By Akira Hirose
This monograph instructs graduate- and undergraduate-level scholars in electric engineering, informatics, keep an eye on engineering, mechanics, robotics, bioengineering at the suggestions of complex-valued neural networks. Emphasizing simple innovations and methods of considering neural networks, the writer makes a speciality of neural networks that care for complicated numbers; the sensible benefits of complex-valued neural networks, and their origins; the advance of primary functions? The e-book makes use of designated examples to reply to those questions and extra.
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Additional info for Complex-Valued Neural Networks
The internal state of a neuron is simply the weighted sum of the input signals or a nonlinear transform of the weighted sum. The nonlinear function is called activation function. Note that, in this Book, we do not deal explicitly with the so-called threshold in the model neuron. Contrarily, model neurons in not a few books possess a threshold so that (internal state) = (weighted sum of inputs) − (threshold). 1 Processing, learning, and self-organization 45 a low one. But it has no relation to the basis of neuron dynamics, which you will ﬁnd in the following sections.
Processing tasks. A neural network reacts to signals, presented by the environment, by processing the presented input information in a manner meaningful to the network or network users. 2. Learning or Self-organization. The network changes itself to process information meaningfully. , network topology. We call the details of the behavior the neurodynamics. 2 and the following sections present several examples of neurodynamics. 3 Task processing “A neural network processes a task” means that the network yields output signals appropriately to input signals.
The output y(t) converges typically with a single or several iterations. In other words, the recall is completed. Why it is capable of recalling the vector nearest to the input? To understand the dynamics, we trace the changes in the signal vector. Assume that the input vector x is near to, say, s2 . 14) 52 4 Constructions and dynamics of neural networks Wx = W(s2 + n) = SST (s2 + n) ⎤ ⎡ ⎥⎡ ⎢ ⎥ ⎢ ⎥⎢ ⎢ ⎥⎢ ⎢ ⎢ = ⎢ s1 s2 · · · sµ ⎥ ⎥⎢ ⎥⎣ ⎢ ⎥ ⎢ ⎦ ⎣ ⎤ (s1 )T (s2 )T .. 15). If the memorized vectors are chosen at random, they are approximately orthogonal to each other.
Complex-Valued Neural Networks by Akira Hirose