The HOSVD Based Canonical Form of Functions and Its Applications

The paper deals with the theoretical background of the higher order singular value decomposition (HOSVD) based canonical form of functions. Furthermore in special case it describes the relation between the canonical form and the Hilbert-Schmidt type integral operators. The described techniques have a variety of applications, e.g. image processing, system identification, data compression, filtering, etc. As an example of application from the field of intelligent systems, a tensor-product based concept is introduced useful for approximating the behavior of a strongly non-linear system by locally tuned neural network models. The proposed approach may be a useful tool for solving many kind of black-box like identification problems. The weights in the corresponding layers of the input local models are jointly expressed in tensor-product form such a way ensuring the efficient approximation. Similar concept has been used by the authors for approximating the system matrix of linear parameter varying systems in state space representation. We hope that the proposed concept could be an efficient compromised modeling view using both the analytical and heuristic approaches.