Time Series Segmentation Using a Novel Adaptive Eigendecomposition Algorithm

In this paper we present a new technique for time series segmentation built around a fast principal component analysis (PCA) algorithm that is on-line and stable. The traditional Generalized Likelihood Ratio Test (GLRT) has been used to solve the segmentation problem, but this has enormous limitations in terms of complexity and speed. Newer methods use gated experts and mixture models to detect transitions in time series. These techniques perform better than GLRT, but most of them require extensive training of relatively large neural networks. The segmentation method discussed in this paper is based on a novel idea that involves solving the generalized eigendecomposition of two consecutive windowed time series and can be formulated as a two-step PCA. Thus, the performance of our segmentation technique mainly depends on the efficiency of the PCA algorithm. Most of the existing techniques for PCA are based on gradient search procedures that are slow and they also suffer from convergence problems. The PCA algorithm presented in this paper is both online, and is proven to converge faster than the current methods.

[1]  Kurt Hornik,et al.  Learning in linear neural networks: a survey , 1995, IEEE Trans. Neural Networks.

[2]  José Carlos Príncipe,et al.  Competitive principal component analysis for locally stationary time series , 1998, IEEE Trans. Signal Process..

[3]  Michael D. Zoltowski,et al.  Self-organizing algorithms for generalized eigen-decomposition , 1997, IEEE Trans. Neural Networks.

[4]  K. Abed-Meraim,et al.  Natural power method for fast subspace tracking , 1999, Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468).

[5]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[6]  Régine André-Obrecht,et al.  A new statistical approach for the automatic segmentation of continuous speech signals , 1988, IEEE Trans. Acoust. Speech Signal Process..

[7]  Irwin W. Sandberg.  Nonlinear dynamical systems : feedforward neural network perspectives , 2001 .

[8]  Bin Yang,et al.  Projection approximation subspace tracking , 1995, IEEE Trans. Signal Process..

[9]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

[10]  Harold J. Kushner,et al.  wchastic. approximation methods for constrained and unconstrained systems , 1978 .

[11]  Ashok N. Srivastava,et al.  Nonlinear gated experts for time series: discovering regimes and avoiding overfitting , 1995, Int. J. Neural Syst..

[12]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[13]  E. Oja.  Simplified neuron model as a principal component analyzer , 1982, Journal of mathematical biology.

[14]  Tamer Basar,et al.  Analysis of Recursive Stochastic Algorithms , 2001 .

[15]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[16]  Yingbo Hua,et al.  Fast subspace tracking and neural network learning by a novel information criterion , 1998, IEEE Trans. Signal Process..

[17]  Terence D. Sanger,et al.  Optimal unsupervised learning in a single-layer linear feedforward neural network , 1989, Neural Networks.

[18]  J. Príncipe,et al.  A fast, on-line algorithm for PCA and its convergence characteristics , 2000, Neural Networks for Signal Processing X. Proceedings of the 2000 IEEE Signal Processing Society Workshop (Cat. No.00TH8501).

[19]  Vwani P. Roychowdhury,et al.  Algorithms for accelerated convergence of adaptive PCA , 2000, IEEE Trans. Neural Networks Learn. Syst..

[20]  Anil K. Jain,et al.  Artificial neural networks for feature extraction and multivariate data projection , 1995, IEEE Trans. Neural Networks.

[21]  P. Regalia.  Adaptive IIR Filtering in Signal Processing and Control , 1994 .

[22]  José Carlos Príncipe,et al.  On the use of neural networks in the generalized likelihood ratio test for detecting abrupt changes in signals , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[23]  J. Príncipe,et al.  A fast on-line generalized eigendecomposition algorithm for time series segmentation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[24]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[25]  José Carlos Príncipe,et al.  Generalized eigendecomposition with an on-line local algorithm , 1998, IEEE Signal Processing Letters.

[26]  J. Rubner,et al.  A Self-Organizing Network for Principal-Component Analysis , 1989 .

[27]  Lei Xu,et al.  Least mean square error reconstruction principle for self-organizing neural-nets , 1993, Neural Networks.

[28]  S.Y. Kung,et al.  Adaptive Principal component EXtraction (APEX) and applications , 1994, IEEE Trans. Signal Process..

[29]  Jose C. Principe,et al.  Gated competitive systems for unsupervised segmentation and modeling of piecewise stationary signals , 1998 .

[30]  Bernie Mulgrew,et al.  IEEE Workshop on Neural Networks for Signal Processing , 1995 .