Complex-valued Radial Basis Function Research Articles

Fast and robust adaptive beamforming method based on complex‐valued RBF neural network

The adaptive beamforming is one of the key techniques for array signal processing. However, the matrix inversion operation in the existing methods will cost a large amount of computational complexity, which results in poor real-time processing ability. In order to reduce the amount of computational cost, a fast and robust adaptive beamforming method based on complex-valued radial basis function (CRBF) neural network is proposed. In the proposed method, the CRBF neural network is established, thus the direct matrix inversion is avoided by the nonlinear mapping processing from the array covariance matrix to the adaptive weight vector, and therefore the calculation speed of adaptive weight vectors is increased. Based on the simulation results, the proposed method is verified that the speed of adaptive beamforming is increased compared with sample matrix inversion (SMI) algorithm method and an improved performance is achieved compared with that of conventional real-valued RBF neural network beamformer.

Indoor object recognition in RGBD images with complex-valued neural networks for visually-impaired people

We present a new multi-modal technique for assisting visually-impaired people in recognizing objects in public indoor environment. Unlike common methods which aim to solve the problem of multi-class object recognition in a traditional single-label strategy, a comprehensive approach is developed here allowing samples to take more than one label at a time. We jointly use appearance and depth cues, specifically RGBD images, to overcome issues of traditional vision systems using a new complex-valued representation. Inspired by complex-valued neural networks (CVNNs) and multi-label learning techniques, we propose two methods in order to associate each input RGBD image to a set of labels corresponding to the object categories recognized at once. The first one, ML-CVNN, is formalized as a ranking strategy where we make use of a fully complex-valued RBF network and extend it to be able to solve multi-label problems using an adaptive clustering method. The second method, L-CVNNs, deals with problem transformation strategy where instead of using a single network to formalize the classification problem as a ranking solution for the whole label set, we propose to construct one CVNN for each label where the predicted labels will be later aggregated to construct the resulting multi-label vector. Extensive experiments have been carried on two newly collected multi-labeled RGBD datasets prove the efficiency of the proposed techniques.

An improved maximum spread algorithm with application to complex-valued RBF neural networks

It has been known that one of the important steps in training a complex-valued radial basis function neural network is to effectively determine its centers and widths of neurons in the hidden layer. In this paper, an improved maximum spread algorithm is propose to solve this issue. Its basic idea is that the choice of centers not only depends on the distances between samples from different classes, but also is heavily affected by the average distance between samples in the same class. The relationship between external and inner distances is taken into account when determining centers. The performance of this algorithm is tested on several datasets. It is shown that much better performance can be achieved by the developed algorithm than by some existing ones.

Forecasting interval time series using a fully complex-valued RBF neural network with DPSO and PSO algorithms

Interval time series prediction is one of the most challenging research topics in the field of time series modeling and prediction. In view of the remarkable function approximation capability of fully complex-valued radial basis function neural networks (FCRBFNNs), we set out to investigate the possibility of forecasting interval time series by denoting the lower and upper bounds of the interval as real and imaginary parts of a complex number, respectively. This results in a complex-valued interval. We then model the resulted complex-valued interval time series via a FCRBFNN. Furthermore, we propose to evolve the FCRBFNN by using particle swarm optimization (PSO) and discrete PSO for joint optimization of the structure and parameters. Finally, the proposed interval time series prediction approach is tested with simulated interval time series data as well as real interval stock price time series data from the New York Stock Exchange. Our experimental results indicate that it is a promising alternative for interval time series forecasting.

WITHDRAWN: An improved maximum spread algorithm with application to complex-valued RBF neural networks

Abstract It has been known that one of the important steps in training a complex-valued radial basis function neural network is to effectively determine its centers and widths of neurons in the hidden layer. In this paper, an improved maximum spread algorithm is propose to solve this issue. Its basic idea is that the choice of centers not only depends on the distances between samples from different classes, but also is heavily affected by the average distance between samples in the same class. The relationship between external and inner distances is taken into account when determining centers. The performance of this algorithm is tested on several datasets. It is shown that much better performance can be achieved by the developed algorithm than by some existing ones.

Improved Complex-valued Radial Basis Function (ICRBF) neural networks on multiple crack identification

This paper introduces a new class of neural networks in complex space called Complex-valued Radial Basis Function (CRBF) neural networks and also an improved version of CRBF called Improved Complex-valued Radial Basis Function (ICRBF) neural networks. They are used for multiple crack identification in a cantilever beam in the frequency domain. The novelty of the paper is that, these complex-valued neural networks are first applied on inverse problems (damage identification) which come under the category of function approximation. The conventional CRBF network was used in the first stage of ICRBF network and in the second stage a reduced search space moving technique was employed for accurate crack identification. The effectiveness of proposed ICRBF neural network was studied first on a single crack identification problem and then applied to a more challenging problem of multiple crack identification in a cantilever beam with zero noise as well as 5% noise polluted signals. The results proved that, the proposed ICRBF and real-valued Improved RBF (IRBF) neural networks have identified the single and multiple cracks with less than 1% absolute mean percentage error as compared to conventional CRBF and RBF neural networks, mainly because of their second stage reduced search space moving technique. It appears that IRBF neural network is a good compromise considering all factors like accuracy, simplicity and computational effort.

