A fast and stable neural network algorithm for principal singular triplet (PST) extraction is proposed to perform the online singular value decomposition (SVD) of the cross-covariance matrix of two high-dimensional data streams. A novel information criterion is firstly proposed and then based on which a dynamical system is derived. Thereafter, an online fast and stable neural network algorithm is developed from the dynamical system. The proposed algorithm can extract the left and right principal singular vectors of the cross-covariance matrix of two high-dimensional data streams. Moreover, the length of each singular vector will converge to a value that is correlated to the corresponding principal singular value. Therefore the singular value can also be estimated from the length of the singular vector. Compared with the conventional algorithms, the proposed algorithm can extract the PST of the cross-covariance matrix, but not only the singular vectors. Furthermore, the proposed algorithm is low in computation complexity, high in convergence speed and good in stability.
