Towards a new multiway array decomposition algorithm: elementwise multiway array high dimensional model representation (EMAHDMR)

Authors:
Muzaffer Ayvaz;Metİn Demİralp
Affiliations:
İTU Informatics Institute, Computational Sci. and Eng. Program, İstanbul, Türkİye;İTU Informatics Institute, Computational Sci. and Eng. Program, İstanbul, Türkİye
Venue:
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
Year:
2011

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Abstract

In this study, very early steps of a new algorithm for multiway array decomposition via High Dimensional Model Representation (HDMR) is proposed. HDMR is originally developed for the multivariate functions and represents them as the sum of lower variate functions inluding the constant term, and thus HDMR is an inherent candidate for decomposing multiway arrays. The proposed algorithm represents given multiway array valued multivariate function as the sum of same type multiway array valued functions with lower multivariances starting from the constancy in ascending multivariance. This algorithm generalizes and unifies the recently proposed algorithms Vector HDMR and Matrix HDMR by Demiralp and his group and thus enlights the big picture of a new family of multiway array decomposition algorithms based on High Dimensional Model Representation.