论文标题
非线性最小二乘样条带有可变结
Nonlinear least-squares spline fitting with variable knots
论文作者
论文摘要
在本文中，我们使用带有自由结的B型平台提出了一种非线性最小二乘拟合算法。由于其性能在很大程度上取决于自由参数的初始估计（即结），因此我们还提出了一种快速有效的打结预测算法，该算法利用了一阶B-Splines的数值特性。使用$ \ ell_p \;（p = 1,2，\ infty）$ norm Solutions，我们还提供了三种不同的策略来正确选择免费结。然后，我们的初始预测将通过基于梯度的变量投影优化进行迭代完善。我们的方法本质上是一般性的，可以用来估计没有APRIORI信息的情况下的最佳结数。为了评估我们方法的性能，我们近似一个一维离散时间序列，并使用合成和现实世界数据进行了广泛的比较研究。我们选择了心电图（ECG）信号压缩的问题作为现实世界中的案例研究。我们对众所周知的Physionet Mit-BIH心律失常数据库的实验表明，所提出的方法在准确性方面优于其他结预测技术，同时需要较低的计算复杂性。
In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and efficient knot-prediction algorithm that utilizes numerical properties of first-order B-splines. Using $\ell_p\;(p=1,2,\infty)$ norm solutions, we also provide three different strategies for properly selecting the free knots. Our initial predictions are then iteratively refined by means of a gradient-based variable projection optimization. Our method is general in nature and can be used to estimate the optimal number of knots in cases in which no a-priori information is available. To evaluate the performance of our method, we approximated a one-dimensional discrete time series and conducted an extensive comparative study using both synthetic and real-world data. We chose the problem of electrocardiogram (ECG) signal compression as a real-world case study. Our experiments on the well-known PhysioNet MIT-BIH Arrhythmia database show that the proposed method outperforms other knot-prediction techniques in terms of accuracy while requiring much lower computational complexity.
