Michael Georgiopoulos

Performance of radial-basis function networks for direction of arrival estimation with antenna arrays

The problem of direction of arrival (DOA) estimation of mobile users using linear antenna arrays is addressed. To reduce the computational complexity of superresolution algorithms, e.g. multiple signal classification (MUSIC), the DOA problem is approached as a mapping which can be modeled using a suitable artificial neural network trained with input output pairs. This paper discusses the application of a three-layer radial-basis function neural network (RBFNN), which can learn multiple source-direction findings of a six-element array. The network weights are modified using the normalized cumulative delta rule. The performance of this network is compared to that of the MUSIC algorithm for both uncorrelated and correlated signals. It is also shown that the RBFNN substantially reduced the CPU time for the DOA estimation computations.

A neural network-based smart antenna for multiple source tracking

This paper considers the problem of multiple-source tracking with neural network-based smart antennas for wireless terrestrial and satellite mobile communications. The neural multiple-source tracking (N-MUST) algorithm is based on an architecture of a family of radial basis function neural networks (RBFNN) to perform both detection and direction of arrival (DOA) estimation. The field of view of the antenna array is divided into spatial angular sectors, which are in turn assigned to a different pair of RBFNNs. When a network detects one or more sources in the first stage, the corresponding second stage network(s) are activated to perform the DOA estimation. Simulation results are performed to investigate the performance of the algorithm for various angular separations, with sources of random relative signal-to-noise ratio and when the system suffers from Doppler spread.

Feed-forward neural networks

One critical aspect neural network designers face today is choosing an appropriate network size for a given application. Network size involves in the case of layered neural network architectures, the number of layers in a network, the number of nodes per layer, and the number of connections. Roughly speaking, a neural network implements a nonlinear mapping of u=G(x). The mapping function G is established during a training phase where the network learns to correctly associate input patterns x to output patterns u. Given a set of training examples (x, u), there is probably an infinite number of different size networks that can learn to map input patterns x into output patterns u. The question is, which network size is more appropriate for a given problem? Unfortunately, the answer to this question is not always obvious. Many researchers agree that the quality of a solution found by a neural network depends strongly on the network size used. In general, network size affects network complexity, and learning time. It also affects the generalization capabilities of the network; that is, its ability-to produce accurate results on patterns outside its training set.<<ETX>>

An ordering algorithm for pattern presentation in fuzzy ARTMAP that tends to improve generalization performance

In this paper we introduce a procedure, based on the max-min clustering method, that identifies a fixed order of training pattern presentation for fuzzy adaptive resonance theory mapping (ARTMAP). This procedure is referred to as the ordering algorithm, and the combination of this procedure with fuzzy ARTMAP is referred to as ordered fuzzy ARTMAP. Experimental results demonstrate that ordered fuzzy ARTMAP exhibits a generalization performance that is better than the average generalization performance of fuzzy ARTMAP, and in certain cases as good as, or better than the best fuzzy ARTMAP generalization performance. We also calculate the number of operations required by the ordering algorithm and compare it to the number of operations required by the training phase of fuzzy ARTMAP. We show that, under mild assumptions, the number of operations required by the ordering algorithm is a fraction of the number of operations required by fuzzy ARTMAP.

Fuzzy ART properties

Abstract This paper presents some important properties of the Fuzzy ART neural network algorithm introduced by Carpenter, Grossberg, and Rosen. The properties described in the paper are distinguished into a number of categories. These include template, access, and reset properties, as well as properties related to the number of list presentations needed for weight stabilization. These properties provide numerous insights as to how Fuzzy ART operates. Furthermore, the effects of the Fuzzy ART parameters a and p on the functionality of the algorithm are clearly illustrated.

