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The study of Antanas Zilinskas has fascinated with constructing types for international optimization, imposing and investigating the corresponding algorithms, and utilizing these algorithms to useful difficulties. This quantity, devoted to Professor Zilinskas at the social gathering of his sixtieth birthday, comprises new survey papers within which best researchers from the sector current numerous types and algorithms for fixing international optimization difficulties. This publication is meant for scientists and graduate scholars in laptop technological know-how and utilized arithmetic who're attracted to optimization algorithms and numerical research.
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24 Introduction to Neural Networks Generative topographic maps are defined by specifying a set of points {xi} in a latent space, together with a set of basis functions {qbj(x)}. A constrained mixture of Gaussians is defined by adaptive parameters W and 13, with centres Wqb(xi) and common covariance 13-11. As a latent variable model, a generative topographic map represents a distribution p(t) of data in an m-dimensional space, t = (h, t2. . tm) in terms of a set of p latent variables x = (Xl, x2, ...
L(W,[3) = In 1-Ik=lNp(tklW,[3) 3 Of course, other models for p(tlx) may also be appropriate. , 1998). , 1977). In contrast, the SOM algorithm does not have an explicit cost function. Moreover, conditions under which self-organisation occurs in SOM neural networks are not quantified and in practice it is necessary to validate the spatial ordering of trained SOM models. 4. Learning vector quantization neural networks Vector quantization for data compression is an important application of competitive learning, and is used for both the storage and transmission of speech and image data.
Similarity matching: Find the winning neuron I(x) at time t, using the minimum distance Euclidean or other criterion: iii. I(x) = argjmin]]x(t) - will, for j = 1, 2, ... p iv. 36) wj(t+ 1) = wj(t), otherwise. where rl(t) is a time-variant learning rate parameter, Ax(x)(t) is the neighbourhood function centred around the winning neuron I(x), all of which are varied dynamically. These parameters are often allowed to decay exponentially, for example rl(t) = rl0e -~*. For example, for Gaussian-type neighbourhood functions the modification of the synaptic weight vector wj of the j'th neuron at a lateral distance dji from the winning neuron I(x) is wj(t+ 1) = wj(t) + rl(t)nj,i(x)(t)[x(t ) - wj(t)] v.