粒子群优化
不连续性分类
结(造纸)
算法
曲线拟合
计算机科学
数学
应用数学
机器学习
数学分析
化学工程
工程类
作者
Antonio Gálvez,Andrés Iglesias
标识
DOI:10.1016/j.cad.2011.07.010
摘要
Data fitting through B-splines improves dramatically if the knots are treated as free variables. However, in that case the approximation problem becomes a very difficult continuous multimodal and multivariate nonlinear optimization problem. In a previous paper, Yoshimoto et al. (2003) [18] solved this problem for explicit curves by using a real-code genetic algorithm. However, the method does not really deal with true multiple knots, so the cases of data with underlying functions having discontinuities and cusps are not fully addressed. In this paper, we present a new method to overcome such a limitation. The method applies the particle swarm optimization (PSO) paradigm to compute an appropriate location of knots automatically. Our scheme yields very accurate results even for curves with singularities and/or cusps. Several experiments show that our proposal is very efficient and improves previous results (including those by Yoshimoto et al. (2003) in [18]) significantly in terms of data points error, AIC and BIC criteria. Furthermore, the important case of true multiple knots is now satisfactorily solved.
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