메뉴 건너뛰기




Volumn 57, Issue 12, 2009, Pages 4744-4764

Adaptive constrained learning in reproducing kernel hilbert spaces: The robust beamforming case

Author keywords

Adaptive learning; Beamforming; Convex analysis; Fixed point set; Reproducing kernel Hilbert space (RKHS)

Indexed keywords

ADAPTIVE BEAMFORMING; ADAPTIVE LEARNING; ADAPTIVE PROJECTED SUBGRADIENT METHODS; APRIORI; BEAM FORMERS; BEAM PATTERN; CLOSED CONVEX SETSS; CONVEX ANALYSIS; GENERAL NATURE; KERNEL REGRESSION; LINEAR COMPLEXITY; LOSS FUNCTIONS; MIN-MAX OPTIMIZATION; NONLINEAR LEARNING; NUMERICAL EXAMPLE; POINT SET; REPRODUCING KERNEL HILBERT SPACES; ROBUST BEAMFORMING; ROBUST STATISTICS; SIMPLE EXPRESSION; STEERING VECTOR ERRORS; STRONG CONVERGENCE; TRAINING DATA; UNKNOWN PARAMETERS;

EID: 70450233513     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2027771     Document Type: Article
Times cited : (68)

References (48)
  • 4
    • 3543096272 scopus 로고    scopus 로고
    • The kernel recursive least-squares algorithm
    • Aug.
    • Y. Engel, S. Mannor, and R. Meir, "The kernel recursive least-squares algorithm," IEEE Trans. Signal Process., vol.52, no.8, pp. 2275-2285, Aug. 2004.
    • (2004) IEEE Trans. Signal Process. , vol.52 , Issue.8 , pp. 2275-2285
    • Engel, Y.1    Mannor, S.2    Meir, R.3
  • 6
    • 45749141285 scopus 로고    scopus 로고
    • Kernel affine projection algorithms
    • Article ID 784292, DOI:10.1155/2008/784292
    • W. Liu and J. Príncipe, "Kernel affine projection algorithms," EURASIP J. Adv. Signal Process., vol.2008, p. 12, 2008, Article ID 784292, DOI:10.1155/2008/784292.
    • (2008) EURASIP J. Adv. Signal Process. , vol.2008 , pp. 12
    • Liu, W.1    Príncipe, J.2
  • 7
    • 46749118074 scopus 로고    scopus 로고
    • Online kernel-based classification using adaptive projection algorithms
    • Jul.
    • K. Slavakis, S. Theodoridis, and I. Yamada, "Online kernel-based classification using adaptive projection algorithms," IEEE Trans. Signal Process., vol.56, no.7, pp. 2781-2796, Jul. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.7 , pp. 2781-2796
    • Slavakis, K.1    Theodoridis, S.2    Yamada, I.3
  • 8
    • 45749106357 scopus 로고    scopus 로고
    • Sliding window generalized kernel affine projection algorithm using projection mappings
    • Article ID 735351, DOI:10.1155/2008/735351
    • K. Slavakis and S. Theodoridis, "Sliding window generalized kernel affine projection algorithm using projection mappings," EURASIP J. Adv. Signal Process., vol.2008, p. 16, 2008, Article ID 735351, DOI:10.1155/2008/ 735351.
    • (2008) EURASIP J. Adv. Signal Process. , vol.2008 , pp. 16
    • Slavakis, K.1    Theodoridis, S.2
  • 9
    • 61549112727 scopus 로고    scopus 로고
    • Online prediction of time series data with kernels
    • Mar.
    • C. Richard, J. Bermudez, and P. Honeine, "Online prediction of time series data with kernels," IEEE Trans. Signal Process., vol.57, no.3, pp. 1058-1067, Mar. 2009.
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.3 , pp. 1058-1067
    • Richard, C.1    Bermudez, J.2    Honeine, P.3
  • 10
    • 33646516358 scopus 로고    scopus 로고
    • A geometric approach to support vector machine (SVM) classification
    • M. Mavroforakis and S. Theodoridis, "A geometric approach to support vector machine (SVM) classification," IEEE Trans. Neural Netw., vol.17, no.3, pp. 671-683, 2006.
