worlds also characterised by small groups of social coalitions which are not demarcated by visible signs or social markers. A critical cognitive challenge for a young child is thus how to extract information concerning coalition structure when coalitions are dynamic and may lack stable and outwardly visible cues to membership. Therefore, the ability to decode behavioural cues of affiliations present in everyday social interactions between individuals would have conferred powerful selective advantages during our evolution. This would suggest that such an ability may emerge early in life, however, little research has investigated the developmental origins of such processing. The present paper will review recent empirical research which indicates that in the first 2 years of life infants achieve a host of social-cognitive abilities that make them well adapted to processing coalition-affiliations of others. We suggest that such an approach can be applied to better understand the origins of intergroup attitudes and biases. Copyright © 2010 John Wiley & Sons, Ltd.

Mean-tracking clustering algorithm for radial basis function centre selection

Radial basis functions can be combined into a network structure that has several advantages over conventional neural network solutions. However, to operate effectively the number and positions of the basis function centres must be carefully selected. Although no rigorous algorithm exists for this purpose, several heuristic methods have been suggested. In this paper a new method is proposed in which radial basis function centres are selected by the mean-tracking clustering algorithm. The mean-tracking algorithm is compared with k means clustering and it is shown that it achieves significantly better results in terms of radial basis function performance. As well as being computationally simpler, the mean-tracking algorithm in general selects better centre positions, thus providing the radial basis functions with better modelling accuracy