Séparation de sources. Principes et algorithmes - Gretsi

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Définition Problème ACI Indépendance Décomposition de l’IM à l’aide d’entropie I (Y) = . . . pY(u) log pY(u) du (12) ΠpYi (ui) = H(Yi) − H(Y) (13) i avec les définitions suivantes des entropies marginales et jointes H(Yi) = pYi (ui) log pYi (ui)dui (14) H(Y) = . . . pY(u) log pY(u)du (15) Problème L’estimation des entropies, jointe et marginales, nécessite l’estimation des densités, jointe et marginales, resp. P.Comon & C.Jutten, Peyresq July 2011 BSS I.Le problème et les principes de résolution 30
Problème ACI Indépendance Une astuce dans le cas linéaire Dans le cas déterminé, avec une matrice de mélange A inversible, on a : L’astuce I (Y) = H(Yi) − H(Y) (16) i = H(Yi) − H(X) − E[log | det B |] (17) i Conséquence minB i H(Yi) − H(Y) ⇔ minB i H(Yi) − log | det B | L’astuce évite l’estimation de l’entropie jointe ! P.Comon & C.Jutten, Peyresq July 2011 BSS I.Le problème et les principes de résolution 31
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Page 17 and 18: Modèle de mélange Problème ACI I
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Page 29: Définition Problème ACI Indépend
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Page 39 and 40: Algebraic tools Statistical tools C
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Algebraic tools Statistical tools C
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Principle Algebraic tools Statistic
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Introduction Colored Nonstationary
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Intro Dim2 Orthogonal Deflation Dis
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Invertible Iterative SemiAlg ConclR
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Intro Inversibility Time Frequ VI.
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Intro Inversibility Time Frequ Nota
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Global filter Intro Inversibility T
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Intro Inversibility Time Frequ Cont
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Interest Intro Inversibility Time F
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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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Fourier domain ? Intro Inversibilit
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Intro Inversibility Time Frequ Intr
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Identifiability ICA for NL Discussi
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Undeterminacy Identifiability ICA f
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Comments Identifiability ICA for NL
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Theorem Identifiability ICA for NL
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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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Example [CR06] Problem Algorithms B
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Problem Algorithms Biblio SCA Spars
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Problem Algorithms Biblio SCA Solvi
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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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Introduction NMF NTF NN ICA Algorit
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Newton-like method Introduction NMF
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Noisy mixtures Introduction NMF NTF
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Introduction NMF NTF NonNegative Te
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Intro Determ Mars Cum Chemical Show
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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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