Represent¶
Decompose, transform, rank, and measure functional data.
The Represent module brings together the core tools for analyzing functional data beyond simple summary statistics. Whether you need to extract the dominant modes of variation, project curves onto a finite basis, rank observations by their centrality, or quantify how different two functional samples are, this section has you covered.
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:material-chart-bell-curve-cumulative:{ .lg .middle } Functional PCA
Extract the dominant modes of variation via Karhunen-Loeve decomposition. Reduce dimensionality, denoise, and build features for downstream models.
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:material-sine-wave:{ .lg .middle } Basis Representation
Project raw discrete curves onto B-spline or Fourier bases. Smooth with P-splines, select the optimal basis automatically, and convert between representations.
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:material-layers-triple:{ .lg .middle } Depth Functions
Rank functional observations from center to outward using 10+ depth measures. Identify the functional median, detect outliers, and build robust statistics.
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:material-ruler:{ .lg .middle } Distance Metrics
Compute pairwise distances between curves using \(L^p\), Hausdorff, DTW, elastic, and Fourier-based metrics. Feed distance matrices into clustering, classification, and regression.