An Orthonormal Decomposition Method for Multidimensional Matrices
Metin Demіralp, Emre Demiralp, Theodore E. Simos, George Psihoyios, Ch. Tsitouras · AIP conference proceedings · 2009
The utilization of arrays with more than two indices which which are also called also multidimensional matrices has noticably increased in recent years. This brought the need for their decompositions to be used in practical applications. Especially signal processing, computer vision and neuroscience studies are relevant to this issue. This work aims at the construction of an orthogonal decomposition. It is formed by multidimensional outer products each of which is composed of a one and one less than the original input array type components. These components are obtained via a semi optimization type algorithm. Each outer product is constructed as a unit norm entity and its proportionality constant can be considered as an eigenvalue or a scalar measuring contribution. Certain illustrative numerical implementations are also reported.