Skip to main content
Log in

Robust Physiological Mappings: From Non-Invasive to Invasive

Cybernetics and Systems Analysis Aims and scope

Cite this article


The goal of this paper is to highlight the challenges on the three methods of data analysis, namely: robust, component, and dynamical analysis with respect to the epilepsy. A forward and inverse mapping models for the human brain are presented. Research directions for obtaining robust inverse mapping and conducting dynamical analysis of the epileptic brain are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others


  1. J. Tukey, “The future of data analysis,” The Annals of Mathematical Statistics, 33, No. 1, 1–67 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Huber, Data Analysis: What Can be Learned from the Past 50 Years, Vol. 874, Wiley (2012).

  3. J. Tukey, “A survey of sampling from contaminated distributions,” Contributions to Probability and Statistics, Vol. 2, 448–485 (1960).

  4. S. Eddington, Stellar Movements and the Structure of the Universe, Macmillan and Co., Ltd. (1914).

    Google Scholar 

  5. R. Fisher et al., “A mathematical examination of the methods of determining the accuracy of an observation by the mean error, and by the mean square error,” Monthly Notices of the Royal Astronomical Society, 80, 758–770 (1920).

    Article  Google Scholar 

  6. P. Huber, Robust Statistical Procedures. No. 27, SIAM (1997).

  7. P. Huber, Robust Statistics, Wiley, New York (1981).

    Book  MATH  Google Scholar 

  8. F. Hampel, E. Ronchetti, P. Rousseeuw, and W. Stahel, Robust Statistics: The Approach Based on Influence Functions, Wiley, New York (2011).

    Google Scholar 

  9. M. Fischler and R. Bolles, “Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,” Communications of the ACM, 24, No. 6, 381–395 (1981).

    Article  MathSciNet  Google Scholar 

  10. S. Choi, T. Kim, and W. Yu, “Performance evaluation of RANSAC family,” in: Proc. British Machine Vision Conference, 81.1–81.12 (2009).

  11. O. Chum and J. Matas, “Optimal randomized ransac,” Pattern Analysis and Machine Intelligence, IEEE Trans., 30, No. 8, 1472–1482 (2008).

    Article  Google Scholar 

  12. H. Beyer and B. Sendho, “Robust optimization: A comprehensive survey,” Computer Methods in Applied Mechanics and Engineering, 196, No. 33, 3190–3218 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Ben-Tal, L. El Ghaoui, and A. Nemirovski, Robust Optimization, Princeton University Press (2009).

  14. P. Pardalos, J. Sackellares, P. Carney, and L. Iasemidis, Quantitative Neuroscience: Models, Algorithms, Diagnostics, and Therapeutic Applications, Series: Biocomputing, Vol. 2, Springer (2004).

  15. J. Holsheimer and B. Feenstra, “Volume conduction and EEG measurements within the brain: A quantitative approach to the influence of electrical spread on the linear relationship of activity measured at different locations,” Electroencephalography and Clinical Neurophysiology, 43, No. 1, 52–58 (1977).

    Article  Google Scholar 

  16. S. Makeig, A. Bell, T. Jung, T. Sejnowski, et al., “Independent component analysis of electroencephalographic data,” Advances in Neural Information Processing Systems, 145–151 (1996).

  17. B. Porat, A Course in Digital Signal Processing, Vol. 1, Wiley (1997).

  18. M. van Putten, J. Peters, S. Mulder, J. de Haas, C. Bruijninckx, and D. Tavy, “A brain symmetry index (BSI) for online EEG monitoring in carotid endarterectomy,” Clinical Neurophysiology, 115, No. 5, 1189–1194 (2004).

    Article  Google Scholar 

  19. M. van Putten, “Extended BSI for continuous EEG monitoring in carotid endarterectomy,” Clinical Neurophysiology, 117, No. 12, 2661–2666 (2006).

    Article  Google Scholar 

  20. M. van Putten, “The revised brain symmetry index,” Clinical Neurophysiology, 118, No. 11, 2362–2367 (2007).

    Article  Google Scholar 

  21. D. Stoffers, J. Bosboom, J. Deijen, E. Wolters, H. Berendse, and C. Stam, “Slowing of oscillatory brain activity is a stable characteristic of Parkinson’s disease without dementia,” Brain, 130, No. 7, 1847–1860 (2007).

    Article  Google Scholar 

  22. K. Lehnertz, F. Mormann, H. Osterhage, A. Müller, J. Prusseit, A. Chernihovskyi, M. Staniek, D. Krug, S. Bialonski, and C. Elger, “State-of-the-art of seizure prediction,” J. of Clinical Neurophysiology, 24, No. 2, 147–153 (2007).

    Article  Google Scholar 

  23. L. Iasemidis, “Epileptic seizure prediction and control,” IEEE Trans. on Biomedical Engineering, 50, No. 5, 549–558 (2003).

