Abstract
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.
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Rao, Y.N., Principe, J.C. Time Series Segmentation Using a Novel Adaptive Eigendecomposition Algorithm. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 32, 7–17 (2002). https://doi.org/10.1023/A:1016355116053
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DOI: https://doi.org/10.1023/A:1016355116053