Additivity and deviation multiplicativity measurers for uniform discrete multivariate data via high dimensional model representation varieties
Metin Demіralp · Annual Conference on Computers · 2006
The main goal of this paper is to construct certain scalars to measure how constant, how univariate, how bivariate (and so on) a given uniform discrete multivariate data is in accordance with the additive and multiplicative high dimensional model representations respectively. The additivity measurers were defined in the previous publications of the author's group and they will be briefly given here again for making a good logical background for the paper. The additivity measurers form a finite monotonous sequence approaching 1 from below as the order of multivariance increases. In spite of our all efforts we could not be able to construct the multiplicativity measurers in the same way. Although we have constructed the factorized high dimensional model representation for purely or dominantly multiplicative multivariate functions we could have not been able to construct a set of monotonously increasing scalars to measure how constant, how univariate, how bivariate (and so on) a given uniform discrete multivariate data is with respect to factorized high dimensional model representation. This paper cures this problem and enables us to construct the sequence we need conveniently.