On Revealing Replicating Structures in Multiway Data: A Novel Tensor Decomposition Approach

A novel tensor decomposition called pattern or P-decomposition is proposed to make it possible to identify replicating structures in complex data, such as textures and patterns in music spectrograms. In order to establish a computational framework for this paradigm, we adopt a multiway (tensor) approach. To this end, a novel tensor product is introduced, and the analysis of its properties shows a perfect match to the identification of recurrent data structures. Out of a whole class of possible algorithms, we illuminate those derived so as to cater for orthogonal and nonnegative patterns. Simulations on texture images and music sequence confirm the benefits of the proposed model and of the associated learning algorithms.