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 fully complex-valued radial basis function classifier for real-valued classification problems

In this paper, we investigate the decision making ability of a fully complex-valued radial basis function (FC-RBF) network in solving real-valued classification problems. The FC-RBF classifier is a single hidden layer fully complex-valued neural network with a nonlinear input layer, a nonlinear hidden layer, and a linear output layer. The neurons in the input layer of the classifier employ the phase encoded transformation to map the input features from the Real domain to the Complex domain. The neurons in the hidden layer employ a fully complex-valued Gaussian-like activation function of the type of hyperbolic secant (sech). The classification ability of the classifier is first studied analytically and it is shown that the decision boundaries of the FC-RBF classifier are orthogonal to each other. Then, the performance of the FC-RBF classifier is studied experimentally using a set of real-valued benchmark problems and also a real-world problem. The study clearly indicates the superior classification ability of the FC-RBF classifier.

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.

A FULLY COMPLEX-VALUED RADIAL BASIS FUNCTION NETWORK AND ITS LEARNING ALGORITHM

In this paper, a fully complex-valued radial basis function (FC-RBF) network with a fully complex-valued activation function has been proposed, and its complex-valued gradient descent learning algorithm has been developed. The fully complex activation function, sech(.) of the proposed network, satisfies all the properties needed for a complex-valued activation function and has Gaussian-like characteristics. It maps C(n) --> C, unlike the existing activation functions of complex-valued RBF network that maps C(n) --> R. Since the performance of the complex-RBF network depends on the number of neurons and initialization of network parameters, we propose a K-means clustering based neuron selection and center initialization scheme. First, we present a study on convergence using complex XOR problem. Next, we present a synthetic function approximation problem and the two-spiral classification problem. Finally, we present the results for two practical applications, viz., a non-minimum phase equalization and an adaptive beam-forming problem. The performance of the network was compared with other well-known complex-valued RBF networks available in literature, viz., split-complex CRBF, CMRAN and the CELM. The results indicate that the proposed fully complex-valued network has better convergence, approximation and classification ability.

Symmetric Complex-Valued RBF Receiver for Multiple-Antenna-Aided Wireless Systems

A nonlinear beamforming assisted detector is proposed for multiple-antenna-aided wireless systems employing complex-valued quadrature phase shift-keying modulation. By exploiting the inherent symmetry of the optimal Bayesian detection solution, a novel complex-valued symmetric radial basis function (SRBF)-network-based detector is developed, which is capable of approaching the optimal Bayesian performance using channel-impaired training data. In the uplink case, adaptive nonlinear beamforming can be efficiently implemented by estimating the system's channel matrix based on the least squares channel estimate. Adaptive implementation of nonlinear beamforming in the downlink case by contrast is much more challenging, and we adopt a cluster-variation enhanced clustering algorithm to directly identify the SRBF center vectors required for realizing the optimal Bayesian detector. A simulation example is included to demonstrate the achievable performance improvement by the proposed adaptive nonlinear beamforming solution over the theoretical linear minimum bit error rate beamforming benchmark.

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 growing and pruning RBF neural networks for communication channel equalisation

A complex-valued radial basis function (RBF) network is proposed for solving the communication channel equalisation problem with quadrature amplitude modulation signals. The network uses a sequential learning scheme, referred to as the complex-valued growing and pruning (CGAP) algorithm, and is an extension of the generalised growing and pruning network of Huang et al. developed for real-valued radial basis function (RBF) networks. The learning algorithm in this network makes use of the concept of ‘significance’ for hidden neurons. By linking the significance of a neuron to the learning accuracy, a growing and pruning strategy for an RBF neural network with complex inputs is derived. Further, for both growing and pruning, one needs to check only the nearest neuron (based on the Euclidean distance to the latest input data) for its significance, resulting in a more compact network. When there is no growing or pruning, a complex, extended Kalman filter is used to adjust the RBF network parameters. The performance of the CGAP-RBF equaliser is compared with several other equalisers such as CMRAN, CRBF and ASNN on several nonlinear, complex channel equalisation problems. The results show that the CGAP-RBF equaliser is superior to other equalisers in terms of symbol error rate and network complexity.

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.