PARAFAC-Based Blind Identification of Underdetermined Mixtures Using Gaussian Mixture Model |
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Authors: | Fanglin Gu Hang Zhang Wenwu Wang Desheng Zhu |
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Affiliation: | 1. Institute of Communication Engineering, PLA University of Science & Technology, Nanjing, 210007, P.R. China 2. Department of Electronic Engineering, University of Surrey, Guildford, GU2 7XK, UK
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Abstract: | This paper presents a novel algorithm, named GMM-PARAFAC, for blind identification of underdetermined instantaneous linear mixtures. The GMM-PARAFAC algorithm uses Gaussian mixture model (GMM) to model non-Gaussianity of the independent sources. We show that the distribution of the observations can also be modeled by a GMM, and derive a maximum-likelihood function with regard to the mixing matrix by estimating the GMM parameters of the observations via the expectation-maximization algorithm. In order to reduce the computation complexity, the mixing matrix is estimated by maximizing a tight upper bound of the likelihood instead of the log-likelihood itself. The maximum of the tight upper bound is obtained by decomposition of a three-way tensor which is obtained by stacking the covariance matrices of the GMM of the observations. Simulation results validate the superiority of the GMM-PARAFAC algorithm. |
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