    • (2006) IEEE Trans. Neural Netw. , vol.17 , Issue.3 , pp. 671-683
    • Mavroforakis, M.1    Theodoridis, S.2
  • 12
    • 0034323731 scopus 로고    scopus 로고
    • Support vector machine techniques for nonlinear equalization
    • Nov.
    • D. J. Sebald and J. A. Bucklew, "Support vector machine techniques for nonlinear equalization," IEEE Trans. Signal Process., vol.48, no.11, pp. 3217-3226, Nov. 2000.
    • (2000) IEEE Trans. Signal Process. , vol.48 , Issue.11 , pp. 3217-3226
    • Sebald, D.J.1    Bucklew, J.A.2
  • 13
    • 0003238552 scopus 로고    scopus 로고
    • Incremental and decremental support vector machine learning
    • Cambridge, MA: MIT Press
    • G. Cauwenberghs and T. Poggio, "Incremental and decremental support vector machine learning," in Adv. Neural Information Processing Systems (NIPS). Cambridge, MA: MIT Press, 2000, vol.13, pp. 409-415.
    • (2000) Adv. Neural Information Processing Systems (NIPS) , vol.13 , pp. 409-415
    • Cauwenberghs, G.1    Poggio, T.2
  • 14
    • 33745777639 scopus 로고    scopus 로고
    • Incremental support vector learning: Analysis, implementation and applications
    • P. Laskov, C. Gehl, S. Krüger, and K.-R. Müller, "Incremental support vector learning: Analysis, implementation and applications," J. Mach. Learn. Res., vol.7, pp. 1909-1936, 2006.
    • (2006) J. Mach. Learn. Res. , vol.7 , pp. 1909-1936
    • Laskov, P.1    Gehl, C.2    Krüger, S.3    Müller, K.-R.4
  • 15
    • 4243078179 scopus 로고    scopus 로고
    • Adaptive projected subgradient method: A unified view for projection based adaptive algorithms
    • Aug. in Japanese
    • I. Yamada, "Adaptive projected subgradient method: A unified view for projection based adaptive algorithms," J. IEICE, vol.86, no.8, pp. 654-658, Aug. 2003, in Japanese.
    • (2003) J. IEICE , vol.86 , Issue.8 , pp. 654-658
    • Yamada, I.1
  • 16
    • 11144235357 scopus 로고    scopus 로고
    • Adaptive projected subgradient method for asymptotic minimization of sequence of nonnegative convex functions
    • I. Yamada and N. Ogura, "Adaptive projected subgradient method for asymptotic minimization of sequence of nonnegative convex functions," Numer. Funct. Anal. Optim., vol. 25, no. 7&8, pp. 593-617, 2004.
    • (2004) Numer. Funct. Anal. Optim. , vol.25 , Issue.7-8 , pp. 593-617
    • Yamada, I.1    Ogura, N.2
  • 17
    • 34547495662 scopus 로고    scopus 로고
    • The adaptive projected subgradient method over the fixed point set of strongly attracting nonexpansive mappings
    • K. Slavakis, I. Yamada, and N. Ogura, "The adaptive projected subgradient method over the fixed point set of strongly attracting nonexpansive mappings," Num. Funct. Anal. Optim., vol. 27, no. 7&8, pp. 905-930, 2006.
    • (2006) Num. Funct. Anal. Optim. , vol.27 , Issue.7-8 , pp. 905-930
    • Slavakis, K.1    Yamada, I.2    Ogura, N.3
  • 19
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • Sep.
    • H. H. Bauschke and J. M. Borwein, "On projection algorithms for solving convex feasibility problems," SIAM Rev., vol.38, no.3, pp. 367-426, Sep. 1996.
    • (1996) SIAM Rev. , vol.38 , Issue.3 , pp. 367-426
    • Bauschke, H.H.1    Borwein, J.M.2
  • 20
    • 0027541192 scopus 로고
    • The foundations of set theoretic estimation
    • P. L. Combettes, "The foundations of set theoretic estimation," Proc. IEEE, vol.81, no.2, pp. 182-208, 1993.
    • (1993) Proc. IEEE , vol.81 , Issue.2 , pp. 182-208
