Robust Two-Layer Partition Clustering of Sparse Multivariate Functional Data

In this work, a novel elastic time distance for sparse multivariate functional data is proposed. Subsequently, a robust distance-based two-layer partition clustering is introduced. With the proposed distance, our 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. The 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 our proposed distance. Numerical experiments on the simulated data highlight that the performance of the proposed algorithm is superior to the performances of the existing model-based and extended distance-based methods. Using Northwest Pacific cyclone track data as an example, we demonstrate the effectiveness of the proposed approach. The code is available online for readers to apply our clustering method and replicate our analyses.