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Trends in Neural Computation by Ke Chen

By Ke Chen

These days neural computation has turn into an interdisciplinary box in its personal correct; researches were carried out starting from different disciplines, e.g. computational neuroscience and cognitive technology, arithmetic, physics, desktop technology, and different engineering disciplines. From diversified views, neural computation offers an alternate method to appreciate mind capabilities and cognitive strategy and to resolve hard real-world difficulties successfully. pattern in Neural Computation comprises twenty chapters both contributed from top specialists or shaped by means of extending good chosen papers provided within the 2005 foreign convention on normal Computation. The edited ebook goals to mirror the most recent progresses made in numerous parts of neural computation, together with theoretical neural computation, biologically believable neural modeling, computational cognitive technological know-how, man made neural networks architectures and studying algorithms and their purposes in real-world difficulties.

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The simulation setup is the same as in Section 2, except the size of the training data is n = 8 + 8, the number of input variables is p = 5, and only the first variable x1 is relevant to the optimal classification boundary. The solid line corresponds to β1 , the dashed lines correspond to β2 , . . , β5 . The left panel is for βλ2 (λ1 ) (with λ2 = 30), and the right panel is for βλ1 (λ2 ) (with λ1 = 6). and facilitates the adaptive selection of the tuning parameter. 5 illustrates the piecewise linearity property; any segment between two adjacent vertical lines is linear.

Main reason for the fast computing speed is that no initialization is needed and the solution can be obtained in a single-step which is also least-squares optimal. While awaiting for possibly optimal solutions or tuning to universal approximators like Neural Networks, RBF and SVM to appear in the research literature, we hope that this simple network model can provide a benchmark considering both accuracy and efficiency for good classification algorithms design. Notes 1. For instance, in the Statlog-heart, Attitude-smoking and Waveform problems, a total of respectively 42, 288 and 198 weight parameters are needed for gRM to get a similar or comparable classification accuracy as that using the TanhNet which needs only respectively 15, 45 and 69 weight parameters.

Introduction In a standard two-class classification problem, we are given a set of training data (x1 , y1 ), (x2 , y2 ), . . (xn , yn ), where the input (predictor variable) xi ∈ Rp is a p-dimensional vector and the output (response variable) yi ∈ {1, −1} is a binary categorical variable. The aim is to find a classification rule from the training data, so that when given a new input x, we can assign a class label, either 1 or −1, to it. The support vector machine (SVM) has been a popular tool for the two-class classification problem in the machine learning field.

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