By Rudolf Kruse, Christian Borgelt, Frank Klawonn, Christian Moewes, Matthias Steinbrecher, Pascal Held
This clearly-structured, classroom-tested textbook/reference provides a methodical advent to the sector of CI. delivering an authoritative perception into all that's precious for the winning program of CI equipment, the ebook describes primary techniques and their functional implementations, and explains the theoretical history underpinning proposed ideas to universal difficulties. just a simple wisdom of arithmetic is needed. gains: presents digital supplementary fabric at an linked web site, together with module descriptions, lecture slides, routines with recommendations, and software program instruments; includes a variety of examples and definitions during the textual content; provides self-contained discussions on synthetic neural networks, evolutionary algorithms, fuzzy platforms and Bayesian networks; covers the newest ways, together with ant colony optimization and probabilistic graphical versions; written through a group of highly-regarded specialists in CI, with wide adventure in either academia and industry.
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Example text
21 Geometry of the learned threshold logic unit for x1 ∧ x2 . 5 Training of a threshold logic unit for the biimplication epoch x1 x2 o 1 2 3 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 xw y 0 0 −1 −2 0 0 0 −3 0 0 0 −3 1 1 0 0 1 1 1 0 1 1 1 0 e 0 −1 0 1 0 −1 −1 1 0 −1 −1 1 Δθ Δw1 Δw2 θ 0 1 0 −1 0 1 1 −1 0 1 1 −1 0 0 1 1 0 0 1 2 1 0 1 2 1 0 0 0 1 0 0 −1 1 0 0 −1 1 0 −1 0 1 0 −1 0 1 0 −1 0 1 w1 w2 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 −1 −1 0 0 −1 −1 0 0 −1 −1 0 the threshold θ = 3 and the weights w1 = 2 and w2 = 1.
Addison-Wesley, Stuttgart, Germany, 1996 Chapter 4 General Neural Networks In this chapter, we introduce a general model of (artificial) neural networks that captures (more or less) all special forms, which we consider in the following chapters. We start by defining the structure of an (artificial) neural network and then describe generally the operation and finally the training of an (artificial) neural network. 1 Structure of Neural Networks In the preceding chapter, we already considered briefly networks of threshold logic units.
19. As another example, we consider a threshold logic unit with two inputs that is to be trained in such a way that it computes the conjunction of its inputs. Such a threshold logic unit is shown, together with the corresponding training examples, in Fig. 20. For this example, we only consider online training. 4. 5 −1 Fig. 5 Training the Parameters 31 x1 x2 0 0 1 0 0 1 1 1 y 0 0 0 1 Fig. 4 Training of a threshold logic unit for the conjunction Epoch x1 x2 o xw y 1 0 −1 −1 −1 0 0 −1 −1 −1 0 0 −2 −2 −1 0 −1 −2 0 −1 0 −3 −2 −1 0 2 3 4 5 6 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 e −1 0 0 1 −1 −1 0 1 0 −1 −1 1 0 0 −1 1 0 −1 0 0 0 0 0 0 Δθ Δw1 Δw2 θ 1 0 0 −1 1 1 0 −1 0 1 1 −1 0 0 1 −1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 2 2 1 1 2 3 2 2 2 3 2 2 3 3 3 3 3 3 3 0 0 0 1 0 0 0 1 0 0 −1 1 0 0 −1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 −1 0 1 0 −1 0 1 0 0 0 1 0 −1 0 0 0 0 0 0 w1 w2 0 0 0 0 1 1 1 1 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 2 2 1 1 1 1 1 1 1 Fig.