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

A novel tensor 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 subsequent analysis of its properties shows a perfect match to the task of identification of recurrent structures present in the data. 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 a complex music sequence confirm the benefits of the proposed model and of the associated learning algorithms.