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.

Nonlinear model structure design and construction using orthogonal least squares and D-optimality design

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the model subset selection cost function includes a D-optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness, adequacy, and parsimony of the final model. The proposed approach is based on the forward orthogonal least square (OLS) algorithm, such that new D-optimality-based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward OLS approach. Illustrative examples are included to demonstrate the effectiveness of the new approach.

A theoretical adaptive model of thermal comfort – Adaptive Predicted Mean Vote (aPMV)

This paper presents in detail a theoretical adaptive model of thermal comfort based on the “Black Box” theory, taking into account factors such as culture, climate, social, psychological and behavioural adaptations, which have an impact on the senses used to detect thermal comfort. The model is called the Adaptive Predicted Mean Vote (aPMV) model. The aPMV model explains, by applying the cybernetics concept, the phenomena that the Predicted Mean Vote (PMV) is greater than the Actual Mean Vote (AMV) in free-running buildings, which has been revealed by many researchers in field studies. An Adaptive coefficient (λ) representing the adaptive factors that affect the sense of thermal comfort has been proposed. The empirical coefficients in warm and cool conditions for the Chongqing area in China have been derived by applying the least square method to the monitored onsite environmental data and the thermal comfort survey results.

Turbo channel estimation and equalisation for a superposition-based cooperative system

This study investigates the superposition-based cooperative transmission system. In this system, a key point is for the relay node to detect data transmitted from the source node. This issued was less considered in the existing literature as the channel is usually assumed to be flat fading and a priori known. In practice, however, the channel is not only a priori unknown but subject to frequency selective fading. Channel estimation is thus necessary. Of particular interest is the channel estimation at the relay node which imposes extra requirement for the system resources. The authors propose a novel turbo least-square channel estimator by exploring the superposition structure of the transmission data. The proposed channel estimator not only requires no pilot symbols but also has significantly better performance than the classic approach. The soft-in-soft-out minimum mean square error (MMSE) equaliser is also re-derived to match the superimposed data structure. Finally computer simulation results are shown to verify the proposed algorithm.

Estimation of distances in virtual environments using size constancy

It is reported in the literature that distances from the observer are underestimated more in virtual environments (VEs) than in physical world conditions. On the other hand estimation of size in VEs is quite accurate and follows a size-constancy law when rich cues are present. This study investigates how estimation of distance in a CAVETM environment is affected by poor and rich cue conditions, subject experience, and environmental learning when the position of the objects is estimated using an experimental paradigm that exploits size constancy. A group of 18 healthy participants was asked to move a virtual sphere controlled using the wand joystick to the position where they thought a previously-displayed virtual cube (stimulus) had appeared. Real-size physical models of the virtual objects were also presented to the participants as a reference of real physical distance during the trials. An accurate estimation of distance implied that the participants assessed the relative size of sphere and cube correctly. The cube appeared at depths between 0.6 m and 3 m, measured along the depth direction of the CAVE. The task was carried out in two environments: a poor cue one with limited background cues, and a rich cue one with textured background surfaces. It was found that distances were underestimated in both poor and rich cue conditions, with greater underestimation in the poor cue environment. The analysis also indicated that factors such as subject experience and environmental learning were not influential. However, least square fitting of Stevens’ power law indicated a high degree of accuracy during the estimation of object locations. This accuracy was higher than in other studies which were not based on a size-estimation paradigm. Thus as indirect result, this study appears to show that accuracy when estimating egocentric distances may be increased using an experimental method that provides information on the relative size of the objects used.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

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.

Dielectric properties of process cheese from 0.3 to 3 Ghz

Dielectric properties of 16 process cheeses were determined over the frequency range 0.3-3 GHz. The effect of temperature on the dielectric properties of process cheeses were investigated at temperature intervals of 10 degrees C between 5 and 85 degrees C. Results showed that the dielectric constant decreased gradually as frequency increased, for all cheeses. The dielectric loss factor (epsilon") decreased from above 125 to below 12 as frequency increased. epsilon' was highest at 5 degrees C and generally decreased up to a temperature between 55 and 75 degrees C. epsilon" generally increased with increasing temperature for high and medium moisture/fat ratio cheeses. epsilon" decreased with temperature between 5 and 55 degrees C and then increased, for low moisture/fat ratio cheese. Partial least square regression models indicated that epsilon' and epsilon" could be used as a quality control screening application to measure moisture content and inorganic salt content of process cheese, respectively. (c) 2005 Elsevier Ltd. All rights reserved..

