Adaptive linear discriminant analysis for online feature extraction

In this paper, we present new adaptive algorithms for the computation of the square root of the inverse covariance matrix. In contrast to the current similar methods, these new algorithms are obtained from an explicit cost function that is introduced for the first time. The new adaptive algorithms are used in a cascade form with a well-known adaptive principal component analysis to construct linear discriminant features. The adaptive nature and fast convergence rate of the new adaptive linear discriminant analysis algorithms make them appropriate for online pattern recognition applications. All adaptive algorithms discussed in this paper are trained simultaneously using a sequence of random data. Experimental results using the synthetic and real multiclass, multidimensional input data demonstrate the effectiveness of the new adaptive algorithms to extract the optimal features for the purpose of classification.