Bivariate Nonisotonic Statistical Regression by a Lookup Table Neural System

A Novel Non-Isotonic Statistical Bivariate Regression Method—Application to Stratigraphic Data Modeling and Interpolation

“…Several data sets, each exhibiting different features, were used to tests the monotonicity transformation and the statistical bivariate regression method applied in combination. Figure 1 shows these data sets, which were borrowed from the articles [5,6]. The functional expressions of the synthetic data are explained in [5,6].…”

“…Figure 1 shows these data sets, which were borrowed from the articles [5,6]. The functional expressions of the synthetic data are explained in [5,6]. Some further specifications about these data are as follows:…”

“…When a data set is not non-monotonic, it is harder to obtain a model of the data and to infer the value of missing records by interpolation than for a monotonic data set. One solution is to infer a functional relationship between variables using regression analysis as illustrated, to cite a few, in the paper [2] on evolutionary algorithms, in the contribution [3] on autonomous agents, and in the contributions [4][5][6] which cover several practical aspects of regression analysis. Regression is a computation application of paramount importance as testified by the research paper [7] that illustrates an application to drowsiness estimation using electroencephalographic data, by the book [8] on statistical methods for engineers and scientists, by [9] that explores an improved power law for nonlinear least-squares fitting, in the papers [10][11][12] that exploit regression analysis in forecasting and prediction, by the research paper [13] that compares a number of linear and non-linear regression methods, in the paper [14] that uses support vector regression for the modeling and synthesis of antenna arrays, and by the contribution [15] that applies kernel Ridge regression to short-term wind speed forecasting.…”

“…Since isotonic regression is based on the assumption that the independent variable and the dependent variable are bound by a monotonic relationship, the statistical bivariate regression method cannot be applied directly to data sets that are not monotonically increasing nor decreasing. We proposed in [5,6], as a remedy, to make use of a data-transformation technique referred to as data monotonization. As a novel contribution to this research topic, in Section 2 of the present paper we propose a non-linear integral transformation which turns a bivariate data set into a modified set in which the relation between the dependent variable and the independent variable is monotonically increasing.…”

A New Computational Method Based on Laguerre Polynomials for Solving Certain Nonlinear Partial Integro Differential Equations

“…Nonlinear partial integro-differential equations frequently arise in many fields of engineering, mathematics, physics, finance, biology, and related areas [1][2][3][4][5][6][7][8]. There exists main challenges for solving these type of problems due to large range of variables, nonlinearity, and multidimensionality, and so on.…”