Complex-valued Radial Basis Function Network Research Articles

Metacognitive Learning in a Fully Complex-Valued Radial Basis Function Neural Network

Recent studies on human learning reveal that self-regulated learning in a metacognitive framework is the best strategy for efficient learning. As the machine learning algorithms are inspired by the principles of human learning, one needs to incorporate the concept of metacognition to develop efficient machine learning algorithms. In this letter we present a metacognitive learning framework that controls the learning process of a fully complex-valued radial basis function network and is referred to as a metacognitive fully complex-valued radial basis function (Mc-FCRBF) network. Mc-FCRBF has two components: a cognitive component containing the FC-RBF network and a metacognitive component, which regulates the learning process of FC-RBF. In every epoch, when a sample is presented to Mc-FCRBF, the metacognitive component decides what to learn, when to learn, and how to learn based on the knowledge acquired by the FC-RBF network and the new information contained in the sample. The Mc-FCRBF learning algorithm is described in detail, and both its approximation and classification abilities are evaluated using a set of benchmark and practical problems. Performance results indicate the superior approximation and classification performance of Mc-FCRBF compared to existing methods in the literature.

A Sequential Learning Algorithm for Complex-Valued Self-Regulating Resource Allocation Network-CSRAN

This paper presents a sequential learning algorithm for a complex-valued resource allocation network with a self-regulating scheme, referred to as complex-valued self-regulating resource allocation network (CSRAN). The self-regulating scheme in CSRAN decides what to learn, when to learn, and how to learn based on the information present in the training samples. CSRAN is a complex-valued radial basis function network with a sech activation function in the hidden layer. The network parameters are updated using a complex-valued extended Kalman filter algorithm. CSRAN starts with no hidden neuron and builds up an appropriate number of hidden neurons, resulting in a compact structure. Performance of the CSRAN is evaluated using a synthetic complex-valued function approximation problem, two real-world applications consisting of a complex quadrature amplitude modulation channel equalization, and an adaptive beam-forming problem. Since complex-valued neural networks are good decision makers, the decision-making ability of the CSRAN is compared with other complex-valued classifiers and the best performing real-valued classifier using two benchmark unbalanced classification problems from UCI machine learning repository. The approximation and classification results show that the CSRAN outperforms other existing complex-valued learning algorithms available in the literature.

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.

Complex-valued radial basis function network, Part II: Application to digital communications channel equalisation

In the first part of this paper, a complex-valued multi-output radial basis function network was proposed and two learning algorithms were derived. This second part investigates the adaptive realisation of a Bayesian solution for 4-QAM digital communications channel equalisation using the complex single-output radial basis function network. It is shown that the optimal Bayesian equaliser is structurally equivalent to the complex radial basis function network, and this intimate connection is exploited to develop fast training algorithms for implementing a Bayesian equaliser based on the latter. A novel strategy of utilising decision feedback is employed to improve equaliser performance as well as to reduce computational complexity. The conventional decision feedback equaliser and the maximum likelihood sequence estimator are used as two benchmarks to assess the performance of this Bayesian decision feedback equaliser.