By Stephen Grossberg (auth.), Roberto Pirrone, Filippo Sorbello (eds.)
This publication constitutes the refereed complaints of the twelfth overseas convention of the Italian organization for man made Intelligence, AI*IA 2011, held in Palermo, Italy, in September 2011. The 31 revised complete papers offered including three invited talks and thirteen posters have been rigorously reviewed and chosen from fifty eight submissions. The papers are prepared in topical sections on laptop studying; allotted AI: robotics and MAS; theoretical matters: wisdom illustration and reasoning; making plans, cognitive modeling; typical language processing; and AI applications.
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Extra resources for AI*IA 2011: Artificial Intelligence Around Man and Beyond: XIIth International Conference of the Italian Association for Artificial Intelligence, Palermo, Italy, September 15-17, 2011. Proceedings
In defense of one-vs-all classiﬁcation. Journal of Machine Learning Research 5, 101–141 (2004) 15. : Probabilistic discriminative kernel classiﬁers for multi-class problems. , Florczyk, S. ) DAGM 2001. LNCS, vol. 2191, pp. 246–253. Springer, Heidelberg (2001) 16. : Learning with Kernels. MIT Press, Cambridge (2001) 17. : Probability estimates for multi-class classiﬁcation by pairwise coupling. Journal of Machine Learning Research 5, 975–1005 (2004) 18. : Face recognition: A literature survey.
K. Clearly, for xi ∈ L, this information is implicitly embedded on the targets yij , j = 1, . . , k. As a consequence, a hypothetic perfect ﬁtting of labeled points would fulﬁll Eq. 4 ∀x ∈ L. On the other hand, each fj is requested to be smooth in the RKHS, and a perfect ﬁtting is generally not achieved. Interestingly, Eq. 4 gives us a basic domain information on the problem that is supposed to hold in the entire input space. We exploit this information on the relationship among the functions fj , j = 1, .
The optimal solution of Eq. 3 can be expressed as a kernel expansion, as stated in the following Representer Theorem. Theorem 1. Let us consider the minimization problem of Eq. 3, where the function f1 , . . , fk belong to a RKHS H. Then the optimal solution fj∗ , j = 1, . . , k is expressed as fj∗ (x) = n=l+u αij K(x, xi ), j = 1, . . , k i=1 where K(·, ·) is the reproducing kernel associated to H, xi ∈ S, and αij are n scalar values. Proof: Using a simple orthogonality argument, the proof is a straightforward extension of the representer theorem for plain kernel machines .
AI*IA 2011: Artificial Intelligence Around Man and Beyond: XIIth International Conference of the Italian Association for Artificial Intelligence, Palermo, Italy, September 15-17, 2011. Proceedings by Stephen Grossberg (auth.), Roberto Pirrone, Filippo Sorbello (eds.)