By Shotaro Akaho (auth.), Véra Kůrková, Roman Neruda, Jan Koutník (eds.)
This quantity set LNCS 5163 and LNCS 5164 constitutes the refereed complaints of the 18th overseas convention on synthetic Neural Networks, ICANN 2008, held in Prague Czech Republic, in September 2008.
The 2 hundred revised complete papers offered have been conscientiously reviewed and chosen from greater than three hundred submissions. the 1st quantity comprises papers on mathematical conception of neurocomputing, studying algorithms, kernel equipment, statistical studying and ensemble suggestions, help vector machines, reinforcement studying, evolutionary computing, hybrid structures, self-organization, regulate and robotics, sign and time sequence processing and snapshot processing.
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Additional info for Artificial Neural Networks - ICANN 2008: 18th International Conference, Prague, Czech Republic, September 3-6, 2008, Proceedings, Part I
Jp Abstract. For neural networks, learning from dichotomous random samples is diﬃcult. An example is learning of a Bayesian discriminant function. However, one-hidden-layer neural networks with fewer inner parameters can learn from such signals better than ordinary ones. We show that such neural networks can be used for approximating multi-category Bayesian discriminant functions when the state-conditional probability distributions are two dimensional normal distributions. Results of a simple simulation are shown as examples.
However, the total number of the parameters is not so increased. In the approximation formulae (10) and (11), there are 2d + 1 and 1 2 3 2 2 d + 2 d + 1 outer parameters and d + d and 1 inner parameters respectively. Hence, the total numbers of parameters in (10) and (11) are d2 + 3d + 1 and 1 2 3 2 d + 2 d+2 respectively. The latter is smaller than the former. In these counting, note that the unit vectors uk in (11) are ﬁxed and not regarded as parameters. Training of the outer parameters is easier than the inner parameters.
2. Up-left: Original mixtures, Up-right: Mixtures with reduced dimension, Down: Two dimensional scatter plots of mixtures [Embedding algorithm (for e-PCA, general)] 1. Sort θ(1) , . . , θ(n) in the descending order of the numbers of components. 2. Embed θ(1) in any conﬁguration 3. Repeat the following (a),(b),(c) for i = 2, 3, . . , n (a) Let θec be e-center of already embedded mixtures j = 1, . . , i − 1. (b) Solve (16) to ﬁnd the correspondence between θ(i) and θec . (c) If the number of components of θ (i) is smaller than θ ec , then split the components by (17).