Proceedings of International Conference on Applied Innovation in IT
2020/03/10, Volume 8, Issue 1, pp.49-53

The Steepest Descent Method Using the Empirical Mode Gradient Decomposition


Vasiliy Esaulov, Roman Sinetsky


Abstract: The aim of the article is to study the possibility of improving gradient optimization methods. The leading approach to the chosen concept is based on the possibility of a featured description of the gradient that sets the direction of the search for a solution. A modification of the method of steepest descent of global optimization based on the Hilbert-Huang transform is proposed. The proposed solution is based on the decomposition of the gradient of the objective function into empirical modes. The main results of the work are iterative optimization methods, in which, in addition to the gradient, its empirical modes are also taken into account. New estimates of the descent step are obtained, which could not be deduced in the classical formulation of the steepest descent method. Their correctness is due to the fact that in the absence of the possibility of gradient decomposition, they are reduced to existing estimates for the steepest descent method. The theoretical significance of the results lies in the possibility of expanding the existing gradient methods by a previously not used gradient description method. The practical significance is that the proposed recommendations can help accelerate the convergence of gradient methods and improve the accuracy of their results. Using the Python language, computational experiments were carried out, as a result of which the adequacy of the proposed method and its robustness were confirmed.

Keywords: Steepest Descent Method, Gradient Descent Method, Empirical Mode Decomposition, Optimization Problem

DOI: 10.25673/32748

Download: PDF

References:

  1. A.A. Zhiglyavskii, A.G. Zhilinskas, “Metody poiskaglobal'nogo optimuma” [Methods of search of globaloptimum]. Moscow, Nauka Publ., 1991, p. 247.
  2. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H.Shih, Q. Zheng, N.-C. Yen, C.C. Tung and H.H Liu,“The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time seriesanalysis”, Proc. R. Soc. London Ser. A., vol. 454,1998, p. 903.
  3. N.E. Huang, Z. Shen and S.R. Long, “A new view ofnonlinear water waves”, the Hilbert spectrum, Annu.Rev. Fluid Mech, vol. 31, 1999, p. 417.
  4. N.E. Huang, “The Hilbert–Huang transform and itsapplications”, S.S.P. Shen. Singapore, WorldScientific, 2005.
  5. K.T. Coughlin and K.K. Tung, “11-year solar cyclein the stratosphere extracted by the empirical modedecomposition method”, Adv. Space Res., vol. 34,2004, p. 39.
  6. E.P.S. Neto, M.A. Custaud, C.J. Cejka, P. Abry, J.Frutoso, C. Gharib and P. Flandrin, “Assessment ofcardiovascular autonomic control by the empiricalmode decomposition”, Method. Inform. Med., vol.43, 2004, p. 60.
  7. Z. Wu and N.E. Huang, “A study of thecharacteristics of white noise using the empiricalmode decomposition method”, Proc. R. Soc. London,Ser. A., vol. 460, 2004, p. 1597.
  8. P.O. Pavlovichev and A.L. Priorov, “The empiricalmode decomposition for reduction in speech signals”, DSPA: Digital Signal Processing Issues, vol. 6, no. 2, 2016, pp. 398-403.
  9. A.K. Alimuradov, Y.S. Kvitka, A.P. Zaretskiy andA.P. Kuleshov, “Noiseproof processing of speechsignals based on the complementary ensembleemperical mode decomposition”, Proceedings ofMoscow Institute of Physics and Technology,vol. 3 (31), 2016, pp. 43-53.

    Home

    PARTICIPATION

       - Important Dates
       - Timetable of reports
       - Photos (ICAIIT 2020)
       - Committee
       - Proceedings


    PROCEEDINGS

       - Volume 8, Issue 1 (ICAIIT 2020)
       - Volume 7, Issue 1 (ICAIIT 2019)
       - Volume 6, Issue 1 (ICAIIT 2018)
       - Volume 5, Issue 1 (ICAIIT 2017)
       - Volume 4, Issue 1 (ICAIIT 2016)
       - Volume 3, Issue 1 (ICAIIT 2015)
       - Volume 2, Issue 1 (ICAIIT 2014)
       - Volume 1, Issue 1 (ICAIIT 2013)


    PAST CONFERENCES

       ICAIIT 2020
         - Photos
         - Reports

       ICAIIT 2019
         - Photos
         - Reports

       ICAIIT 2018
         - Photos
         - Reports

    ETHICS IN PUBLICATIONS

    ACCOMODATION

    CONTACT US

 


           ISSN 2199-8876
           Copyright © 2013-2020 Leonid Mylnikov. All rights reserved.