Robust Two-Layer Partition Clustering of Sparse Multivariate Functional Data

Abstract

In this work, a novel elastic time distance for sparse multivariate functional data is proposed. This concept serves as the foundation for clustering functional data with various time measurements per subject. Subsequently, a robust two-layer partition clustering is introduced. With the proposed distance, our approach not only is applicable to both complete and imbalanced multivariate functional data but also is resistant to outliers and capable of detecting outliers that do not belong to any clusters. The classical distance-based clustering methods such as K-medoids and agglomerative hierarchical clustering 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 modelbased 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.