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Regression analysis using a blending type spline construction

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https://hdl.handle.net/10037/11795
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Date
2017-10-18
Type
Peer reviewed
Chapter
Bokkapittel

Author
Kravetc, Tatiana; Bang, Børre; Dalmo, Rune
Abstract
Regression analysis allows us to track the dynamics of change in measured data and to investigate their properties. A sufficiently good model allows us to predict the behavior of dependent variables with higher accuracy, and to propose a more precise data generation hypothesis. By using polynomial approximation for big data sets with complex dependencies we get piecewise smooth functions. One way to obtain a smooth spline representation of an entire data set is to use local curves and to blend them using smooth basis functions. This construction allows the computation of derivatives at any point on the spline. Properties such as tangent, velocity, acceleration, curvature and torsion can be computed, which gives us the opportunity to exploit these data in the subsequent analysis. We can adjust the accuracy of the approximation on the different segments of the data set by choosing a suitable knot vector. This article describes a new method for determining the number and location of the knot-points, based on changes in the Frenet frame. We present a method of implementation using generalized expo-rational B-splines (GERBS) for regression problems (in two and three variables) and we evaluate the accuracy of the model using comparison of the residuals.
Description
Accepted manuscript version. Open Access Publishing in Springer Computer Proceedings Link to publisher's (Springer International Company) version: http://doi.org/10.1007/978-3-319-67885-6_8
Publisher
Springer International company
Series
Lecture Notes in Computer Science, vol. 10521
Citation
Kravetc T, Bang BEJ, Dalmo R: Regression analysis using a blending type spline construction. In: Floater MS, Lyche T, Mazure M, Mørken KMM, Schumaker LL. Mathematical Methods for Curves and Surfaces: 9th International Conference, MMCS 2016 Tønsberg, Norway, June 23-28, 2016 Revised Selected Papers, 2017. Springer Publishing Company p. 145-161
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