How to Apply Nonlinear Subspace Techniques to Univariate Biomedical Time Series

• Published in: IEEE transactions on instrumentation and measurement Vol. 58; no. 8; pp. 2433 - 2443
• Main Authors: Teixeira, A.R., Tome, A.M., Bohm, M., Puntonet, C.G., Lang, E.W.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Channels; Covariance matrix; Electroencephalogram (EEG); Electroencephalography; electrooculogram (EOG); Electrooculograms; Electrooculography; Geophysics computing; Instrumentation; Kernel; kernel principal component analysis (KPCA); local singular spectrum analysis (SSA); Mathematical analysis; Multidimensional systems; Nonlinearity; Principal component analysis; removing artifacts; Signal analysis; Signal processing; subspace techniques; Subspaces; Time series; Transformations
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2009.2016385

In this paper, we propose an embedding technique for univariate single-channel biomedical signals to apply projective subspace techniques. Biomedical signals are often recorded as 1-D time series; hence, they need to be transformed to multidimensional signal vectors for subspace techniques to be applicable. The transformation can be achieved by embedding an observed signal in its delayed coordinates. We propose the application of two nonlinear subspace techniques to embedded multidimensional signals and discuss their relation. The techniques consist of modified versions of singular-spectrum analysis (SSA) and kernel principal component analysis (KPCA). For illustrative purposes, both nonlinear subspace projection techniques are applied to an electroencephalogram (EEG) signal recorded in the frontal channel to extract its dominant electrooculogram (EOG) interference. Furthermore, to evaluate the performance of the algorithms, an experimental study with artificially mixed signals is presented and discussed.