Joint Independent Subspace Analysis: A Quasi-Newton Algorithm

Dana Lahat 1 Christian Jutten 1
1 GIPSA-VIBS - VIBS
GIPSA-DIS - Département Images et Signal
Abstract : In this paper, we present a quasi-Newton (QN) algorithm for joint independent subspace analysis (JISA). JISA is a recently proposed generalization of independent vector analysis (IVA). JISA extends classical blind source separation (BSS) to jointly resolve several BSS problems by exploiting statistical dependence between latent sources across mixtures, as well as relaxing the assumption of statistical independence within each mixture. Algebraically, JISA based on second-order statistics amounts to coupled block diagonalization of a set of covariance and cross-covariance matrices, as well as block diagonalization of a single permuted covariance matrix. The proposed QN algorithm achieves asymptotically the minimal mean square error (MMSE) in the separation of multidimensional Gaussian components. Numerical experiments demonstrate convergence and source separation properties of the proposed algorithm.
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Dana Lahat, Christian Jutten. Joint Independent Subspace Analysis: A Quasi-Newton Algorithm. 12th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2015), Aug 2015, Liberec, Czech Republic. pp.111-118, ⟨10.1007/978-3-319-22482-4_13⟩. ⟨hal-01164651⟩

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