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 kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

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.

Sparse kernel regression modeling using combined locally regularized orthogonal least squares and D-optimality experimental design

The note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious model with excellent generalization performance. The D-optimality design criterion further enhances the model efficiency and robustness. An added advantage is that the user only needs to specify a weighting for the D-optimality cost in the combined 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.

Kernel density construction using orthogonal forward regression

An automatic algorithm is derived for constructing kernel density estimates based on a regression approach that directly optimizes generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. Local regularization is incorporated into the density construction process to further enforce sparsity. Examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample Parzen window density estimate.

Sparse kernel density construction using orthogonal forward regression with leave-one-out test score and local regularization

This paper presents an efficient construction algorithm for obtaining sparse kernel density estimates based on a regression approach that directly optimizes model generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. A local regularization method is incorporated naturally into the density construction process to further enforce sparsity. An additional advantage of the proposed algorithm is that it is fully automatic and the user is not required to specify any criterion to terminate the density construction procedure. This is in contrast to an existing state-of-art kernel density estimation method using the support vector machine (SVM), where the user is required to specify some critical algorithm parameter. Several examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample optimized Parzen window density estimate. Our experimental results also demonstrate that the proposed algorithm compares favorably with the SVM method, in terms of both test accuracy and sparsity, for constructing kernel density estimates.

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.

An orthogonal forward regression technique for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the desired response, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density (SKD) estimates. The proposed algorithm incrementally minimises a leave-one-out test score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights of the selected sparse model are finally updated using the multiplicative nonnegative quadratic programming algorithm, which ensures the nonnegative and unity constraints for the kernel weights and has the desired ability to reduce the model size further. Except for the kernel width, the proposed method has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Several examples demonstrate the ability of this simple regression-based approach to effectively construct a SKID estimate with comparable accuracy to that of the full-sample optimised PW density estimate. (c) 2007 Elsevier B.V. All rights reserved.

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.

Sparse modeling using orthogonal forward regression with PRESS statistic and regularization

The paper introduces an efficient construction algorithm for obtaining sparse linear-in-the-weights regression models based on an approach of directly optimizing model generalization capability. This is achieved by utilizing the delete-1 cross validation concept and the associated leave-one-out test error also known as the predicted residual sums of squares (PRESS) statistic, without resorting to any other validation data set for model evaluation in the model construction process. Computational efficiency is ensured using an orthogonal forward regression, but the algorithm incrementally minimizes the PRESS statistic instead of the usual sum of the squared training errors. A local regularization method can naturally be incorporated into the model selection procedure to further enforce model sparsity. The proposed algorithm is fully automatic, and the user is not required to specify any criterion to terminate the model construction procedure. Comparisons with some of the existing state-of-art modeling methods are given, and several examples are included to demonstrate the ability of the proposed algorithm to effectively construct sparse models that generalize well.

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.

Orthogonal-least-squares regression: A unified approach for data modelling

A unified approach is proposed for data modelling that includes supervised regression and classification applications as well as unsupervised probability density function estimation. The orthogonal-least-squares regression based on the leave-one-out test criteria is formulated within this unified data-modelling framework to construct sparse kernel models that generalise well. Examples from regression, classification and density estimation applications are used to illustrate the effectiveness of this generic data-modelling approach for constructing parsimonious kernel models with excellent generalisation capability. (C) 2008 Elsevier B.V. All rights reserved.

Kernel classifier construction using orthogonal forward selection and boosting with Fisher ratio class separability measure

A greedy technique is proposed to construct parsimonious kernel classifiers using the orthogonal forward selection method and boosting based on Fisher ratio for class separability measure. Unlike most kernel classification methods, which restrict kernel means to the training input data and use a fixed common variance for all the kernel terms, the proposed technique can tune both the mean vector and diagonal covariance matrix of individual kernel by incrementally maximizing Fisher ratio for class separability measure. An efficient weighted optimization method is developed based on boosting to append kernels one by one in an orthogonal forward selection procedure. Experimental results obtained using this construction technique demonstrate that it offers a viable alternative to the existing state-of-the-art kernel modeling methods for constructing sparse Gaussian radial basis function network classifiers. that generalize well.

Comparison of extrasystolic ECG signal classifiers using discrete wavelet transforms

This work compares and contrasts results of classifying time-domain ECG signals with pathological conditions taken from the MITBIH arrhythmia database. Linear discriminant analysis and a multi-layer perceptron were used as classifiers. The neural network was trained by two different methods, namely back-propagation and a genetic algorithm. Converting the time-domain signal into the wavelet domain reduced the dimensionality of the problem at least 10-fold. This was achieved using wavelets from the db6 family as well as using adaptive wavelets generated using two different strategies. The wavelet transforms used in this study were limited to two decomposition levels. A neural network with evolved weights proved to be the best classifier with a maximum of 99.6% accuracy when optimised wavelet-transform ECG data wits presented to its input and 95.9% accuracy when the signals presented to its input were decomposed using db6 wavelets. The linear discriminant analysis achieved a maximum classification accuracy of 95.7% when presented with optimised and 95.5% with db6 wavelet coefficients. It is shown that the much simpler signal representation of a few wavelet coefficients obtained through an optimised discrete wavelet transform facilitates the classification of non-stationary time-variant signals task considerably. In addition, the results indicate that wavelet optimisation may improve the classification ability of a neural network. (c) 2005 Elsevier B.V. All rights reserved.