    Article  Google Scholar 

  24. L. Te-Won, Independent Component Analysis: Theory and Applications, Kluwer, Boston (1998).

    MATH  Google Scholar 

  25. A. Hyvärinen and E. Oja, “Independent component analysis: Algorithms and applications,” Neural Networks, 13, No. 4, 411–430 (2000).

    Article  Google Scholar 

  26. A. Cichocki, R. Zdunek, and S. Amari, “New algorithms for non-negative matrix factorization in applications to blind source separation,” in: Proc. 2006 IEEE Intern. Conf. on Acoustics, Speech, and Signal Processing (ICASSP 2006), Vol. 5, V-V, 621–624 (2006).

  27. W. Naanaa and J. Nuzillard, “Blind source separation of positive and partially correlated data,” Signal Processing, 85, No. 9, 1711–1722 (2005).

    Article  MATH  Google Scholar 

  28. P. Georgiev, P. Pardalos, and F. Theis, “A bilinear algorithm for sparse representations,” Computational Optimization and Applications, 38, No. 2, 249–259 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  29. P. Georgiev, F. Theis, and A. Cichocki, “Sparse component analysis and blind source separation of underdetermined mixtures,” IEEE Trans. on Neural Networks, 16, No. 4, 992–996 (2005).

    Article  Google Scholar 

  30. I. Daubechies, E. Roussos, S. Takerkart, M. Benharrosh, C. Golden, K. D’Ardenne, W. Richter, J. Cohen, and J. Haxby, “Independent component analysis for brain FMRI does not select for independence,” in: Proc. National Academy of Sciences, 106, No. 26, 10415–10422 (2009).

  31. S. Makeig, T.-P. Jung, D. Ghahremani, A. J. Bell, and T. J. Sejnowski, “What (not where) are the sources of the EEG?,” in: Proc. 18th Annual Meeting of The Cognitive Science Society (1996).

  32. P. G. Georgiev and F. J. Theis, Optimization techniques for data representations with biomedical applications, Series: Springer Optimization and Its Applications, Vol. 26, Ch. 8. Springer (2009).

  33. M. N. Syed, P. M. Pardalos, and J. C. Principe, “On the optimization of the correntropic loss function in data analysis,” Optimization Letters, 8, No. 3, 823–839 (2014).

    Article  MATH  MathSciNet  Google Scholar 

  34. T. Sauer, J. Yorke, and M. Casdagli, “Embedology,” J. of Statistical Physics, 65, No. 3, 579–616 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  35. M. Sznaier, O. Camps, N. Ozay, T. Ding, G. Tadmor, and D. Brooks, “The role of dynamics in extracting information sparsely encoded in high dimensional data streams,” Dynamics of Information Systems, 1–27 (2010).

  36. P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D: Nonlinear Phenomena, 9, No. 1, 189–208 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  37. H. Kantz, “A robust method to estimate the maximal Lyapunov exponent of a time series,” Physics Letters A, 185, No. 1, 77–87 (1994).

    Article  Google Scholar 

  38. A. Cohen and I. Procaccia, “Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems,” Physical Review A, 31, No. 3, 1872–1982 (1985).

    Article  MathSciNet  Google Scholar 

  39. L. Iasemidis, P. Pardalos, J. Sackellares, and D. Shiau, “Quadratic binary programming and dynamical system approach to determine the predictability of epileptic seizures,” J. of Combinatorial Optimization, 5, No. 1, 9–26 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  40. L. Iasemidis, D. Shiau, J. Sackellares, P. Pardalos, and A. Prasad, “Dynamical resetting of the human brain at epileptic seizures: Application of nonlinear dynamics and global optimization techniques,” IEEE Trans. on Biomedical Engineering, 51, No. 3, 493–506 (2004).

    Article  Google Scholar 

  41. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Vol. 12, Cambridge Univ. Press (2003).

  42. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. Doyne Farmer, “Testing for nonlinearity in time series: the method of surrogate data,” Physica D: Nonlinear Phenomena, 58, No. 1, 77–94 (1992).

    Article  MATH  Google Scholar 

  43. M. N. Syed, P. G. Georgiev, and P. M. Pardalos, “Seizure manifold of the epileptic brain: A state space reconstruction approach,” In: BIOMAT 2012 Intern. Symposium on Mathematical and Computational Biology (R. P. Mondaini, ed.), World Scientific, Aug. (2013), pp. 86–114.

  44. L. Iasemidis, D. Shiau, W. Chaovalitwongse, J. Sackellares, P. Pardalos, J. Principe, P. Carney, A. Prasad, B. Veeramani, and K. Tsakalis, “Adaptive epileptic seizure prediction system,” IEEE Trans. on Biomedical Engineering, 50, No. 5, 616–627 (2003).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to M. N. Syed.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2015, pp. 111–120.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Syed, M.N., Georgiev, P.G. & Pardalos, P.M. Robust Physiological Mappings: From Non-Invasive to Invasive. Cybern Syst Anal 51, 96–104 (2015).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: