By Alexander A. Frolov, Dušan Húsek, Pavel Yu. Polyakov (auth.), Jun Wang, Gary G. Yen, Marios M. Polycarpou (eds.)

The two-volume set LNCS 7367 and 7368 constitutes the refereed court cases of the ninth overseas Symposium on Neural Networks, ISNN 2012, held in Shenyang, China, in July 2012. The 147 revised complete papers offered have been rigorously reviewed and chosen from quite a few submissions. The contributions are dependent in topical sections on mathematical modeling; neurodynamics; cognitive neuroscience; studying algorithms; optimization; development attractiveness; imaginative and prescient; photo processing; details processing; neurocontrol; and novel applications.

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Additional info for Advances in Neural Networks – ISNN 2012: 9th International Symposium on Neural Networks, Shenyang, China, July 11-14, 2012. Proceedings, Part I

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Aim at this problem, a novel modeling approach based on mutual information and extreme learning machines is proposed in this paper. Simple mutual information based feature selection method is integrated with the fast learning kernel based extreme learning machines to obtain better modeling performance. In the method, optimal number of the features and learning parameters of models are selected simultaneously. The simulation results based on the near-infrared spectrum show that the proposed approach has better prediction performance and fast leaning speed.

S, ∀w ∈ WPE } . 1. For a standard sigmoid function f(z) = 1/(1+e-z) over a finite interval [a, b] ∈ R, the maximum of its gradient (a Lipschitz constant) Lf is given by  f ' (a) if a > 0  L f = f (1 − f ) =  f ' (b) if b < 0 1 4 if a ≤ 0 ≤ b  (6) Pruning Feedforward Neural Network Search Space Using Local Lipschitz Constants 17 Now let us consider the four maximization problems one at a time. First, consider the problem 1  2 P1 = max γ f j (1 − f j ) 1 +  xi2  . i   1  2 For a given input pattern xp, 1 +  xi2  is a constant.

Notice that if the target values are binary, we will have t p − f (a ) if t p = 1 P4 =   f (b) − t p if t p = 0 Even if the target value is not binary, computing P4 would be easy since the interval [a, b] used for P3 could be used in a simple calculation, as only the end points of the interval need to be evaluated. Thus we have Lo = P1 P2 P3 LFp = P4 Lo 5 Illustrative Example Let us apply the above procedure to estimating the Lipschitz constant of the 2x2x1 XOR network. Table 1 shows Lipschitz constants computed for a number of subregions.

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