Artificial Neural Networks – ICANN 2007: 17th International by Shinichi Nakajima, Sumio Watanabe (auth.), Joaquim Marques

By Shinichi Nakajima, Sumio Watanabe (auth.), Joaquim Marques de Sá, Luís A. Alexandre, Włodzisław Duch, Danilo Mandic (eds.)

This quantity set LNCS 4668 and LNCS 4669 constitutes the refereed lawsuits of the seventeenth foreign convention on synthetic Neural Networks, ICANN 2007, held in Porto, Portugal, in September 2007.

The 197 revised complete papers provided have been conscientiously reviewed and chosen from 376 submissions. The ninety eight papers of the 1st quantity are prepared in topical sections on studying thought, advances in neural community studying tools, ensemble studying, spiking neural networks, advances in neural community architectures neural community applied sciences, neural dynamics and complicated structures, information research, estimation, spatial and spatio-temporal studying, evolutionary computing, meta studying, brokers studying, complex-valued neural networks, in addition to temporal synchronization and nonlinear dynamics in neural networks.

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Extra resources for Artificial Neural Networks – ICANN 2007: 17th International Conference, Porto, Portugal, September 9-13, 2007, Proceedings, Part I

Example text

Watanabe distances when the inverse covariance matrix corresponds to the graph with a single loop. Next, we develop the results to the more general case that the graph has a single loop and an arbitrary tree structure. , multiloops). The situation in which LBP is applied to a multi-dimensional Gaussian distribution can be seen for example in probabilistic image processing based on Gaussian graphical models [7][8] and Markov random fields [4]. Besides, clarifying the theoretical properties of LBP in the standard models such as a Gaussian distribution helps to know the properties of more complex LBP and to design LBP algorithms efficiently.

Theorem1 shows that the learning coefficient is determined by the Kullback information and the a priori distribution. From the definition of analytic equivalence, the following theorem holds. Theorem 2. If K(w) and H(w) are analytically equivalent, then two zeta functions K(w)z dw, ζ1 (z) = U H(w)z dw ζ2 (z) = V have the same largest pole. 14 T. Matsuda and S. Watanabe Proof. The proof of this theorem is to see [6]. Note that two zeta functions do not have the same second largest pole in general. Now, we will explain the concept of weighted resolution of singularities of Kullback information.

We will do two simple experiments. In the first one, Echo State neural network will be trained independently fifty times and only the values of synaptic weights in its hidden part will be randomly changed. In the second experiment we will do the same thing, but with one difference. Now we will change the network topology of the dynamic reservoir. We can see graphical representation of these experiments in the Fig. 2. These results led us to one important conclusion from the results shown in the Fig.

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