Behnam Bavarian

On the rate of convergence in topology preserving neural networks

A formal analysis of the neighborhood interaction function selection in the topology preserving unsupervised neural network is presented in this paper. The definition of the neighborhood interaction function is motivated by anatomical evidence as opposed to what is currently used, which is a uniform neighborhood interaction set. By selecting a neighborhood interaction function with a neighborhood amplitude of interaction which is decreasing in spatial domain the topological order is always enforced and the rate of self-organization to final equilibrium state is improved. Several simulations are carried out to show the improvement in rate between using a neighborhood interaction function vs. using a neighborhood interaction set. An error measure functional is further defined to compare the two approaches quantitatively.

Analysis of neighborhood interaction in Kohonen neural networks

A formal analysis of the neighborhood interaction of Kohonen neural networks is presented. The authors propose a new neighborhood interaction to improve the topological order of the neural network. The neighborhood interaction which depends on lateral distance is motivated by anatomical evidence as opposed to what is currently used, which is a constant. The authors also mathematically show that using the new neighborhood interaction will enforce the topological order in the neighborhood set for every iteration. One simulation is presented to show that the topological order is improved by using the new neighborhood interaction.<<ETX>>

Improved rate of convergence in Kohonen neural network

The neighborhood interaction function selection in the Kohonen self-organizing feature map neural network is analyzed for improving the rate of convergence. The definition of the neighborhood interaction function is motivated by anatomical evidence as opposed to what is currently used, which is a uniform neighborhood interaction set. By selecting a neighborhood interaction function with a neighborhood amplitude of interaction which is decreasing in the spatial domain the topological order is always enforced and the rate of self-organization to final equilibrium state is improved. A simulation is carried out to show the convergence rate improvement achieved using a neighborhood interaction function vs. using a neighborhood interaction set. An error measure functional is further defined to compare the two approaches quantitatively.<<ETX>>

Multiple job scheduling with artificial neural networks

Abstract This paper presents an application of neural networks in a multiple task scheduling problem. We take the crossbar Hopfield network which is used to solve the classical traveling salesman problem and extend it to a 3-D neuro-box network (NBN) to solve multiple task scheduling on multiple servers. The approach is presented in several stages starting with a brief review of the Hopfield network, the formulation of the traveling salesman problem on the Hopfield network, the extension to the multiple traveling salesman problem, and the formulation of the manufacturing task scheduling problem, in increasing order of difficulty. At every step, the topology of the network, the energy function (or the cost function which is to be minimized) of the network, the differential equations defining the characteristics of the neurons and illustrative simulations are presented in the paper.

A neural piecewise linear classifier for pattern classification

A neural piecewise linear classifier, based on the Kohonen learning vector quantization (LVQ2) and the Kohonen self-organizing feature map is proposed. The classifier has two stages and a feedback loop. In the first stage, the Kohonen self-organizing feature map network is used to find the approximate position of the prototype vectors for each class. In the second stage, the Kohonen LVQ2 supervised learning algorithm is used to fine-tune the position of the approximate prototype vectors. The accuracy of the classifier is improved by adding an adaptive feedback scheme. Depending on the intrinsic complexity of the class distribution and overall partitioning of the space, the neural classifier automatically increases the number of neurons, improving the error performance. The classifier was tested on a set of high-dimensional real data obtained from ship images. The performance is compared with a piecewise linear tree classifier and a neural classifier.<<ETX>>

Job scheduling on parallel machines using simulated annealing

The authors consider the problem of scheduling a set of simultaneously available jobs on several parallel machines. Specifically, the minimization of the time to finish all the jobs assigned to all machines of scheduling sequence under job deadline constraints for the n jobs, m machines problem is formulated. The simulated annealing and fast simulated annealing algorithms are reviewed and adopted for the scheduling problem. A large number of simulations were carried out which provides an empirical basis for comparing the application of classical simulated annealing and fast simulated annealing algorithms to the scheduling problem.<<ETX>>

Comparison of a neural network and a piecewise linear classifier

Abstract A neural algorithm proposed by Kohonen is used to design a neural classifier. We use the algorithm to classify a real multiple-class data set obtained from ship images and compare the results with the results of the piecewise linear classifier. The error performance of the neural classifier is slightly better than the piecewise linear classifier, however the training algorithm is much simplier and easier to implement.

Compensation of unstructured uncertainty in manipulators using neural networks

A neurocompensator-augmented computed torque control scheme for the compensation of unmodeled frictional effects in manipulators is proposed. The proposed compensator is implemented by a three-layer network structure. A weight adaptation methodology based on the extended Kalman filter algorithm is used. Computer simulations are performed to verify and study the stability, convergence, and trajectory tracking performance of the proposed control architecture. The simulations also verified the stability of the computed torque control law augmented by the neurocompensator approximating unmodeled frictional effects.<<ETX>>

Derivation of learning vector quantization algorithms

A formal derivation of three learning rules for the adaptation of the synaptic weight vectors of neurons representing the prototype vectors of the class distribution in a classifier is presented. A decision surface function and a set of adaptation algorithms for adjusting this surface which are derived by using the gradient-descent approach to minimize the classification error are derived. This also provides a formal analysis of the Kohonen learning vector quantization (LVQ1 and LVQ2) algorithms. In particular, it is shown that to minimize the classification error, one of the learning equations in the LVQ1 algorithm is not required. An application of the learning algorithms for designing a neural network classifier is presented. The performance of the classifier was tested and compared to the K-NN decision rule for the Iris real data set.<<ETX>>

Analysis and application of self-organizing sensory mapping

The authors present a mathematical analysis of self-organizing sensory mapping which was first proposed by Kohonen. It is shown that using the sensory mapping learning rule is equivalent to minimizing an energy function of the network outlined. The underlying work of Kohonen and the topology preserving networks are reviewed, along with the algorithm for implementing the network. The concept of the energy of a network is defined and a detailed analysis of the mapping algorithm is outlined.<<ETX>>