Nguyen Van Thoai (auth.), Ngoc Thanh Nguyen, Tien van Do,'s Advanced Computational Methods for Knowledge Engineering PDF

By Nguyen Van Thoai (auth.), Ngoc Thanh Nguyen, Tien van Do, Hoai An le Thi (eds.)

ISBN-10: 3319002929

ISBN-13: 9783319002927

ISBN-10: 3319002937

ISBN-13: 9783319002934

The publication comprises 29 prolonged chapters which were chosen and invited from the submissions to the 1st overseas convention on desktop technological know-how, utilized arithmetic and Applications (ICCSAMA 2013) hung on 9-10 may perhaps, 2013 in Warsaw, Poland. The publication is equipped into 5 components, that are: complex Optimization tools and Their purposes, Queuing thought and functions, Computational equipment for wisdom Engineering, wisdom Engineering with Cloud and Grid Computing, and good judgment dependent equipment for selection Making and knowledge Mining, respectively. All chapters within the e-book talk about theoretical and sensible matters hooked up with computational tools and optimization equipment for wisdom engineering.

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Acta Mathematica Vietnamica (dedicated to Professor Hoang Tuy on the occasion of his 70th birthday) 22(1), 289–355 (1997) 11. c. optimazation algorithm for solving the trust region subproblem. fr Abstract. This paper addresses the problem of feature selection for Multi-class Support Vector Machines (MSVM). Basing on the l0 and the l2 -l0 regularization we consider two models for this problem. The l0 -norm is approximated by a suitable way such that the resulting optimization problems can be expressed as DC (Difference of Convex functions) programs for which DC programming and DC Algorithms (DCA) are investigated.

It is worth noting that DCA works with the convex DC components G and H but not the DC function F itself (see [5, 6, 10, 11]). ) of DCA. Convergence properties of DCA and its theoretical basis can be found in [5, 6, 10]. For instant, it is important to mention that (for simplify we omit here the dual part) – DCA is a descent method (the sequences {G(xk ) − H(xk )} is decreasing) without linesearch. – If the optimal value α of problem (11) is finite and the infinite sequence {xk } is bounded then every limit point x of the sequence {xk } is a critical point of G − H.

Thus, we assume that f (y) > 0 ∀y ∈ Q(S), and our method for computing a lower bound μ(S) is based on the following. Proposition 1. Let U be the n × n matrix with columns u1 , · · · , un . t. i )λi − t ≤ 0, y ∈ Q(S) i=1 Uλ ∈ D (12) n λi = 1 i=1 λ ≥ 0, where for each y ∈ Q(S), the point py is constructed by (5) and the min-type function py (x) is defined by (3). Proof. From (4) and (6) it follows that min{f (x) : x ∈ S ∩ D} ≥ min{ max y∈Q(S) py (x) = min{t : max y∈Q(S) = min{t : py (x) : x ∈ S ∩ D} py (x) − t ≤ 0, x ∈ S ∩ D} (13) − t ≤ 0 ∀y ∈ Q(S), x ∈ S ∩ D}.

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Advanced Computational Methods for Knowledge Engineering by Nguyen Van Thoai (auth.), Ngoc Thanh Nguyen, Tien van Do, Hoai An le Thi (eds.)

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