Adaptive spline fitting with particle swarm optimization
Adaptive spline fitting with particle swarm optimization
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DOI：
10.1007/s00180-020-01022-x
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发表时间：
2019-07
影响因子：
1.3
通讯作者：
S. Mohanty;E. Fahnestock
中科院分区：
文献类型：
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作者：
S. Mohanty;E. Fahnestock
在使用样条线拟合数据时，找到节点的最佳位置可以显著提高拟合质量。然而，与完全自由节点放置相关的具有挑战性的高维非凸优化问题一直是使用该方法的主要障碍。我们提出了一种将粒子群优化(PSO)与模型选择相结合的方法来解决这一挑战。该方法通过显式正则化缓解了自由节点放置过程中节点聚类带来的过拟合问题，显著提高了对高噪声数据的处理性能。描述了该方法中可用的主要设计选择，并使用模拟数据和各种基准函数对它们对性能的影响进行了统计严格的研究。我们的结果表明，基于粒子群优化算法的自由节点放置导致了一种可行的、灵活的自适应样条拟合方法，该方法允许对光滑和非光滑函数进行拟合。
In fitting data with a spline, finding the optimal placement of knots can significantly improve the quality of the fit. However, the challenging high-dimensional and non-convex optimization problem associated with completely free knot placement has been a major roadblock in using this approach. We present a method that uses particle swarm optimization (PSO) combined with model selection to address this challenge. The problem of overfitting due to knot clustering that accompanies free knot placement is mitigated in this method by explicit regularization, resulting in a significantly improved performance on highly noisy data. The principal design choices available in the method are delineated and a statistically rigorous study of their effect on performance is carried out using simulated data and a wide variety of benchmark functions. Our results demonstrate that PSO-based free knot placement leads to a viable and flexible adaptive spline fitting approach that allows the fitting of both smooth and non-smooth functions.