    • Combettes, P.L.1
  • 22
    • 85052721784 scopus 로고    scopus 로고
    • Radar and Imaging, B. Allen, M. Dohler, E. Okon, W. Malik, A. Brown, and D. Edwards, Eds. New York: Wiley
    • Ultra Wideband Antennas and Propagation for Communications, Radar and Imaging, B. Allen, M. Dohler, E. Okon, W. Malik, A. Brown, and D. Edwards, Eds. New York: Wiley, 2006.
    • (2006) Ultra Wideband Antennas and Propagation for Communications
  • 24
    • 34548252441 scopus 로고    scopus 로고
    • Robust wideband beamforming by the hybrid steepest descent method
    • Sep.
    • K. Slavakis and I. Yamada, "Robust wideband beamforming by the hybrid steepest descent method," IEEE Trans. Signal Process., vol.55, no.9, pp. 4511-4522, Sep. 2007.
    • (2007) IEEE Trans. Signal Process. , vol.55 , Issue.9 , pp. 4511-4522
    • Slavakis, K.1    Yamada, I.2
  • 25
    • 0037304809 scopus 로고    scopus 로고
    • Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem
    • Feb.
    • S. A. Vorobyov, A. B. Gershman, and Z.-Q. Luo, "Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem," IEEE Trans. Signal Process., vol.51, no.2, pp. 313-324, Feb. 2003.
    • (2003) IEEE Trans. Signal Process. , vol.51 , Issue.2 , pp. 313-324
    • Vorobyov, S.A.1    Gershman, A.B.2    Luo, Z.-Q.3
  • 26
    • 5844297152 scopus 로고
    • Theory of reproducing kernels
    • N. Aronszajn, "Theory of reproducing kernels," Trans. Amer. Math. Soc., vol.68, no.3, pp. 337-404, 1950.
    • (1950) Trans. Amer. Math. Soc. , vol.68 , Issue.3 , pp. 337-404
    • Aronszajn, N.1
  • 29
    • 70449553188 scopus 로고    scopus 로고
    • Signal processing in dual domain by Adaptive Projected Subgradient Method
    • Santorini, Greece, Jul. 5-7
    • M. Yukawa, K. Slavakis, and I. Yamada, "Signal processing in dual domain by Adaptive Projected Subgradient Method," in Proc. Int. Conf. Digital Signal Processing (DSP), Santorini, Greece, Jul. 5-7, 2009.
    • (2009) Proc. Int. Conf. Digital Signal Processing (DSP)
    • Yukawa, M.1    Slavakis, K.2    Yamada, I.3
  • 30
    • 0035351666 scopus 로고    scopus 로고
    • A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces
    • May
    • H. H. Bauschke and P. L. Combettes, "A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces," Math. Oper. Res., vol.26, no.2, pp. 248-264, May 2001.
    • (2001) Math. Oper. Res. , vol.26 , Issue.2 , pp. 248-264
    • Bauschke, H.H.1    Combettes, P.L.2
  • 31
    • 0001336448 scopus 로고
    • The method of successive projections for finding a common point of convex sets
    • L. M. Bregman, "The method of successive projections for finding a common point of convex sets," Soviet Math. Dokl., vol.6, pp. 688-692, 1965.
    • (1965) Soviet Math. Dokl. , vol.6 , pp. 688-692
    • Bregman, L.M.1
  • 32
    • 33845708830 scopus 로고
    • The method of projections for finding the common point of convex sets
    • L. G. Gubin, B. T. Polyak, and E. V. Raik, "The method of projections for finding the common point of convex sets," USSR Comput. Math. Phys., vol.7, pp. 1-24, 1967.
    • (1967) USSR Comput. Math. Phys. , vol.7 , pp. 1-24
    • Gubin, L.G.1    Polyak, B.T.2    Raik, E.V.3
  • 33
    • 0020191832 scopus 로고
    • Image restoration by the method of convex projections: Part 1-Theory
    • Oct.
    • D. C. Youla and H.Webb, "Image restoration by the method of convex projections: Part 1-Theory," IEEE Trans. Med. Imag., vol.MI-1, pp. 81-94, Oct. 1982.
