Implicit Target Regression Algorithm And Its Corresponding Application

For the regression analysis, there are many classical and effective algorithms, such asminimum mean-squares error, ridge regression, support vector regression and so on. Thosealgorithms achieve their success in both clear geometric interpretation and simple solution.However, before introducing these methods to a real application, we have to define/assumecause-and-effect relationship, i.e., relationship between dependent variables (target/responsevariables) and independent variables, even if this relationship is not always true. Based on suchresearch background, we propose some new methods to relieve such symptoms. Compared tothe foresaid classical methods, we aim to accomplish something including geometric intuitionand computational expenses, no matter there exists cause-and-effect assumption or not.Main contributions of this paper are described as follow:1.Regression analysis algorithm at home and board are summarized in this paper, anddifferences between these algorithms are discussed including their advantages anddisadvantages.2.For the fact that common regression algorithms have to define/assume cause-and-effectrelationship, this paper proposes a regression method with implicit relationship betweendependent variables and independent variables, for which it is not necessary to assume adependent variable. Compare to foresaid methods, the proposed has many advantages in4-folds.First, it also has geometric interpretation like common regression algorithms. Second, thereexists analytical solution for the algorithm, i.e., it can be solved through algebraic methods.Third, least-squares regression method can be seen as its special case. Also, it is easy to begeneralized to solve nonlinear regression problems with kernel tricks.3.For nonlinear regression problems, one of the effective way to solve them is to usepiecewise approximation method, i.e., one can use a series of the subsection function toapproximate the unknown functions. In this paper, we propose a piecewise implicit regressionalgorithm based on k-plane clustering algorithm.The method can obtain segments adaptively.Compared with the central-point clustering algorithm, for example, k-means, the proposedsubsection regression method is more aligned with people’s intuition and easier to solveproblems, considering that the former algorithm is mostly oval clustering and that the later oneis linear clustering differently, using a straight line or plane to approach each sample clusterdirectly.Finally, corresponding experiments on the artificial and standard data sets are to show theeffectiveness of the proposed algorithm in this paper.