Robust Two-Layer Partition Clustering of Sparse Multivariate Functional Data

TL;DR

This paper introduces a new elastic time distance for sparse multivariate functional data, enabling a robust two-layer clustering method that effectively detects clusters and outliers, outperforming existing methods in simulations and real cyclone data.

Contribution

A novel elastic time distance for sparse multivariate functional data and a robust two-layer clustering approach that improves outlier detection and cluster accuracy.

Findings

Proposed method outperforms existing clustering techniques in simulations.

Effective detection of outliers not belonging to any cluster.

Demonstrated success on real cyclone track data.

Abstract

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.