Decomposition of Neurological Multivariate Time Series by State Space Modelling

Bulletin of Mathematical Biology

Volumn 73, Issue 2, 2011, Pages 285-324

  Galka, Andreas ^a   Wong, Kin Foon Kevin ^b   Ozaki, Tohru ^c   Muhle, Hiltrud ^a   Stephani, Ulrich ^a   Siniatchkin, Michael ^a  

^a UNIVERSITY OF KIEL   (Germany)

^b MASSACHUSETTS GENERAL HOSPITAL   (United States)

^c TOHOKU UNIVERSITY   (Japan)

Author keywords

Artifact removal; EEG FMRI fusion; Electroencephalogram; Independent Component Analysis; Kalman filtering; Time series analysis

Indexed keywords

ADULT; ALGORITHM; ARTICLE; ARTIFACT; CHILD; ELECTROCARDIOGRAPHY; ELECTROENCEPHALOGRAPHY; FACTORIAL ANALYSIS; FEMALE; FETUS; HUMAN; MALE; METHODOLOGY; NONLINEAR SYSTEM; NUCLEAR MAGNETIC RESONANCE IMAGING; PATHOPHYSIOLOGY; PHYSIOLOGY; PREGNANCY; PRINCIPAL COMPONENT ANALYSIS; REGRESSION ANALYSIS; ROLANDIC EPILEPSY; SIGNAL PROCESSING; STATISTICAL MODEL;

ADULT; ALGORITHMS; ARTIFACTS; CHILD; ELECTROCARDIOGRAPHY; ELECTROENCEPHALOGRAPHY; EPILEPSY, ROLANDIC; FACTOR ANALYSIS, STATISTICAL; FEMALE; FETUS; HUMANS; LEAST-SQUARES ANALYSIS; LIKELIHOOD FUNCTIONS; LINEAR MODELS; MAGNETIC RESONANCE IMAGING; MALE; MODELS, STATISTICAL; NONLINEAR DYNAMICS; PREGNANCY; PRINCIPAL COMPONENT ANALYSIS; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 79952102685     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-010-9563-y     Document Type: Article

References (70)

