Towards Nonstationary, Nonparametric Independent Process Analysis with Unknown Source Component Dimensions

The goal of this paper is to extend independent subspace analysis (ISA) to the case of (i) nonparametric, not strictly stationary source dynamics and (ii) unknown source component dimensions. We make use of functional autoregressive (fAR) processes to model the temporal evolution of the hidden sources. An extension of the ISA separation principle--which states that the ISA problem can be solved by traditional independent component analysis (ICA) and clustering of the ICA elements--is derived for the solution of the defined fAR independent process analysis task (fAR-IPA): applying fAR identification we reduce the problem to ISA. A local averaging approach, the Nadaraya-Watson kernel regression technique is adapted to obtain strongly consistent fAR estimation. We extend the Amari-index to different dimensional components and illustrate the efficiency of the fAR-IPA approach by numerical examples.

[1]  John Odenckantz,et al.  Nonparametric Statistics for Stochastic Processes: Estimation and Prediction , 2000, Technometrics.

[2]  N. Hilgert,et al.  Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models , 2009, 0905.2327.

[3]  Fabian J. Theis,et al.  Towards a general independent subspace analysis , 2006, NIPS.

[4]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[5]  Jean-François Cardoso,et al.  Multidimensional independent component analysis , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[6]  Jianbo Shi,et al.  Multiclass spectral clustering , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[7]  Zoltán Szabó,et al.  Separation Principles in Independent Process Analysis , 2009 .

[8]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[9]  Barnabás Póczos,et al.  Independent Subspace Analysis on Innovations , 2005, ECML.

[10]  Michael I. Jordan,et al.  Kernel independent component analysis , 2003 .

[11]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[12]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[13]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[14]  Pierre Comon.  Independent component analysis - a new concept? signal processing , 1994 .

[15]  Jörn Anemüller,et al.  Second-Order Separation of Multidimensional Sources with Constrained Mixing System , 2006, ICA.

[16]  Fabian J. Theis,et al.  Blind signal separation into groups of dependent signals using joint block diagonalization , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[17]  Barnabás Póczos,et al.  Undercomplete Blind Subspace Deconvolution , 2007, J. Mach. Learn. Res..