    • (1982) IEEE Trans. Med. Imag. , vol.MI-1 , pp. 81-94
    • Youla, D.C.1    Webb, H.2
  • 34
    • 0021201713 scopus 로고
    • Decomposition through formalization in a product space
    • Jan.
    • G. Pierra, "Decomposition through formalization in a product space," Math. Program., vol.28, pp. 96-115, Jan. 1984.
    • (1984) Math. Program. , vol.28 , pp. 96-115
    • Pierra, G.1
  • 35
    • 0031118954 scopus 로고    scopus 로고
    • Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections
    • Apr.
    • P. L. Combettes, "Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections," IEEE Trans. Image Process., vol.6, no.4, pp. 493-506, Apr. 1997.
    • (1997) IEEE Trans. Image Process. , vol.6 , Issue.4 , pp. 493-506
    • Combettes, P.L.1
  • 39
    • 28544451131 scopus 로고    scopus 로고
    • The multiple sets split feasibility problem and its applications for inverse problems
    • Y. Censor, T. Elfving, N.Kopf, and T. Bortfeld, "The multiple sets split feasibility problem and its applications for inverse problems," Inverse Probl., vol.21, pp. 2071-2084, 2005.
    • (2005) Inverse Probl. , vol.21 , pp. 2071-2084
    • Censor, Y.1    Elfving, T.2    Kopf, N.3    Bortfeld, T.4
  • 40
    • 84918441630 scopus 로고
    • Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition
    • T. M. Cover, "Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition," IEEE Trans. Electron. Comput., vol.14, pp. 326-334, 1965.
    • (1965) IEEE Trans. Electron. Comput. , vol.14 , pp. 326-334
    • Cover, T.M.1
  • 42
    • 33846451627 scopus 로고
    • A learning method for system identification
    • J. Nagumo and J. Noda, "A learning method for system identification," IEEE Trans. Autom. Control, vol.12, no.3, pp. 282-287, 1967.
    • (1967) IEEE Trans. Autom. Control , vol.12 , Issue.3 , pp. 282-287
    • Nagumo, J.1    Noda, J.2
  • 44
    • 84985773174 scopus 로고
    • Extended theory of learning identification
    • in Japanese
    • T. Hinamoto and S. Maekawa, "Extended theory of learning identification," Trans. IEE Jpn., vol.95-C, no.10, pp. 227-234, 1975, in Japanese.
    • (1975) Trans. IEE Jpn. , vol.95 C , Issue.10 , pp. 227-234
    • Hinamoto, T.1    Maekawa, S.2
  • 45
    • 0000506677 scopus 로고
    • An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties
    • in Japanese
    • K. Ozeki and T. Umeda, "An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties," IEICE Trans., vol.67-A, no.5, pp. 126-132, 1984, in Japanese.
    • (1984) IEICE Trans. , vol.67 A , Issue.5 , pp. 126-132
    • Ozeki, K.1    Umeda, T.2
  • 46
    • 0036571426 scopus 로고    scopus 로고
    • An efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques
    • May
    • I. Yamada, K. Slavakis, and K. Yamada, "An efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques," IEEE Trans. Signal Process., vol.50, no.5, pp. 1091-1101, May 2002.
    • (2002) IEEE Trans. Signal Process. , vol.50 , Issue.5 , pp. 1091-1101
    • Yamada, I.1    Slavakis, K.2    Yamada, K.3
  • 47
    • 0015000439 scopus 로고
    • Some results on Tchebycheffian spline functions
    • G. S. Kimeldorf and G.Wahba, "Some results on Tchebycheffian spline functions," J. Math. Anal. Appl., vol.33, pp. 82-95, 1971.
    • (1971) J. Math. Anal. Appl. , vol.33 , pp. 82-95
    • Kimeldorf, G.S.1    Wahba, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.