1. Aït-Sahalia, Y., & Kimmel, R. (2007). Maximum likelihood estimation of stochastic volatility models. J. Financ. Econ., 83, 413-452.
2. Akaike, H. (1974a). Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes. Ann. Inst. Stat. Math., 26, 363-387.
3. Akaike, H. (1974b). A new look at the statistical model identification. IEEE Trans. Autom. Control, 19, 716-723.
4. Akaike, H., & Nakagawa, T. (1988). Statistical analysis and control of dynamic systems. Dordrecht: Kluwer Academic.
5. Allen, P. J., Josephs, O., & Turner, R. (2000). A method for removing imaging artifact from continuous EEG recorded during functional MRI. NeuroImage, 12, 230-239.
6. Åström, K. J. (1980). Maximum likelihood and prediction error methods. Automatica, 16, 551-574.
7. Attias, H., & Schreiner, C. E. (1998). Blind source separation and deconvolution: the dynamic component analysis algorithm. Neural Comput., 10, 1373-1424.
8. Baldick, R. (Ed.) (2006). Applied optimization: formulation and algorithms for engineering systems. Cambridge: Cambridge University Press.
9. Bar-Shalom, Y., & Fortmann, T. (1988). Tracking and data association. San Diego: Academic Press.
10. Barros, A. K., & Cichocki, A. (2001). Extraction of specific signals with temporal structure. Neural Comput., 13, 1995-2000.
11. Basilevsky, A. (1994). Statistical factor analysis and related methods: theory and applications. New York: Wiley-Interscience.
12. Beckmann, C., & Smith, S. (2004). Probabilistic independent component analysis for functional magnetic resonance imaging. IEEE Trans. Med. Imaging, 23, 137-152.
13. Beckmann, C., & Smith, S. (2005). Tensorial extensions of independent component analysis for multisubject FMRI analysis. NeuroImage, 25, 294-311.
14. Belouchrani, A., Abed-Meraim, K., Cardoso, J.-F., & Moulines, E. (1997). A blind source separation technique using second order statistics. IEEE Trans. Signal Process., 45, 434-444.
15. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Econom., 31, 307-327.
16. Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis, forecasting and control. San Francisco: Holden-Day.
17. Brockwell, P. J., & Davis, R. A. (1987). Time series: theory and methods. Berlin: Springer.
18. Cheung, Y. M., & Xu, L. (2003). Dual multivariate auto-regressive modeling in state space for temporal signal separation. IEEE Trans. Syst. Man Cybern., 33, 386-398.
19. Choi, S., Cichocki, A., Park, H., & Lee, S. (2005). Blind source separation and independent component analysis: a review. Neural Inf. Process. Lett. Rev., 6, 1-57.
20. Chui, C. K., & Chen, G. (1999). Springer series in information sciences: Vol. 17. Kalman filtering: with real-time applications (3rd ed.). Berlin: Springer.
21. Cichocki, A., & Amari, S. (2002). Adaptive blind signal and image processing. Chichester: Wiley.
22. Comon, P. (1994). Independent component analysis, a new concept? Signal Process., 36, 287-314.
23. Delorme, A., Sejnowski, T., & Makeig, S. (2007). Enhanced detection of artifacts in EEG data using higher-order statistics and independent component analysis. NeuroImage, 34, 1443-1449.
24. Durbin, J., & Koopman, S. J. (2001). Time series analysis by state space methods. Oxford: Oxford University Press.
25. Dyrholm, M., Makeig, S., & Hansen, L. K. (2007). Model selection for convolutive ICA with an application to spatiotemporal analysis of EEG. Neural Comput., 19, 934-955.
26. Engle, R. F., & Watson, M. (1981). A one-factor multivariate time series model of metropolitan wage rates. J. Am. Stat. Assoc., 76, 774-781.
27. Galka, A., Yamashita, O., & Ozaki, T. (2004). GARCH modelling of covariance in dynamical estimation of inverse solutions. Phys. Lett. A, 333, 261-268.
28. Galka, A., Ozaki, T., Bosch-Bayard, J., & Yamashita, O. (2006). Whitening as a tool for estimating mutual information in spatiotemporal data sets. J. Stat. Phys., 124, 1275-1315.
29. Galka, A., Wong, K., & Ozaki, T. (2010). Generalized state space models for modeling non-stationary EEG time series. In A. Steyn-Ross & M. Steyn-Ross (Eds.), Springer series in computational neuroscience. Modeling phase transitions in the brain (pp. 27-52). Berlin: Springer.
30. Gevers, M. (2006). A personal view of the development of system identification. IEEE Control Syst. Mag., 26, 93-105.
31. Gnedenko, B. V. (1969). The theory of probability. Moscow: Mir Publishers.
32. Grewal, M. S., & Andrews, A. P. (2001). Kalman filtering: theory and practice using MATLAB. New York: Wiley-Interscience.
33. Harman, H. H. (1976). Modern factor analysis (3rd ed.). Chicago: University of Chicago Press.
34. Harvey, A., Koopman, S. J., & Shephard, N. (Eds.) (2004). State space and unobserved component models. Cambridge: Cambridge University Press.
35. Hyvärinen, A. (1999). Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. Neural Netw., 10, 626-634.
36. Hyvärinen, A., Karhunen, J., & Oja, E. (2001). Independent component analysis. New York: Wiley.
37. James, C., & Hesse, C. (2005). Independent component analysis for biomedical signals. Physiol. Meas., 26, R15-R39.
