Subspace Techniques and Biomedical Time Series Analysis

Abstract

The application of subspace techniques to univariate (single-sensor) biomedical time series is presented. Both linear and non-linear methods are described using algebraic models, and the dot product is the most important operation concerning data manipulations. The covariance/ correlationmatrices, computed in the space of time-delayed coordinates or in a feature space created by a non-linear mapping, are employed to deduce orthogonal models. Linear methods encompass singular spectrum analysis (SSA), singular value decomposition (SVD) or principal component analysis (PCA). Local SSA is a variant of SSA which can approximate non-linear trajectories of the embedded signal by introducing a clustering step. Generically non-linear methods encompass kernel principal component analysis (KPCA) and greedy KPCA. The latter is a variant where the subspace model is based on a selected subset of data only

Keywords: Kernel methods, projective subspace techniques, time series analysis.

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