Artificial Neural Networks and Machine Learning – ICANN by Shinya Suzumura, Ryohei Nakano (auth.), Alessandro E. Villa,

By Shinya Suzumura, Ryohei Nakano (auth.), Alessandro E. Villa, Włodzisław Duch, Péter Érdi, Francesco Masulli, Günther Palm (eds.)

The two-volume set LNCS 7552 + 7553 constitutes the complaints of the twenty second foreign convention on man made Neural Networks, ICANN 2012, held in Lausanne, Switzerland, in September 2012. The 162 papers integrated within the court cases have been conscientiously reviewed and chosen from 247 submissions. they're equipped in topical sections named: theoretical neural computation; details and optimization; from neurons to neuromorphism; spiking dynamics; from unmarried neurons to networks; advanced firing styles; circulate and movement; from sensation to conception; item and face attractiveness; reinforcement studying; bayesian and echo nation networks; recurrent neural networks and reservoir computing; coding architectures; interacting with the mind; swarm intelligence and decision-making; mulitlayer perceptrons and kernel networks; education and studying; inference and popularity; aid vector machines; self-organizing maps and clustering; clustering, mining and exploratory research; bioinformatics; and time weries and forecasting.

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Extra resources for Artificial Neural Networks and Machine Learning – ICANN 2012: 22nd International Conference on Artificial Neural Networks, Lausanne, Switzerland, September 11-14, 2012, Proceedings, Part II

Example text

K }, given k , taken from the permutation space ΩL . Each example xn consists of m attributes xn = {a1 , . . , am } and is taken from the example space X. The position of λa in a ranking πn is denoted by πn (a) and assumes a value in the set {1, . . , k}. 1 Label Ranking Given T = { xn , πn }, the goal in LR is to learn a function f : X → ΩL that mint imizes a given loss function function l = 1t n=1 τ (πn , πˆn ). With this mapping, we are able to predict a ranking πˆn of the labels in L for a new example xn .

The experimental results are presented in Section 4, and Section 5 concludes this paper. 2 Preliminaries Throughout this paper, we assume a training set T = { xn , πn } consisting of t examples xn and their associated label rankings πn . Such a ranking is a permutation of a finite set of labels L = {λ1 , . . , λk }, given k , taken from the permutation space ΩL . Each example xn consists of m attributes xn = {a1 , . . , am } and is taken from the example space X. The position of λa in a ranking πn is denoted by πn (a) and assumes a value in the set {1, .

2 To illustrate our results, consider the Gaussian kernel K(x, y) := e− x−y . It was shown in [24] that the set a>0 GK a (Rd ) of Gaussians with all widths and centers is linearly independent. Thus for a = b, span GK a (Rd ) ∩ span GK b (Rd ) = ∅. By Theorem 1 and Corollary 1, all these sets are dense subspaces of L2 (Rd ) and C(X), resp. So we have a family of disjoint dense subsets, each formed by input-output functions of Gaussian networks with some fixed width. However by Theorem 4, for 0 < b < a, the whole space HK b (Rd ) and hence also its subset span GK b (Rd ) is contained in the space HK a (Rd ).

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