This research presents FDASynthesis, a novel algorithm designed to generate synthetic GPS trajectory data while preserving privacy. After pre-processing the input GPS data, human mobility traces are modeled as multidimensional curves using Functional Data Analysis (FDA). Then, the synthesis process identifies the K-nearest trajectories and averages their Square-Root Velocity Functions (SRVFs) to generate synthetic data. This results in synthetic trajectories that maintain the utility of the original data while ensuring privacy. Although applied for human mobility research, FDASynthesis is highly adaptable to different types of functional data, offering a scalable solution in various application domains.

翻译：本研究提出FDASynthesis，一种旨在生成合成GPS轨迹数据同时保护隐私的新算法。在对输入GPS数据进行预处理后，利用功能数据分析（FDA）将人类移动轨迹建模为多维曲线。随后，合成过程通过识别K个最近邻轨迹并对其平方根速度函数（SRVF）进行平均来生成合成数据。该方法产生的合成轨迹在确保隐私的同时保持了原始数据的实用性。尽管应用于人类移动研究，FDASynthesis能高度适应不同类型的功能数据，为多种应用领域提供了可扩展的解决方案。