Align¶
Register and align curves to separate amplitude from phase variability.
Functional observations often exhibit two fundamentally different sources of variation: amplitude (how tall or deep the features are) and phase (when those features occur). Standard statistical methods conflate the two, leading to washed-out means and inflated variance estimates. The Align module provides elastic alignment tools built on the Fisher-Rao metric and the Square Root Slope Function (SRSF) framework to cleanly decompose these sources of variability.
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:material-swap-horizontal:{ .lg .middle } Elastic Alignment
Pairwise and group alignment via the SRSF transform, Karcher mean, and elastic distances. Separate amplitude from phase, compute warping functions, and build elastic distance matrices.
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:material-shape:{ .lg .middle } Shape Analysis
Quotient-space shape distances, elastic depth measures, and elastic FPCA. Decompose functional data into amplitude and phase principal components for downstream modeling.