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DTSTART;TZID=Europe/Paris:20181129T130000
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DTSTAMP:20260429T132031
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SUMMARY:Germain Van Bever (UNamur)
DESCRIPTION:Title: Symmetric Component Analysis and Functional Independent Component Analysis \nAbstract: With the increase in measurement precision\, functional data is becoming common practice. Relatively few techniques for analysing such data have been developed\, however\, and a first step often consists in reducing the dimension via Functional PCA\, which amounts to diagonalising the covariance operator. Joint diagonalisation of a pair of scatter functionals has proved useful in many different setups\, such has Independent Component Analysis (ICA)\, Invariant Coordinate Selection (ICS)\, etc.\nAfter an introduction to classical ICA techniques (and a look into several extensions of ICS)\, the main part of this talk will consist in extending the Fourth Order Blind Identification procedure to the case of data on a separable Hilbert space (with classical FDA setting being the go-to example). In the finite-dimensional setup\, this procedure provides a matrix Γ such that ΓX has independent components\, if one assumes that the random vector X satisfies X = ΨZ\, where Z has independent marginals and Ψ is an invertible mixing matrix. When dealing with distributions on Hilbert spaces\, two major problems arise: (i) the notion of marginals is not naturally defined and (ii) the covariance operator is\, in general\, non invertible. These limitations are tackled by reformulating the problem in a coordinate-free manner and by imposing natural restrictions on the mixing model.\nThe proposed procedure is shown to be Fisher consistent and affine invariant. A sample estimator is provided and its convergence rates are derived. The procedure is amply illustrated on simulated and real datasets.\nReferences\n[1] J.-F. Cardoso\, Source Separation Using Higher Moments Proceedings of IEEE international conference on acoustics\, speech and signal processing 2109-2112.\n[2] D. Tyler\, F. Critchley\, L. Dumbgen and H. Oja\, Invariant Co-ordinate Selection J. R. Statist. Soc. B.\, 2009\, 71\, 549–592.\n[3] J. Ramsay and B.W. Silverman Functional Data Analysis 2nd edn. Springer\, New York\, 2006.
URL:https://www.naxys.be/event/germain-van-bever-unamur/
LOCATION:E25
CATEGORIES:NAXYS Seminar
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