Simultaneous Denoising and Heterogeneity Learning for Time Series Data

Noisy time series data are often collected in biomedical applications, and it remains an important task to understand the data heterogeneity. We propose an approach that combines the strength of trend filtering and distance-based clustering to simultaneously perform temporal mean denoising and subject-level clustering. We discuss an iterative algorithm that efficiently computes the cluster structure and clusterwise mean trends. Simulation studies confirm the excellent numerical performance of our method. We further consider two data application examples including an U.S. lung cancer mortality study and a suicide rate study.