funBIalign: a hierachical algorithm for functional motif discovery based on mean squared residue scores.

Area of Science:

• Functional data analysis
• Statistical pattern recognition
• Time series analysis

Background:

• Motif discovery is crucial for understanding complex patterns in functional data.
• Existing methods may struggle with identifying motifs in both single and multiple, potentially misaligned, curves.
• There is a need for robust algorithms to detect recurring shapes within functional datasets.

Purpose of the Study:

• To introduce and evaluate funBIalign, a novel method for functional motif discovery and evaluation.
• To define functional motifs using an additive model framework.
• To demonstrate the method's applicability on both simulated and real-world functional data.

Main Methods:

• funBIalign employs a multi-step procedure inspired by clustering and biclustering.
• It utilizes agglomerative hierarchical clustering with complete linkage.
• A functional distance based on mean squared residue scores is central to the motif discovery process.

Main Results:

• The performance of funBIalign was assessed through extensive simulations.
• funBIalign was compared against other recent functional motif discovery methods.
• The method successfully identified functional motifs in real-world case studies on food price inflation and temperature changes.

Conclusions:

• funBIalign provides an effective approach for discovering functional motifs in diverse datasets.
• The method demonstrates robust performance in simulations and practical applications.
• This work contributes a valuable tool for pattern identification in functional data analysis.