In the framework of the paper a HOSVD-based approach is introduced for LPV model reduction and multidimensional data representation. By these approaches in case of model reduction the system matrix is expressed with the help of a so called core tensor and a system of specially determined polylinear orthonormal functions. Similar approach will be applied also in case of data representation. The paper gives a detailed description on how to determine the polylinear functions and the core tensor and how the model can be expressed and reduced with their help. Furthermore, the HOSVD-based domain proposed for data representation will be compared to the well known frequency domain - related to Fourier transformation - from the point of view of their common application possibilities and their effectiveness.