Methods for alignment of multi-class signal sets

• Published in: Signal processing Vol. 83; no. 5; pp. 983 - 1000
• Main Authors: Wahlberg, Patrik, Salomonsson, Göran
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-05-2003; Elsevier Science
• Subjects: Alignment; Applied sciences; Clustering; Detection, estimation, filtering, equalization, prediction; Electrical Engineering, Electronic Engineering, Information Engineering; Elektroteknik och elektronik; Engineering and Technology; Epileptic EEG spikes; Exact sciences and technology; Information, signal and communications theory; Multi-class signal sets; quotient; Rayleigh; Rayleigh quotient; Signal and communications theory; Signal, noise; Teknik; Telecommunications and information theory; Time jitter; Alignment; Rayleigh quotient; Epileptic EEG spikes; Time jitter; Clustering; Multi-class signal sets; Waveform; Estimation error; Averaging method; Automatic classification; Error estimation; Correlation matrix; Jitter; Electroencephalography; Mean value; Algorithm; Matched filter; Simulation
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/S0165-1684(02)00501-7

The paper treats jitter estimation for alignment of a set of signals which contains several unknown classes of waveforms. The motivating application is epileptic EEG spikes, where alignment prior to clustering and averaging is desired. The assumption that the signal waveforms are unknown precludes the use of classical techniques, notably matched filtering. Instead we treat two other classes of methods. In the first class the jitter of each signal is estimated with aid of the whole data set, using the Rayleigh quotient of the sample correlation matrix. The main idea of the paper is the suggestion of two such methods, consisting respectively of mean value computation and maximization of the Rayleigh quotient as a function of translation of a given signal. In the second class of methods each signal is processed individually, and one such method is estimation of the jitter of a signal by its centre of gravity. By means of deduction, simulations and evaluation on real life epileptic EEG signals, we show that the first class of methods is preferable to the second. Simulations also show that the method of maximization of the Rayleigh quotient seems to be a generally good method, which gives small estimation error and is applicable in a wide range of circumstances. For seven investigated sets of real life EEG data, the maximization algorithm turned out to give the best results, and improved alignment in the majority of signal clusters.