A framework for data representation, processing, and dimensionality reduction with the best-rank tensor decomposition

The paper addresses the problem of efficient multi-dimensional data representation, processing and dimensionality reduction. For this purpose the framework for the best rank-R tensor decomposition is presented. This allows any multi-dimensional data reduction in accordance with chosen ranks. Since computations of tensor decomposition require floating-point operations, we propose special data scaling procedure to allow memory efficient representation in the fixed-point representation. The proposed method is exemplified with processing of the monochrome and color video sequences. The method shows promising results and can be easily applied to other types of multidimensional data.