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Network traffic matrix estimation is an ill-posed linear inverse problem: itrequires to estimate the unobservable origin destination traffic flows, X,given the observable link traffic flows, Y, and a binary routing matrix, A,which are such that Y = AX. This is a challenging but vital problem as accurateestimation of OD flows is required for several network management tasks. Inthis paper, we propose a novel model for the network traffic matrix estimationproblem which maps high-dimension OD flows to low-dimension latent flows withthe following three constraints: (1) nonnegativity constraint on the estimatedOD flows, (2) autoregression constraint that enables the proposed model toeffectively capture temporal patterns of the OD flows, and (3) orthogonalityconstraint that ensures the mapping between low-dimensional latent flows andthe corresponding link flows to be distance preserving. The parameters of theproposed model are estimated with a training algorithm based on Nesterovaccelerated gradient and generally shows fast convergence. We validate theproposed traffic flow estimation model on two real backbone IP networkdatasets, namely Internet2 and G'EANT. Empirical results show that the proposedmodel outperforms the state-of-the-art models not only in terms of tracking theindividual OD flows but also in terms of standard performance metrics. Theproposed model is also found to be highly scalable compared to the existingstate-of-the-art approaches.

Structured Nonnegative Matrix Factorization for Traffic Flow Estimation of Large Cloud Networks