Computational complexity of combinatorial problems related to piecewise linear committee pattern-recognition learning procedures / Khachai M.Y., Poberii M.I. // Pattern Recognition and Image Analysis. - 2012. - V. 22, l. 2. - P. 278-290.

ISSN:
10546618
Type:
Article
Abstract:
A class of combinatorial optimization problems related to optimal pattern recognition learning is studied by the method of structural risk minimization in the class of piecewise linear committee decision rules. Most of the problems are shown to be intractable and the thresholds of their efficient approximability are estimated and approximation polynomial algorithms are given. © 2012 Pleiades Publishing, Ltd.
Author keywords:
affine committee; committee decision rule; computational complexity; empirical risk minimization; learning theory; point covering; strongly NP hardness
Index keywords:
affine committee; Decision rules; Empirical risk minimization; Learning Theory; NP-hardness; point covering; Combinatorial optimization; Computational complexity; Pattern recognition; Piecewise linear
DOI:
10.1134/S1054661812020046
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84862255552&doi=10.1134%2fS1054661812020046&partnerID=40&md5=5fcbb52145db9401c1e5204f47d3ec07
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Affiliations Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg 620990, Russian Federation
Author Keywords affine committee; committee decision rule; computational complexity; empirical risk minimization; learning theory; point covering; strongly NP hardness
References Vapnik, V.N., (1998) Statistical Learning Theory, , New York: Wiley; Zhuravlev, Y.I., The Algebraic Approach for Solving the Recognition or Classification Problems (1978) Probl. Kibernet., (33), pp. 5-68; Blum, A., Rivest, R.L., Training a 3-Node Neural Network Is NP-Complete (1988) Advances in Neural Information Processing Systems, , D. S. Touretzky (Ed.), San Mateo: M. Kaufmann; Lin, J.H., Vitter, J.S., Complexity Results on Learning by Neural Nets (1991) Mach. Learn., 6, pp. 211-230; Khachay, M., On the Computational Complexity of the Minimum Committee Problem (2007) J. Math. Model. Algor., 6 (4), pp. 547-561; Khachai, M., Poberii, M., Complexity and Approximability of Committee Polyhedral Separability of Sets in General Position (2009) Informatica, 20 (2), pp. 217-234; Dinur, I., The PCP Theorem by Gap Amplification (2007) J. ACM, 54 (3); Mazurov, V.D., Committees for Sets of Inequalities and the Problem of Pattern Recognition (1971) Kibernet., (3), pp. 140-146; Khachai, M., Mazurov, V., Rybin, A., Committee Construction for Solving Problems of Selection, Diagnostics, and Prediction (2002) Proc. Steklov Inst. Math., (SUPPL. 1), pp. 67-101; Khachai, M., Computational and Approximational Complexity of Combinatorial Problems Related to the Committee Polyhedral Separability of Finite Sets (2008) Pattern Recogn. Image Anal., 18 (2), pp. 237-242; Megiddo, N., Tamir, A., On the Complexity of Locating Linear Facilities in the Plane (1982) Oper. Res. Lett., 1 (5), pp. 194-197; Khachai, M.Y., On Computational and Approximation Complexity of the Problem on Minimal Affine Separating Component (2006) Tavrich. Vestn. Inf. Mat., (1), pp. 34-43; Johnson, D.S., Approximation Algorithms for Combinatorial Problems (1974) J. Comput. Syst. Sci., 9 (3), pp. 256-278; Yablonskii, S.V., (1986) Introduction into Discrete Mathematics, , Moscow: Nauka; Johnson, D.S., Preparata, F.P., The Densest Hemisphere Problem (1978) Theor. Comput. Sci., (6), pp. 93-107; Khachay, M.Y., A Game against Nature Related to Majority Vote Decision Making (2002) Computational Mathematics and Mathematical Physics, 42 (10), pp. 1547-1555
Correspondence Address Khachai, M. Y.; Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg 620990, Russian Federation; email: mkhachay@imm.uran.ru
Language of Original Document English
Abbreviated Source Title Pattern Recogn. Image Anal.
Source Scopus