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In this paper, we present new self-organized networks to extract optimal features from multidimensional Gaussian data while preserving class separability. For this purpose, we introduce new adaptive algorithms for the computation of the square root of the inverse covariance matrix Sigma-1/2. Then we construct self-organized networks based on the proposed algorithms and use them for optimal feature extraction from Gaussian data. Convergence proof of the proposed algorithms and networks is given by introducing the related cost function and discussion about its properties. Adaptive nature of the new feature extraction method makes it appropriate for on-line pattern recognition applications. Experimental results using two-class multidimensional Gaussian data demonstrated the effectiveness of the new adaptive feature extraction method.