Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Restructuring forward step of MARS algorithm using a new knot selection procedure based on a mapping approach
Date
2014-09-01
Author
Koc, Elcin Kartal
İyigün, Cem
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
234
views
0
downloads
Cite This
In high dimensional data modeling, Multivariate Adaptive Regression Splines (MARS) is a popular nonparametric regression technique used to define the nonlinear relationship between a response variable and the predictors with the help of splines. MARS uses piecewise linear functions for local fit and apply an adaptive procedure to select the number and location of breaking points (called knots). The function estimation is basically generated via a two-stepwise procedure: forward selection and backward elimination. In the first step, a large number of local fits is obtained by selecting large number of knots via a lack-of-fit criteria; and in the latter one, the least contributing local fits or knots are removed. In conventional adaptive spline procedure, knots are selected from a set of all distinct data points that makes the forward selection procedure computationally expensive and leads to high local variance. To avoid this drawback, it is possible to restrict the knot points to a subset of data points. In this context, a new method is proposed for knot selection which bases on a mapping approach like self organizing maps. By this method, less but more representative data points are become eligible to be used as knots for function estimation in forward step of MARS. The proposed method is applied to many simulated and real datasets, and the results show that it proposes a time efficient forward step for the knot selection and model estimation without degrading the model accuracy and prediction performance.
Subject Keywords
Data mining
,
Multivariate adaptive regression splines (MARS)
,
Computational efficiency
,
High dimensional data reduction
,
Mapping
,
Self-organizing maps
URI
https://hdl.handle.net/11511/48000
Journal
JOURNAL OF GLOBAL OPTIMIZATION
DOI
https://doi.org/10.1007/s10898-013-0107-5
Collections
Department of Industrial Engineering, Article
Suggestions
OpenMETU
Core
EVALUATING THE CMARS PERFORMANCE FOR MODELING NONLINEARITIES
Batmaz, İnci; Kartal-Koc, Elcin; Köksal, Gülser (2010-02-04)
Multivariate Adaptive Regression Splines (MARS) is a very popular nonparametric regression method particularly useful for modeling nonlinear relationships that may exist among the variables. Recently, we developed CMARS method as an alternative to backward stepwise part of the MARS algorithm. Comparative studies have indicated that CMARS performs better than MARS for modeling nonlinear relationships. In those studies, however, only main and two-factor interaction effects were sufficient to model the nonline...
An Algorithm for the forward step of adaptive regression slines via mapping approach
Kartal Koç, Elçin; Batmaz, İnci; İyigün, Cem; Department of Statistics (2012)
In high dimensional data modeling, Multivariate Adaptive Regression Splines (MARS) is a well-known nonparametric regression technique to approximate the nonlinear relationship between a response variable and the predictors with the help of splines. MARS uses piecewise linear basis functions which are separated from each other with breaking points (knots) for function estimation. The model estimating function is generated in two stepwise procedures: forward selection and backward elimination. In the first st...
Efficient adaptive regression spline algorithms based on mapping approach with a case study on finance
Koc, Elcin Kartal; İyigün, Cem; Batmaz, İnci; Weber, Gerhard-Wilhelm (2014-09-01)
Multivariate adaptive regression splines (MARS) has become a popular data mining (DM) tool due to its flexible model building strategy for high dimensional data. Compared to well-known others, it performs better in many areas such as finance, informatics, technology and science. Many studies have been conducted on improving its performance. For this purpose, an alternative backward stepwise algorithm is proposed through Conic-MARS (CMARS) method which uses a penalized residual sum of squares for MARS as a T...
Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method
Yerlikaya-Ozkurt, F.; Vardar Acar, Ceren; Yolcu-Okur, Y.; Weber, G. -W. (2014-03-15)
In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm). Our approach is superior to others in that it not only estimates the Hurst parameter but also finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated tes...
Refinements, extensions and modern applications of conic multivariate adaptive regression splines
Yerlikaya Özkurt, Fatma; Weber, Gerhard Wilhelm; Department of Scientific Computing (2013)
Conic Multivariate Adaptive Regression Splines (CMARS) which has been developed at the Institute of Applied Mathematics, METU, as an alternative approach to the well-known data mining tool Multivariate Adaptive Regression Splines (MARS). CMARS is based on given data and a penalized residual sum of squares for MARS, interpreted as a Tikhonov Regularization problem. CMARS treats this problem by a continuous optimization technique called Conic Quadratic Programming (CQP). This doctoral thesis adapts the CMARS ...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
E. K. Koc and C. İyigün, “Restructuring forward step of MARS algorithm using a new knot selection procedure based on a mapping approach,”
JOURNAL OF GLOBAL OPTIMIZATION
, pp. 79–102, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48000.