Search

A new neural network for convex quadratic optimization is presented in this brief. The proposed network can handle both equality and inequality constraints, as well as bound constraints on the optimization variables. It is based on the Lagrangian approach, but exploits a partial dual method in order to keep the number of variables at minimum. The dynamic evolution is globally convergent and the steady-state solutions satisfy the necessary and sufficient conditions of optimality. The circuit implementation is simpler with respect to existing solutions for the same class of problems. The validity of the proposed approach is verified through some simulation examples. Index Terms--Analog circuits, Lagrangian networks, mathematical programming, quadratic optimization, recurrent neural networks.

In this paper, we analyze a model of recurrent kernel associative memory (RKAM) recently proposed by Garcia and Moreno. We show that this model consists in a kernelization of the recurrent correlation associative memory (RCAM) of Chiueh and Goodman. In particular, using an exponential kernel, we obtain a generalization of the well-known exponential correlation associative memory (ECAM), while using a polynomial kernel, we obtain a generalization of higher order Hopfield networks with Hebbian weights. We show that the RKAM can outperform the aforementioned associative memory models, becoming equivalent to them when a dominance condition is fulfilled by the kernel matrix. To ascertain the dominance condition, we propose a statistical measure which can be easily computed from the probability distribution of the interpattern Hamming distance or directly estimated from the memory vectors. The RKAM can be used below saturation to realize associative memories with reduced dynamic range with respect to the ECAM and with reduced number of synaptic coefficients with respect to higher order Hopfield networks. Index Terms--Exponential correlation associative memory (ECAM), feature space, higher order Hopfield network, kernel associative memory, recurrent correlation associative memory (RCAM), support vector machine (SVM).

In the framework of computer-aided diagnosis of eye diseases, retinal vessel segmentation based on line operators is proposed. A line detector, previously used in mammography, is applied to the green channel of the retinal image. It is based on the evaluation of the average grey level along lines of fixed length passing through the target pixel at different orientations. Two segmentation methods are considered. The first uses the basic line detector whose response is thresholded to obtain unsupervised pixel classification. As a further development, we employ two orthogonal line detectors along with the grey level of the target pixel to construct a feature vector for supervised classification using a support vector machine. The effectiveness of both methods is demonstrated through receiver operating characteristic analysis on two publicly available databases of color fundus images. Index Terms--Classification, line detector, retinal imaging, support vector machines (SVM), vessel segmentation.

A retinal vessel segmentation method based on cellular neural networks (CNNs) is proposed. The CNN design is characterized by a virtual template expansion obtained through a multistep operation. It is based on linear space-invariant 3 x 3 templates and can be realized using existing chip prototypes like the ACE16K. The proposed design is capable of performing vessel segmentation within a short computation time. It was tested on a publicly available database of color images of the retina, using receiver operating characteristic curves. The simulation results show good performance comparable with that of the best existing methods. Index Terms--Cellular neural networks (CNNs), line detection, retinal imaging, vessel segmentation.

The relation existing between support vector machines (SVMs) and recurrent associative memories is investigated. The design of associative memories based on the generalized brain-state-in-a-box (GBSB) neural model is formulated as a set of independent classification tasks which can be efficiently solved by standard software packages for SVM learning. Some properties of the networks designed in this way are evidenced, like the fact that surprisingly they follow a generalized Hebb's law. The performance of the SVM approach is compared to existing methods with nonsymmetric connections, by some design examples. Index Terms--Associative memories, brain-state-in-a-box neural model, support vector machines (SVMs).

An analog neural network for support vector machine learning is proposed, based on a partially dual formulation of the quadratic programming problem. It results in a simpler circuit implementation with respect to existing neural solutions for the same application. The effectiveness of the proposed network is shown through some computer simulations concerning benchmark problems. Index Terms--Analog circuits, quadratic optimization, recurrent neural networks, support vector machines.

