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Stationary subspace analysis : ウィキペディア英語版
Stationary subspace analysis

Stationary Subspace Analysis (SSA)〔
von Bünau P, Meinecke F C, Király F J, Müller K-R (2009). (Finding Stationary Subspaces in Multivariate Time Series ) ''Phys. Rev. Letter'' 103, 214101.
〕 is a blind source separation algorithm which factorizes a multivariate time series into stationary and non-stationary components.
== Introduction ==

In many settings, the measured time series contains contributions from various underlying sources that cannot be measured directly. For instance, in EEG analysis, the electrodes on the scalp record the activity of a large number of sources located inside the brain.〔Niedermeyer E, da Silva F L. Electroencephalography: Basic Principles, Clinical Applications, and Related Fields. Lippincott Williams & Wilkins, 2004. ISBN 0-7817-5126-8〕 These sources can be stationary or non-stationary, but they are not discernible in the electrode signals, which are a mixture of these sources. SSA allows the separation of the stationary from the non-stationary sources in an observed time series.
According to the SSA model,〔 the observed multivariate time series x(t) is assumed to be generated as a linear superposition of stationary sources s^\mathfrak(t) and non-stationary sources s^\mathfrak(t),
:
x(t) = A s(t) = \begin A^\mathfrak & A^\mathfrak \end \begin s^\mathfrak(t) \\ s^\mathfrak(t) \\ \end,

where A is an unknown but time-constant mixing matrix; A^\mathfrak and A^\mathfrak are the basis of the stationary and non-stationary subspace respectively.
Given samples from the time series x(t), the aim of Stationary Subspace Analysis is to estimate the inverse mixing matrix A^ separating the stationary from non-stationary sources in the mixture x(t).

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