A saturated linear dynamical network for approximating maximum clique

Cataloged from PDF version of article.We use a saturated linear gradient dynamical network for finding an approximate solution to the maximum clique problem. We show that for almost all initial conditions, any solution of the network defined on a closed hypercube reaches one of the vertices of the hypercube, and any such vertex corresponds to a maximal clique. We examine the performance of the method on a set of random graphs and compare the results with those of some existing methods. The proposed model presents a simple continuous, yet powerful, solution in approximating maximum clique, which may outperform many relatively complex methods, e.g., Hopfield-type neural network based methods and conventional heuristics

Gradient networks for clustering

In this paper, two different optimization formulations for clustering problem are considered. The first one is the common mixed-integer optimization formulation and the second one is the binary integer optimization formulation which was proposed by the authors. The costs of the optimization problems were minimized by two different gradient dynamical networks. The performances of the networks were compared with each other on the image compression applications

Automatic spike detection in EEG by a two-stage procedure based on support vector machines

In this study, we introduce a two-stage procedure based on support vector machines for the automatic detection of epileptic spikes in a multi-channel electroencephalographic signal. In the first stage, a modified non-linear digital filter is used as a pre-classifier to classify the peaks into two subgroups: (i) spikes and spike like non-spikes (ii) trivial non-spikes. The pre-classification done in the first stage not only reduces the computation time but also increases the overall detection performance of the procedure. In the second stage, the peaks falling into the first group are aimed to be separated from each other by a support vector machine that would function as a post-classifier. Visual evaluation, by two experts, of 19 channel EEG records of 7 epileptic patients showed that the best performance is obtained providing 90.3% sensitivity, 88.1% selectivity and 9.5% false detection rate. (C) 2003 Elsevier Ltd. All rights reserved

A Boolean Hebb rule for binary associative memory design

We propose a binary associative memory design method to be applied to a class of dynamical neural networks. The method is based on introducing the memory vectors as maximal independent sets to an undirected graph and on designing a dynamical network in order to find a maximal independent set whose characteristic vector is close to the given distorted vector. We show that our method provides the attractiveness for each memory vector and avoids the occurance of spurious states whenever the set of given memory vectors satisfies certain compatibility conditions. We also analyze the application of this design method to the discrete Hopfield network

Automatic recognition of sleep spindles in EEG by using artificial neural networks

In this paper, we introduce a two-stage procedure based on artificial neural networks for the automatic recognition of sleep spindles (SSs) in a multi-channel electroencephalographic signal. In the first stage, a discrete perceptron is used to eliminate definite non-SSs. The pre-classification done in the first stage not only reduces the computation time but also increases the overall detection performance of the procedure. In the second stage, the remaining SS candidates after pre-classification procedure are aimed to be separated from each other by an artificial neural network that would function as a post-classifier. Two different networks, i.e. a backpropagation multilayer perceptron and radial basis support vector machine (SVM), are proposed as the post-classifier and compared in terms of their classification performances. Visual evaluation, by two electroencephalographers (EEGers), of 19 channel EEG records of 6 subjects showed that the best performance is obtained with a radial basis SVM providing an average sensitivity of 94.6% and an average false detection rate of 4.0%. (C) 2004 Elsevier Ltd. All rights reserved

Robust spherical clustering as mixed integer optimization problem and its gradient network solution

Support vector based spherical clustering is described as an optimization problem posed in the input space where the cluster indicators are also considered as variables. The robust clustering is attempted to be found by taking the objective function of the optimization problem as energy function of the gradient network. The proposed method is an extension of the work by the authors formulating the clustering problem as a mixed integer optimization by considering the cluster indicators and centers as variables

A Boolean Hebb rule for binary associative memory design

A binary associative memory design procedure that gives a Hopfield network with a symmetric binary weight matrix is introduced in this paper. The proposed method is based on introducing the memory vectors as maximal independent sets to an undirected graph, which is constructed by Boolean operations analogous to the conventional Hebb rule. The parameters of the resulting network is then determined via the adjacency matrix of this graph in order to find a maximal independent set whose characteristic vector is close to the given distorted vector. We show that the method provides attractiveness for each memory vector and avoids spurious memories whenever the set of given memory vectors satisfy certain compatibility conditions, which implicitly imply sparsity. The applicability of the design method is finally investigated by a quantitative analysis of the compatibility conditions

An application of support vector machine in bioinformatics: Automated recognition of epileptiform patterns in EEG using SVM classifier designed by a perturbation method

We introduce an approach based on perturbation method for input dimension reduction in Support Vector Machine (SVM) classifiers. If there exists redundant data components in training data set, they can be discarded by analyzing the total disturbance of the SVM output corresponding to the perturbed inputs. Thus, input dimension size is reduced and network becomes smaller. Algorithm for input dimension reduction is first formulated and then applied to real electroencephalography (EEG) data for recognition of epileptiform patterns

Automatic recognition of sleep spindles in EEG via radial basis support vector machine based on a modified feature selection algorithm

This paper presents an application of a radial basis support vector machine (RB-SVM) to the recognition of the sleep spindles (SSs) in electroencephalo-graphic (EEG) signal. The proposed system comprises of two stages. In the first stage, for feature extraction, a set of raw amplitude values, a set of discrete cosine transform (DCT) coefficients, a set of discrete wavelet transform (DWT) approximation coefficients and a set of adaptive autoregressive (AAR) parameters are calculated and extracted from signals separately as four different sets of feature vectors. Thus, four different feature vectors for the same data are comparatively examined. In the second stage, these features are then selected by a modified adaptive feature selection method based on sensitivity analysis, which mainly supports input dimension reduction via selecting the most significant feature elements. Then, the feature vectors are classified by a support vector machine (SVM) classifier, which is relatively new and powerful technique for solving supervised binary classification problems due to it's generalization ability. Visual evaluation, by two electroencephalographers (EEGers), of 19 channel EEG records of six subjects showed that the best performance is obtained with an RB-SVM providing an average sensitivity of 97.7%, an average specificity of 97.4% and an average accuracy of 97.5%