The Eilers-Whittaker method for data smoothing effectiveness depends on the choice of the regularisation parameter, and automatic selection is a necessity for large datasets. Common methods, such as leave-one-out cross-validation, can perform poorly when serially correlated noise is present. We propose a novel procedure for selecting the control parameter based on the spectral entropy of the residuals. We define an S-curve from the Euclidean distance between points in a plot of the spectral entropy of the residuals versus that of the smoothed signal. The regularisation parameter corresponding to the absolute maximum of this S-curve is chosen as the optimal parameter. Using simulated data, we benchmarked our method against cross-validation and the V-curve. Validation was also performed on diverse experimental data. This robust and straightforward procedure can be a valuable addition to the available selection methods for the Eilers smoother.

翻译：Eilers-Whittaker数据平滑方法的有效性依赖于正则化参数的选择，对于大型数据集，自动选择是必要的。常见方法，如留一交叉验证，在存在序列相关噪声时可能表现不佳。我们提出了一种基于残差谱熵来选择控制参数的新方法。我们通过绘制残差谱熵与平滑信号谱熵的关系图，并计算图中点之间的欧几里得距离，定义了一条S曲线。选择该S曲线绝对最大值所对应的正则化参数作为最优参数。使用模拟数据，我们将本方法与交叉验证和V曲线法进行了基准比较。同时也在多种实验数据上进行了验证。这一稳健且直接的方法可以成为Eilers平滑器现有选择方法的一个有价值的补充。