A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct clusters for sparse multivariate functional data under outlier settings but also can detect those outliers that do not belong to any clusters. Classical distance-based clustering methods such as density-based spatial clustering of applications with noise (DBSCAN), agglomerative hierarchical clustering, and $K$-medoids are extended to the sparse multivariate functional case based on the newly-proposed distance. Numerical experiments on simulated data highlight that the performance of the proposed algorithm is superior to the performances of existing model-based and extended distance-based methods. The effectiveness of the proposed approach is demonstrated using Northwest Pacific cyclone tracks data as an example.
翻译:提出了一种新颖的弹性时间距离用于稀疏多变量函数数据,并利用该距离开发了一种鲁棒的基于距离的两层分割聚类方法。使用该距离,新方法不仅可以在异常值设置下检测到稀疏多变量函数数据的正确聚类,还可以检测到这些不属于任何聚类的异常值。根据新提出的距离,将经典的基于距离的聚类方法如DBSCAN、凝聚层次聚类和K-medoids扩展到稀疏多变量函数数据的情况。通过对模拟数据的数值实验,突出了所提出算法的性能优于现有的基于模型和扩展距离的方法的表现。通过使用西北太平洋气旋路径数据作为示例,证明了所提出方法的有效性。