Functional Data Analysis (FDA) for Biomechanics

Functions for functional data analysis including functional PCA (fPCA), functional regression, and curve registration. These methods treat biomechanical waveforms as continuous functions. Functional Principal Component Analysis (fPCA)

Usage

fPCA(x, n_components = 5, smooth = FALSE, smooth_param = 10)

Arguments

x

A PhysioExperiment object or matrix (time x observations).

n_components

Number of principal components to retain.

smooth

Logical; if TRUE, smooths the data before analysis.

smooth_param

Smoothing parameter (higher = smoother).

Value

A list of class "fpca_result" containing:

scores

PC scores for each observation (observations x components)

loadings

PC loadings/eigenfunctions (time x components)

variance_explained

Proportion of variance explained by each PC

cumulative_variance

Cumulative variance explained

mean_function

Mean waveform across observations

Details

Performs functional PCA on waveform data to identify the main modes of variation in movement patterns.

fPCA decomposes waveform variability into orthogonal modes. In gait analysis, PC1 often represents overall amplitude, PC2 timing/phase shifts, and subsequent PCs capture more subtle shape variations.

References

Ramsay JO, Silverman BW (2005). "Functional Data Analysis." 2nd ed. Springer.

See also

reconstructFPCA() for waveform reconstruction from fPCA results, plotFPCA() (in PhysioMoCap) for visualization of fPCA results, registerCurves() for separating phase and amplitude variation.

Examples

# Simulate gait angle data (100 time points x 30 subjects)
set.seed(123)
t <- seq(0, 100, length.out = 100)
base_curve <- sin(2 * pi * t / 100) * 30

# Add subject variability
data <- sapply(1:30, function(i) {
  amplitude <- rnorm(1, 1, 0.2)
  phase <- rnorm(1, 0, 5)
  base_curve * amplitude + rnorm(100, 0, 2)
})

pe <- PhysioExperiment(assays = list(values = data), samplingRate = 100)
fpca_result <- fPCA(pe, n_components = 4)