Volume 20 , Issue 2 , PP: 40-54, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Omar A. abd Alwahab 1 *
Doi: https://doi.org/10.54216/IJNS.200204
In this study, the research aims to use some methods that deal with several independent variables with a dependent variable, where two methods were used to deal with, which is the method of slice inverse regression (SIR), which is considered a non-classical method, and two methods of machine learning, which is (TLBO, PSO), which is most popular of the teaching methods machine learning, the work of (SIR), (TLBO, PSO) is based on making reduced linear combinations of a partial set of the original explanatory variables, which may suffer from the problem of heterogeneity and the problem of multicollinearity between most of the explanatory variables. These new combinations of linear compounds resulting from the two methods will reduce the largest number of explanatory variables to reach one or more new dimensions called the effective dimension. The root mean square error criterion will be used to compare the two methods to indicate the preference of the methods.
multivariate , Slice inverse regression , machine learning , Projection Pursuit
[1] Ai-Qin Mu , De-Xin Cao , Xiao-Hug Wang ; (2009)" Amodified particle swarm optimization algorithm ", WCICA, Vol. (1) , No. (2) , PP. (151-155).
[2] Alexander Mitev , Michael Marefat , Dongsheng Ma and Janet Wang ; (2008) " Parameter reduction for variability analysis by Sliced Inverse Regression (SIR) Method " , IET, Vol.(2) , Issue.1 , PP.(16-22).
[3] Ali Akenani and Tahir R.Dikheel ; (2016) " Sparse Sliced Inverse Quantile Regression " ,Mathematics and Statistics ,PP. (192-200).
[4] Ali Gannoun , Christiane Guinot and Jerome Saracco ; (2004) " Reference Curve estimation Via alternating Sliced Inverse Regression " , Environmetrics , Vol.(15) , PP.(81-99).
[5] Anil Kumar Ghosh and Smarajit Bose ; (2004) " Backfitting Neural Network " , Computational Statistic , No.(19) , PP.(193-210).
[6] Arunasakthi .K. and Kamatchipriya.L ; (2014) " A Review on Linear and Non-Linear Dimensionality Reduction Techniques " Machine Learning and Applications, Vol.(1) , No.(1) , PP.(65-76).
[7] Charles B.Roosen and Trevor J.Hastie ; (1993) " Logistic Response Projection Pursuit " ,AT&T Bell Laboratories , PP.(1-25).
[8] Christopher J.C. Burges ;(2009) " Dimension Reduction : A Guided Tour " , Foundations and Trends , Vol.(2) ,No.(4) , PP.(275-365).
[9] Cook .R.D and Weisberg .S. ; (1991) " Sliced Inverse Regression for Dimension Redaction , comment " ,JASA , PP.(328-332).
[10] D. Napoleon and S. Pavalakodi ; (2011) " A New method for Dimensionality Reduction using K-means Clustering algorithm for High Dimensional Data set " , Computer Applications , Vol.(13) , No.(7) , PP.(41-46).
[11] Dan Xu and Hualing Deng ; (2012) " Application of Projection Pursuit Regression in the Forecast of the Percentage of Damaged seeds of Leguminivora Glycinivorella " , Advances in System Science and Applications ,Vol.(12) , No.(1) .
[12] El-Dereny , M. Rashwan , N. ; (2011) " Solving Multicollinearity Problem Using Ridge Regression Models ",Int. J. Contemp. Math. Sciences , Vol. (12) , PP.(585-600).
[13] Francis Bach ; (2017) " Breaking the Curse of Dimensionality with convex Neural Networks " , JMLR , Vol.(18) ,Issue.(1) ,PP.(1-53).
[14] G.E.Hinton and R.R Salakhutdinor ; (2006) " Reducing the Dimensionality of data with Neural Network" , Science , Vol.(313) ,Issue.(5786) ,PP.(504-507).
[15] Guo Qianjian and Yang Jianguo ; (2011) " Application of Projection Pursuit Regression to thermal error Modeling of CNC Machine Tool " , AMT , Nol.(55), Issue.(5) , PP,(623-629).
[16] Guy Martial Nkiet ; (2008) " Consistent Estimation of the Dimensionality in Sliced Inverse Regression" , Annals of the Institute of Statistical Mathematics , Vol.(60) ,Issue.( 2 ) , PP.( 257–271).
[17] Hamparsum Bozdogan ; (2004) "Statistical Data Mining and Knowledge Discovery " , CRC ,Ch.13 .
[18] Han .Ming Wu ; (2008) " Kernel Sliced Inverse Regression with Applications to Classification ' , Computational and Graphical Statistics , Vol.(17) , Issue.(3) , No.(3) , PP.(590-610).
[19] Hardle .W ;(1990) " Applied Nonparametric Regression " , Cambridge University Press.
http://econpapers.repec.org/scripts/redir..pdf.
[20] Jerome H. Friedman , Werne Stuetzie ; (1981) " Projection Pursuit Regression ", JASA ,Vol.(76) , No.(376) , PP. (817-823) .
[21] Jerome H.Friedman and John W.Tukey ; (1974) " A Projection Pursuit Algorithm for Exploratory data analysis " , IEEE , Vol.(23) ,No.(90)
[22] R.V.Rao , V.J.Savsaini , D.P.Vakharia ; (2011) "Teaching Learning Based Optimization : Anovel method for constrained mechanical design ,PP. (303-315), No.(43).
