Reductive enhanced multivariance product representation for multi-way arrays

Abstract

The main purpose of this work is to develop a new multi-way decomposition technique by considering statistical structure of target multi-way array. To this end enhanced multivariance products representation (EMPR), which is an expansion extended from high dimensional model representation (HDMR), is used. EMPR provides quite successful results on representation and approximation of multivariate functions when they have high level multiplicativity. Hence this urges us to reconstruct EMPR as a multi-way array decomposer. This paper presents this decomposition technique with all reconstruction formulations and numerical experiments on synthetic and real-life data sets to denote EMPR's efficiency as a decomposer and also presents a combined method Reductive-EMPR (R-EMPR) as a multi-way array decomposition technique.

Block tridiagonal matrix enhanced multivariance products representation (BTMEMPR)

“…which can be finalized to the following result a 2 = A T u − αv (16) when the following vanishing-to-vector projection condition is imposed…”

“…The properties are almost same as the case of continuous functions except the need to change continuity with discreteness. Curious readers can find sufficiently detailed resources in scientific literature [12][13][14][15][16][17][18][19].…”