Séparation de sources. Principes et algorithmes - Gretsi

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Algebraic tools Statistical tools Criteria 4 Algebraic tools Spatial whitening Tensors 5 Statistical tools Independence Cumulants Mutual Information 6 Optimization Criteria Cumulant matching Contrasts Contents of course II P.Comon & C.Jutten, Peyresq July 2011 BSS II.Tools and optimization criteria 40
Algebraic tools Statistical tools Criteria Spatial whitening Tensors Spatial whitening (1) Standardization via Cholesky or QR Let x be a zero-mean r.v. with covariance matrix: Then Cholesky yields: Γx def = E{x x H } ∃L / L L H = Γx Consequence: L −1 x has a unit variance. Variable ˜x def = L −1 x is a standardized random variable. QR factorization of data matrix as X = L ˜X yields same L as Cholesky factorization of sample covariance, but more accurate. Limitation: L may not be invertible if the covariance Γx is not full rank. P.Comon & C.Jutten, Peyresq July 2011 BSS II.Tools and optimization criteria 41
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Principle Algebraic tools Statistic
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Introduction Colored Nonstationary
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Kronecker notation Intro Inversibil
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⎛ ⎜ ⎝ Intro Inversibility Tim
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Source separation Intro Inversibili
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Identifiability Identifiability ICA
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Problem Algorithms Biblio SCA Conte
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Problem Algorithms Biblio SCA nCF I
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Problem Algorithms Biblio SCA Dim.2
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Lemma Problem Algorithms Biblio SCA
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32 Introduction Titre sous-section
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Introduction NMF NTF Titre sous-sec
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Introduction NMF NTF NN ICA Algorit
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Bibliography XI. Bibliography I II
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[BCMT10] J. Brachat, P. Comon, B. M
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[Com95] P. Comon. Supervised classi
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[F´88] L. Féty. Méthodes de trai
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[LISC11] R. Llinares, J. Igual, A.
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[PAB + 02] M. Plumbley, S.A. Abdall
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[TF07] T. Tanaka and S. Fiori. Leas
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Séparation de sources. Principes et algorithmes - Gretsi

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