A new rational approximation technique based on transformational high dimensional model representation

Abstract

In this work, a new rational approximation scheme, based on the recently developed Transformational High Dimensional Model Representation (THDMR) approximation method is developed. As an initial step to the construction of a rational approximation for multivariate functions via THDMR, this paper focuses on the general theoretical background of the method and gives explicit formulae for the computation of such approximants. The performance of the technique is shown by several examples both in univariate and bivariate cases.

Detecting GSM churners by using Euclidean Indexing HDMR

“…A two-dimensional confusion matrix is used to test the performance of a method on modeling the given binary problem. In this sense, the confusion matrix for a binary classification problem can be defined as follows (25) Using the elements of this confusion matrix, accuracy, sensitivity, specificity and precision can be evaluated as the performance checking tools.…”

“…There are some works about applying HDMR to different topics such as small scale geometries [23], multivariate analysis [24], rational approximation [25], weight optimization [26], random sampling of the input variables [27,28], complex bionetwork structures [29], probabilistic analysis [30], reliability [31] and sensitivity analysis [32,33], piece-wise function approximation [34], decision making [35], finite element modeling [36] and HDMR component formulation with independent and correlated variables [37].…”

Logarithmic high dimensional model representation in image processing

“…Sobol [1]. After his work, various types of HDMR based methods were produced to solve different kinds of problems in many scientific areas [2,3,4,5,6,7,8].…”

Fundamental elements of vector enhanced multivariance product representation

“…In last two decades there have been an increasing tendency to employ the so-called High Dimensional Model Representation (HDMR) which was first proposed by Sobol [1] at the beginning of 1990s. There came many contributions, like Cut-HDMR, Multi-cut HDMR, Random Sampling HDMR by first H. Rabitz and his group [2,3,4,5], and then, the new HDMR varieties plus important mathematical aspects by M. Demiralp's group [6,7,8,9,10,11,12]. Now there are some other interesting applications of the issue although it is unnecessary to get into further details.…”