Short communicationAn overview of properties and extensions of FOBI
Section snippets
Independent component analysis
Independent component analysis (ICA) is a well-established multivariate method introduced in the mid-1980’s (for an account of its early history, see [1]). The first driving force of ICA was the computer science and signal processing community but in the recent years also statisticians have gotten more and more interested in ICA, i.e., deriving statistical properties of the existing ICA methods and suggesting new estimators. For some overviews, see for example [2], [3], [4].
The most basic model
Fourth order blind identification
The problem of finding the eigenvectors of can be written as , where is a diagonal matrix of eigenvalues in decreasing order and is the so-called matrix of fourth moments (note that in some references is divided by to make it consistent for at the multivariate normal model). can be seen as a member of the class of functionals of the form , where and
Conclusion
Recently [5] rediscovered FOBI, a well-known ICA estimator with many nice properties established mainly in the statistics literature in the previous years. Despite being quite inefficient when compared to other ICA methods, the simplicity, ease of computation and numerous useful properties (both outside and inside the IC model) of FOBI help explain its persisting popularity. These aspects also make FOBI the perfect method for generalizing ICA to complex non-standard data structures, as the many
Acknowledgment
The work of KN was partly supported by CRoNoS COST Action (Austria) IC1408.
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