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

TL;DR

funBIalign is a hierarchical algorithm designed to discover functional motifs in time series and multiple curves by leveraging mean squared residue scores, with demonstrated effectiveness on simulated and real-world data.

Contribution

It introduces a novel hierarchical clustering-based method for functional motif discovery using mean squared residue scores, applicable to single and multiple curves.

Findings

Effective in identifying motifs in simulated data

Successfully applied to real-world case studies on food prices and temperature

Outperforms some existing methods in motif detection accuracy

Abstract

Motif discovery is gaining increasing attention in the domain of functional data analysis. Functional motifs are typical "shapes" or "patterns" that recur multiple times in different portions of a single curve and/or in misaligned portions of multiple curves. In this paper, we define functional motifs using an additive model and we propose funBIalign for their discovery and evaluation. Inspired by clustering and biclustering techniques, funBIalign is a multi-step procedure which uses agglomerative hierarchical clustering with complete linkage and a functional distance based on mean squared residue scores to discover functional motifs, both in a single curve (e.g., time series) and in a set of curves. We assess its performance and compare it to other recent methods through extensive simulations. Moreover, we use funBIalign for discovering motifs in two real-data case studies; one on food price inflation and one on temperature changes.