By Prof. Giacomo Della Riccia, Prof. Dr. Hans-Joachim Lenz, Prof. Dr. Rudolf Kruse (eds.)
ISBN-10: 3211829105
ISBN-13: 9783211829103
ISBN-10: 3709126681
ISBN-13: 9783709126684
The contents of those court cases replicate the purpose of the organizers of the workshop to collect scientists and engineers having a robust curiosity in interdisciplinary paintings within the fields of computing device technological know-how, arithmetic and utilized information. result of this collaboration are illustrated in difficulties facing neural nets, facts and networks, category and information mining, and (machine) learning.
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Extra resources for Learning, Networks and Statistics
Example text
There have been several attempts to apply control engineering methods for economic systems modeling [11], [12]. g. g. markets). Social systems have a much higher degree of unpredictability than technical systems have. Social systems lack the laws of nature engineers successfully use for accurate prediction and control of technical systems. Therefore, model based prediction of social systems and describing the proper rules of state transformation is not only gradually different from technical system modeling but fundamentally different.
X xout as (7) aEA where s is a d-dimensional vector of coordinates on the hypersurface. The vectorial coefficients Wa are the adaptable parameters and play the role of support points through which the hypersurface shall pass. Like in a SOM, each Wa is "attached" to a node a in ad-dimensional discrete (and usually hypercubic) lattice A, over which the summation runs. The second requirement, Eq. (6), guarantees that the resulting manifold w(s) does not change its shape under a translation Wa---+ Wa + t of all reference vectors.
Th~ 5 "Harmonic" PSOMs The simplest choice for the basis functions H( a,·) is to make them linear in each coordinate s; separately. For a d-dimensional space, there are 2d such polynomials that are independent, and a convenient, orthogonal basis set is given by the 2d products obtained by choosing for the i-th factor either s; or 1 - s;, i = 0 ... d- 1. Each such basis polynomial can be considered as "belonging" to a corner s = a E {0, 1}d of the d-dimensional hypercube [0, l]d selected by the condition H( a, s) = 1 and zero on the remaining 2d -I corners s' -::/= s.
Learning, Networks and Statistics by Prof. Giacomo Della Riccia, Prof. Dr. Hans-Joachim Lenz, Prof. Dr. Rudolf Kruse (eds.)
by Richard
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