Variograms for kriging and clustering of spatial functional data with phase variation.

Area of Science:

• Statistics
• Functional Data Analysis
• Spatial Statistics

Background:

• Spatial functional data analysis often confounds spatial, amplitude, and phase variations.
• Existing methods like the functional trace-variogram can yield misleading results with misaligned data exhibiting phase variation.

Purpose of the Study:

• To develop a framework for amplitude-phase separation in spatial functional data.
• To enable more accurate spatial clustering and prediction by addressing phase variation.

Main Methods:

• Decomposition of the trace-variogram into amplitude and phase components.
• Quantification of spatial correlations within amplitude and phase.
• Development of separate clustering methods for amplitude and phase.
• Creation of a novel spatial functional interpolant combining amplitude and phase predictions.

Main Results:

• Demonstrated advantages over standard methods that ignore phase variation.
• Achieved more accurate predictions in simulations and real-world data.
• Provided more interpretable clustering results.

Conclusions:

• The proposed amplitude-phase separation framework enhances spatial functional data analysis.
• Accounting for phase variation leads to improved predictive performance and clustering interpretability.