An Algorithm for the forward step of adaptive regression slines via mapping approach

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2012
Kartal Koç, Elçin
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 step, a general model including too many basis functions so the knot points are generated; and in the second one, the least contributing basis functions to the overall fit are eliminated. In the conventional adaptive spline procedure, knots are selected from a set of distinct data points that makes the forward selection procedure computationally expensive and leads to high local variance. To avoid these drawbacks, it is possible to select the knot points from a subset of data points, which leads to data reduction. In this study, a new method (called S-FMARS) is proposed to select the knot points by using a self organizing map-based approach which transforms the original data points to a lower dimensional space. Thus, less number of knot points is enabled to be evaluated for model building in the forward selection of MARS algorithm. The results obtained from simulated datasets and of six real-world datasets show that the proposed method is time efficient in model construction without degrading the model accuracy and prediction performance. In this study, the proposed approach is implemented to MARS and CMARS methods as an alternative to their forward step to improve them by decreasing their computing time

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Citation Formats
E. Kartal Koç, “An Algorithm for the forward step of adaptive regression slines via mapping approach,” Ph.D. - Doctoral Program, Middle East Technical University, 2012.