Download Complex-Valued Neural Networks with Multi-Valued Neurons by Igor Aizenberg (auth.) PDF

By Igor Aizenberg (auth.)

ISBN-10: 3642203523

ISBN-13: 9783642203527

Complex-Valued Neural Networks have larger performance, research speedier and generalize greater than their real-valued counterparts.

This booklet is dedicated to the Multi-Valued Neuron (MVN) and MVN-based neural networks. It encompasses a complete statement of MVN concept, its studying, and purposes. MVN is a complex-valued neuron whose inputs and output can be found at the unit circle. Its activation functionality is a functionality in simple terms of argument (phase) of the weighted sum. MVN derivative-free studying relies at the error-correction rule. A unmarried MVN can study these input/output mappings which are non-linearly separable within the actual area. Such classical non-linearly separable difficulties as XOR and Parity n are the easiest that may be discovered via a unmarried MVN. one other very important benefit of MVN is a formal remedy of the part information.

These houses of MVN develop into much more extraordinary while this neuron is used as a easy one in neural networks. The Multilayer Neural community in response to Multi-Valued Neurons (MLMVN) is an MVN-based feedforward neural community. Its backpropagation studying set of rules is derivative-free and in keeping with the error-correction rule. It doesn't be afflicted by the neighborhood minima phenomenon. MLMVN outperforms many different laptop studying ideas by way of studying velocity, community complexity and generalization strength while fixing either benchmark and real-world type and prediction difficulties. one other fascinating software of MVN is its use as a easy neuron in multi-state associative memories.

The e-book is addressed to these readers who increase theoretical basics of neural networks and use neural networks for fixing a variety of real-world difficulties. it may even be very appropriate for Ph.D. and graduate scholars pursuing their levels in computational intelligence.

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Extra info for Complex-Valued Neural Networks with Multi-Valued Neurons

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Wn xn ) and it does not coincide with the desired output d. This forms the error δ =d−y. , n . 6) We expect that once the weights will be adjusted, our neuron should produce the desired output d = sgn ( w 0 + w1 x1 + ... + w n xn ) . 7) can be transformed as follows d =δ + y = sgn ( ( w0 + Δw0 ) + ( w1 + Δw1 ) x1 + ... + ( wn + Δwn ) xn ) . 8) the following δ+y= sgn ( ( w0 + w1 x1 + ... + wn xn ) + ( Δw0 + Δw1 x1 + ... + Δwn xn ) ) . 5) we have the following two cases for the error 14 1 Why We Need Complex-Valued Neural Networks?

In Chapter 6, we will observe complex-valued associative memories based on networks with multi-valued neurons that do not suffer from these disadvantages. 5 Cellular Neural Network The Hopfield neural network as we have seen is a fully connected network. The MLF is a network with full feedforward connections among adjacent layers neurons. We have also seen that the Hopfield network is a recurrent network. It updates its states iteratively until a stable state is reached. In 1988, Leon Chua and Lin Yang proposed another recurrent network with local connections [24] where each neuron is connected just with neurons from its closest neighborhood.

4 Hopfield Neural Network In 1982, John Hopfield proposed a fully connected recurrent neural network with feedback links [21]. The Hopfield Neural Network is a multiple-loop feedback neural network, which can be used first of all as an associative memory. All the neurons in this network are connected to all other neurons except to themselves that is there are no self-feedbacks in the network (see Fig. 12). Thus, the Hopfield network is a fully connected neural network. Initially, J. 1) as the basic ones in this network.

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Complex-Valued Neural Networks with Multi-Valued Neurons by Igor Aizenberg (auth.)

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