A design procedure is presented for neural associative memories storing gray-scale images. It is an evolution of a previous work based on the decomposition of the image with [2.sup.L] gray levels into L binary patterns, stored in L uncoupled neural networks. In this letter, an L-layer neural network is proposed with both intralayer and interlayer connections. The connections between different layers introduce interactions among all the neurons, increasing the recall performance with respect to the uncoupled case. In particular, the proposed network can store images with the commonly used number of 256 gray levels instead of 16, as in the previous approach. Index Terms--Associative memories, brain-state-in-a-box (BSB) neural networks, gray-scale images, multilayer architectures.

In this paper, we present a neural associative memory storing gray-scale images. The proposed approach is based on a suitable decomposition of the gray-scale image into gray-coded binary images, stored in brain-state-in-a-box-type binary neural networks. Both learning and recall can be implemented by parallel computation, with time saving. The learning algorithm, used to store the binary images, guarantees asymptotic stability of the stored patterns, low computational cost, and control of the weights precision. Some design examples and computer simulations are presented to show the effectiveness of the proposed method. Index Terms--Associative memories, brain-state-in-a-box (BSB) neural networks, gray-scale images, neural networks with finite precision weights.

This paper describes a neural network for solving flow problems, which are of interest in many areas of application as in fuel, hydro, and electric power scheduling. The neural network consists of two layers: a hidden layer and an output layer. The hidden units correspond to the nodes of the flow graph. The output units represent the branch variables. The network has a linear order of complexity, it is easily programmable, and it is suited for analog very large scale integration (VLSI) realization. The functionality of the proposed network is illustrated by a simulation example concerning the maximal flow problem.

In this paper, some new qualitative properties of discrete-time neural networks based on the 'brain-state-in-a-box' model are presented. These properties concern both the characterization of equilibrium points and the global dynamical behavior. Next, the analysis results are used as guidelines in developing an efficient synthesis procedure for networks that function as associative memories. A constrained design algorithm is presented that gives completely stable dynamical neural networks sharing some interesting features. It is guaranteed the absence of nonbinary stable equilibria, that is stable states with nonsaturated components. It is guaranteed that in close proximity (Hamming distance one) of the stored patterns there is no other binary equilibrium point. Moreover, the presented method allows one to optimize a design parameter that controls the size of the attraction basins of the stored vectors and the accuracy needed in a digital realization of the network. Some design examples and computer simulations are presented to demonstrate the effectiveness of the proposed method.

The sensitivity of continuous-time Hopfield neural network is investigated. The relative sensitivity of hyperbolic equilibrium points, with respect to changes in the interconnections, is computed. Then it is shown that the minimum sensitivity of equilibria corresponds to the minimum scattering of weights about their mean value. This permits a selection among the many available synthesis methods for associative memories.

Recently, a neural network for fast computation of discrete Hartley and Fourier transforms has been proposed. In this paper the sensitivity of the network to weight errors is investigated. Sensitivity formulas are derived which give the partial derivatives of the network outputs with respect to weight variations. Then, assuming that the weight errors are independent random variables, the exact probability density functions are derived for the errors in the Hartley transform (DHT) and in both magnitude and phase of the Fourier transform (DFT). It is shown that the magnitude relative error of an N-point DFT decreases as 1/square root of N, when N increases.

The design of fully connected discrete-time neural networks, with threshold units, can be performed by solving a set of linear inequalities. Using this formulation, the design problem can be handled by several powerful algorithms. This approach is extended to the design of continuous-time neural networks with sigmoidal units, which represent a more realistic model of analog circuit implementations. The proposed method is based on some theoretical results proved in this paper

A new learning algorithm is proposed for space-varying cellular neural networks, used to implement associative memories. The algorithm exhibits some peculiar features which make it very attractive: the finite precision of connection weights is automatically taken into account as a design constraint; no multiplication is needed for weight computation; learning can be implemented in fixed point digital hardware or simulated on a digital computer without numerical errors. Index Terms--Associative memories, cellular neural networks, learning.