38. Jung, A., & Kaiser, A. (2003). Considering temporal structures in independent component analysis. In: Proc. 4th int. symp. ICA BSS, ICA 2003 (pp. 95-100). Nara, Japan, Apr. 2003.
39. Jung, T.-P., Makeig, S., McKeown, M., Bell, A., Lee, T.-W., & Sejnowski, T. (2001). Imaging brain dynamics using independent component analysis. IEEE Proc., 88, 1107-1122.
40. Kailath, T. (1968). An innovations approach to least-squares estimation-Part I: linear filtering in additive white noise. IEEE Trans. Autom. Control, 13, 646-655.
41. Kailath, T. (1980). Information and system sciences series. Linear systems. Englewood Cliffs: Prentice-Hall.
42. Kallenberg, O. (2002). Foundations of modern probability. Berlin: Springer.
43. Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. J. Basic Eng., 82, 35-45.
44. Kalman, R. E., Falb, P. L., & Arbib, M. A. (1969). International series in pure and applied mathematics. Topics in mathematical system theory. New York: McGraw-Hill.
45. Ljung, L. (1999). System identification: theory for the user (2nd ed.). Englewood Cliffs: Prentice-Hall.
46. Mehra, R. K. (1971). Identification of stochastic linear systems using Kalman filter representation. AIAA J., 9, 28-31.
47. Mehra, R. K. (1974). Identification in control and econometrics: similarities and differences. Ann. Econ. Soc. Meas., 3, 21-47.
48. Meinecke, F., Ziehe, A., Kawanabe, M., & Müller, K.-R. (2002). A resampling approach to estimate the stability of one- or multidimensional independent components. IEEE Trans. Biomed. Eng., 49, 1514-1525.
49. Miwakeichi, F., Martínez-Montes, E., Valdés-Sosa, P., Nishiyama, N., Mizuhara, H., & Yamaguchi, Y. (2004). Decomposing EEG data into space-time-frequency components using parallel factor analysis. NeuroImage, 22, 1035-1045.
50. Molenaar, P. C. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50, 181-202.
51. Molgedey, L., & Schuster, H. G. (1994). Separation of a mixture of independent signals using time delayed correlations. Phys. Rev. Lett., 72, 3634-3637.
52. Negishi, M., Abildgaard, M., Nixon, T., & Constable, R. (2004). Removal of time-varying gradient artifacts from EEG data acquired during continuous fMRI. Clin. Neurophysiol., 115, 2181-2192.
53. Neumaier, A., & Schneider, T. (2001). Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans. Math. Softw., 27, 27-57.
54. Niazy, R., Beckmann, C., Iannetti, D., Brady, J., & Smith, S. (2005). Removal of FMRI environment artifacts from EEG data using optimal basis sets. NeuroImage, 28, 720-737.
55. Otter, P. (1986). Dynamic structural systems under indirect observation: identifiability and estimation aspects from a system theoretic perspective. Psychometrika, 51, 415-428.
56. Ozaki, T., & Iino, M. (2001). An innovation approach to non-Gaussian time series analysis. J. Appl. Probab., 38, 78-92.
57. Pagan, A. R. (1975). A note on the extraction of components from time series. Econometrica, 43, 163-168.
58. Pearlmutter, B. A., & Parra, L. C. (1997). Maximum likelihood blind source separation: a context-sensitive generalization of ICA. In M. C. Mozer, M. I. Jordan & T. Petsche (Eds.), Advances in neural information processing systems (Vol. 9, pp. 613-619). Cambridge: MIT Press.
59. Protter, P. (1990). Stochastic integration and differential equations. Berlin: Springer.
60. Rauch, H. E., Tung, G., & Striebel, C. T. (1965). Maximum likelihood estimates of linear dynamic systems. AIAA J., 3, 1445-1450.
61. Schwarz, G. (1978). Estimating the dimension of a model. Ann. Stat., 6, 461-464.
62. Schweppe, F. (1965). Evaluation of likelihood functions for Gaussian signals. IEEE Trans. Inf. Theory, 11, 61-70.
63. Sorenson, H. W. (1970). Least-squares estimation: from Gauss to Kalman. IEEE Spectr., 7, 63-68.
64. Stögbauer, H., Kraskov, A., Astakhov, S. A., & Grassberger, P. (2004). Least-dependent-component analysis based on mutual information. Phys. Rev. E, 70, 066123.
65. Tong, L., Liu, R., Soon, V. C., & Huang, Y. (1991). Indeterminacy and identifiability of blind separation. IEEE Trans. Circuits Syst., 38, 499-509.
66. Vigário, R., Sarela, J., Jousmiki, V., Hamalainen, M., & Oja, E. (2000). Independent component approach to the analysis of EEG and MEG recordings. IEEE Trans. Biomed. Eng., 47, 589-593.
67. Waheed, K., & Salem, F. M. (2005). Linear state space feedforward and feedback structures for blind source recovery in dynamic environments. Neural Process. Lett., 22, 325-344.
68. Wong, K. F. K., Galka, A., Yamashita, O., & Ozaki, T. (2006). Modelling non-stationary variance in EEG time series by state space GARCH model. Comput. Biol. Med., 36, 1327-1335.
69. Zhang, L., & Cichocki, A. (2000). Blind deconvolution of dynamical systems: a state space approach. J. Signal Process., 4, 111-130.
70. Ziehe, A., & Müller, K.-R. (1998). TDSEP-an efficient algorithm for blind separation using time structure. In L. Niklasson, M. Bodén & T. Ziemke (Eds.), Proc. 8th int. conf. artificial neural networks, ICANN'98 (pp. 675-680). Berlin: Springer.