Title: Roughness regularization for functional data analysis with free knots spline estimation Show Chinese title

Title: 具有自由节点样条估计的函数数据分析的粗糙正则化

Abstract: In the era of big data, an ever-growing volume of information is recorded, either continuously over time or sporadically, at distinct time intervals. Functional Data Analysis (FDA) stands at the cutting edge of this data revolution, offering a powerful framework for handling and extracting meaningful insights from such complex datasets. The currently proposed FDA me\-thods can often encounter challenges, especially when dealing with curves of varying shapes. This can largely be attributed to the method's strong dependence on data approximation as a key aspect of the analysis process. In this work, we propose a free knots spline estimation method for functional data with two penalty terms and demonstrate its performance by comparing the results of several clustering methods on simulated and real data. Show Chinese abstract

Abstract: 在大数据时代，无论是连续记录还是以离散时间间隔间断记录，都积累了越来越多的信息。函数数据分析（FDA）处于这场数据革命的前沿，为处理和从这些复杂数据集中提取有意义的见解提供了强大的框架。目前提出的许多FDA方法常常会遇到挑战，尤其是在处理形状各异的曲线时。这主要归因于这些方法在分析过程中对数据拟合的高度依赖性。在这项工作中，我们提出了一个带有两个惩罚项的自由结点样条估计方法用于函数数据分析，并通过比较几种聚类方法在模拟数据和真实数据上的结果展示了该方法的表现。