A neurofuzzy classifier for two class problems

A neurofuzzy classifier identification algorithm is introduced for two class problems. The initial fuzzy base construction is based on fuzzy clustering utilizing a Gaussian mixture model (GMM) and the analysis of covariance (ANOVA) decomposition. The expectation maximization (EM) algorithm is applied to determine the parameters of the fuzzy membership functions. Then neurofuzzy model is identified via the supervised subspace orthogonal least square (OLS) algorithm. Finally a logistic regression model is applied to produce the class probability. The effectiveness of the proposed neurofuzzy classifier has been demonstrated using a real data set.

Adaptive noise cancellation with fast tunable RBF network

This paper describes a novel adaptive noise cancellation system with fast tunable radial basis function (RBF). The weight coefficients of the RBF network are adapted by the multi-innovation recursive least square (MRLS) algorithm. If the RBF network performs poorly despite of the weight adaptation, an insignificant node with little contribution to the overall performance is replaced with a new node without changing the model size. Otherwise, the RBF network structure remains unchanged and only the weight vector is adapted. The simulation results show that the proposed approach can well cancel the noise in both stationary and nonstationary ANC systems.

Online modeling with tunable RBF network

In this paper, we propose a novel online modeling algorithm for nonlinear and nonstationary systems using a radial basis function (RBF) neural network with a fixed number of hidden nodes. Each of the RBF basis functions has a tunable center vector and an adjustable diagonal covariance matrix. A multi-innovation recursive least square (MRLS) algorithm is applied to update the weights of RBF online, while the modeling performance is monitored. When the modeling residual of the RBF network becomes large in spite of the weight adaptation, a node identified as insignificant is replaced with a new node, for which the tunable center vector and diagonal covariance matrix are optimized using the quantum particle swarm optimization (QPSO) algorithm. The major contribution is to combine the MRLS weight adaptation and QPSO node structure optimization in an innovative way so that it can track well the local characteristic in the nonstationary system with a very sparse model. Simulation results show that the proposed algorithm has significantly better performance than existing approaches.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

Comparison of a trained sensory panel and an electronic tongue in the assessment of bitter dairy protein hydrolsates

The bitter taste elicited by dairy protein hydrolysates (DPH) is a renowned issue for their acceptability by consumers and therefore incorporation into foods. The traditional method of assessment of taste in foods is by sensory analysis but this can be problematic due to the overall unpleasantness of the samples. Thus, there is a growing interest into the use of electronic tongues (e-tongues) as an alternative method to quantify the bitterness in such samples. In the present study the response of the e-tongue to the standard bitter agent caffeine and a range of both casein and whey based hydrolysates was compared to that of a trained sensory panel. Partial least square regression (PLS) was employed to compare the response of the e-tongue and the sensory panel. There was strong correlation shown between the two methods in the analysis of caffeine (R2 of 0.98) and DPH samples with R2 values ranging from 0.94-0.99. This study exhibits potential for the e-tongue to be used in bitterness screening in DPHs to reduce the reliance on expensive and time consuming sensory panels.

A fast adaptive tunable RBF network for nonstationary systems

This paper describes a novel on-line learning approach for radial basis function (RBF) neural network. Based on an RBF network with individually tunable nodes and a fixed small model size, the weight vector is adjusted using the multi-innovation recursive least square algorithm on-line. When the residual error of the RBF network becomes large despite of the weight adaptation, an insignificant node with little contribution to the overall system is replaced by a new node. Structural parameters of the new node are optimized by proposed fast algorithms in order to significantly improve the modeling performance. The proposed scheme describes a novel, flexible, and fast way for on-line system identification problems. Simulation results show that the proposed approach can significantly outperform existing ones for nonstationary systems in particular.

A new adaptive multiple modelling approach for non-linear and non-stationary systems

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.