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Dynamic tensor time series modeling and analysis

In this paper we propose a model reduction and identification approach for multilinear dynamical system (MLDS) driven by noise. Compared to standard linear dynamical system based approaches which fit vector or matrix models to tensor time series, MLDS provides more natural, compact and accurate representation of tensorial data with fewer model parameters. The proposed algorithm for identifying MLDS parameters employs techniques from multilinear subspace learning: mulilinear Principal Component Analysis and multilinear regression. In addition compact array normal distribution is used to represent and estimate model error and output noise.We illustrate the benefits of the proposed approach on some real world datasets.