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A review of second‐order blind identification methods

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Abstract Second‐order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high‐dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high‐dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second‐order statistics—hence the name “second‐order source separation.” In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed. This article is categorized under: Statistical Models > Time Series Models Statistical and Graphical Methods of Data Analysis > Dimension Reduction Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Schematic representation of the difference when stacking rows and columns respectively
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Electrocardiography latent source components using generalized second‐order blind identification (gSOBI) with w = 0.9, , and
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Electrocardiography latent source components using second‐order blind identification (SOBI) with
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Electrocardiography recordings of a pregnant women using eight sensors
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Schematic representation of an electrocardiography recording with two sensors for a pregnant women. BSS, blind source separation
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Representation of a time series of mode three tensors
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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical and Graphical Methods of Data Analysis > Dimensional Reduction
Statistical Models > Time Series Models

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