Abstract
Complexity pursuit is an extension of projection pursuit to time series data and the method is closely related to blind separation of time-dependent source signals and independent component analysis. The goal is to find projections of time series that have interesting structure, defined using criteria related to Kolmogoroff complexity or coding length. In this paper, we first derive a simple approximation of coding length for unifying model that takes into account nongaussianity of sources, their autocorrelations and their smoothly changing nonstationary variances. Next, a fixed-point algorithm is proposed by using approximate Newton method. Finally, simulations verify the fixed-point algorithm converges faster than the existing gradient algorithm and it is more simple to implement due to it does not need any learning rate.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Common P (1994) Independent component analysis—a new concept?. Signal Process 36: 287–314
Hyvärinen A, Karhunen J, Oja E (2001) Independent component analysis. Wiley, New York
Matsuoka K, Ohya M, Kawamoto M (1995) A neural net for blind separation of nonstationary signals. Neural Netw 8(3): 411–419
Pham D-T, Cardoso J-F (2001) Blind separation of instantaneous mixtures of non stationary sources. IEEE Trans Signal Process 49(9): 1837–1848
Hyvärinen A (2001) Blind source separation by nonstationary of variance: a cumulant-based approach. IEEE Trans Neural Netw 12(6): 1471–1474
Tong L, Liu R-W, Soon VC, Huang Y-F (1991) Indeterminacy and identifiability of blind identification. IEEE Trans Circuit Syst 38: 499–509
Molgedey L, Schuster HG (1994) Separation of a mixture of independent signals using time delayed correlations. Phys Rev Lett 72: 3634–3636
Belouchrani A, Abed Meraim K, Cardoso J-F, Moulines E (1997) A blind source separation technique based on second order statistics. IEEE Trans Signal Process 45(2): 434–444
Pham D-T (2001) Blind separation of instantaneous mixtures of sources via the Gaussian mutual information criterion. Signal Process 81: 855–870
Hyvärinen A (2005) A unifying model for blind separation of independent sources. Signal Process 85: 1419–1427
Pajunen P (1998) Blind source separation using algorithmic information theory. Neurocomputing 22: 35–48
Hyvärinen A (2001) Complexity pursuit: separating interesting components from time-series. Neural Comput 13(4): 883–898
Jutten C, Hérault J (1991) Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture. Signal Process 24: 1–10
Cover TM, Thomas JA (1991) Elements of information theory. Wiley, New York
Hyvärinen A (1999) Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans Neural Netw 10(3): 626–634
Hyvärinen A, Oja E (1997) A fast fixed-point algorithm for independent component analysis. Neural Comput 9(7): 1483–1492
Nocedal J, Wright SJ (1999) Numerical optimization. Springer, Berlin
Amari S-I, Cichocki A, Yang H (1996) A new learning algorithm for blind source separation. In: Advances in neural information processing system, vol 8. MIT Press, Cambridge, pp 757–763
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, Y. Complexity Pursuit for Unifying Model. Neural Process Lett 31, 17–24 (2010). https://doi.org/10.1007/s11063-009-9124-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-009-9124-2