Order of search in fuzzy ART and fuzzy ARTMAP: effect of the choice parameter

This paper focuses on two ART architectures, the Fuzzy ART and the Fuzzy ARTMAP. Fuzzy ART is a pattern clustering machine, while Fuzzy ARTMAP is a pattern classification machine. Our study concentrates on the order according to which categories in Fuzzy ART, or the ART(a) model of Fuzzy ARTMAP are chosen. Our work provides a geometrical, and clearer understanding of why, and in what order, these categories are chosen for various ranges of the choice parameter of the Fuzzy ART module. This understanding serves as a powerful tool in developing properties of learning pertaining to these neural network architectures; to strengthen this argument, it is worth mentioning that the order according to which categories are chosen in ART 1 and ARTMAP provided a valuable tool in proving important properties about these architectures. Copyright 1996 Elsevier Science Ltd.

A fast outlier detection strategy for distributed high-dimensional data sets with mixed attributes

Outlier detection has attracted substantial attention in many applications and research areas; some of the most prominent applications are network intrusion detection or credit card fraud detection. Many of the existing approaches are based on calculating distances among the points in the dataset. These approaches cannot easily adapt to current datasets that usually contain a mix of categorical and continuous attributes, and may be distributed among different geographical locations. In addition, current datasets usually have a large number of dimensions. These datasets tend to be sparse, and traditional concepts such as Euclidean distance or nearest neighbor become unsuitable. We propose a fast distributed outlier detection strategy intended for datasets containing mixed attributes. The proposed method takes into consideration the sparseness of the dataset, and is experimentally shown to be highly scalable with the number of points and the number of attributes in the dataset. Experimental results show that the proposed outlier detection method compares very favorably with other state-of-the art outlier detection strategies proposed in the literature and that the speedup achieved by its distributed version is very close to linear.

Neural network-based adaptive beamforming for one- and two-dimensional antenna arrays

We present a neural network approach to the problem of finding the weights of one- (1-D) and two-dimensional (2-D) adaptive arrays. In modern cellular satellite mobile communications systems and in global positioning systems (GPSs), both desired and interfering signals change their directions continuously. Therefore, a fast tracking system is needed to constantly track the users and then adapt the radiation pattern of the antenna to direct multiple narrow beams to desired users and nulls interfering sources. In the approach suggested in this paper, the computation of the optimum weights is accomplished using three-layer radial basis function neural networks (RBFNN). The results obtained from this network are in excellent agreement with the Wiener solution.

Coupling weight elimination with genetic algorithms to reduce network size and preserve generalization

Recent theoretical results support that decreasing the number of free parameters in a neural network (i.e., weights) can improve generalization. These results have triggered the development of many approaches which try to determine an “appropriate” network size for a given problem. The main goal has been to find a network size just large enough to capture the general class properties of the data. In some cases, however, network size is not reduced significantly or the reduction is satisfactory but generalization is affected. In this paper, we propose the coupling of genetic algorithms with weight elimination. Our objective is not only to significantly reduce network size, by pruning larger size networks, but also to preserve generalization, that is, to come up with pruned networks which generalize as good or even better than their unpruned counterparts. The innovation of our work relies on a fitness function which uses an adaptive parameter to encourage reproduction of networks having small size and good generalization. The proposed approach has been tested using both artificial and real databases demonstrating good performance.

A Scalable and Efficient Outlier Detection Strategy for Categorical Data

Outlier detection has received significant attention in many applications, such as detecting credit card fraud or network intrusions. Most existing research focuses on numerical datasets, and cannot directly apply to categorical sets where there is little sense in calculating distances among data points. Furthermore, a number of outlier detection methods require quadratic time with respect to the dataset size and usually multiple dataset scans. These characteristics are undesirable for large datasets, potentially scattered over multiple distributed sites. In this paper, we introduce Attribute Value Frequency (A VF), a fast and scalable outlier detection strategy for categorical data. A VF scales linearly with the number of data points and attributes, and relies on a single data scan. AVF is compared with a list of representative outlier detection approaches that have not been contrasted against each other. Our proposed solution is experimentally shown to be significantly faster, and as effective in discovering outliers.