Local Clustering for Functional Data.

Area of Science:

• Statistics
• Data Science
• Machine Learning

Background:

• Unsupervised clustering is vital in functional data analysis.
• Existing methods assume a single clustering structure across the entire domain.
• Functions may exhibit different clustering patterns in distinct time subintervals.

Purpose of the Study:

• To develop a flexible local clustering approach for functional data.
• To address the limitations of existing methods in identifying time-varying cluster structures.
• To enable data-dependent identification of subintervals with distinct functional clustering patterns.

Main Methods:

• A novel local clustering approach based on basis expansion technique.
• Incorporation of a new penalization form for simultaneous subinterval identification, clustering, and estimation.
• Rigorous establishment of estimation and clustering consistency properties.

Main Results:

• The proposed method successfully identifies meaningful subintervals and distinct clustering structures.
• Demonstrated superior performance compared to multiple existing methods in simulation studies.
• Applied effectively to analyze normalized COVID-19 daily confirmed cases data.

Conclusions:

• The local functional clustering approach offers enhanced flexibility for analyzing complex functional data.
• This method accurately captures dynamic clustering patterns across different time segments.
• Provides a robust framework for uncovering localized structures in functional datasets.