Functional Principal Component Analysis

These functions are for computing functional principal component anlaysis (fPCA) on aligned data and generating random samples

fPCA Functions

vert_fPCA(fn, timet, qn; no=1)

Calculates vertical functional principal component analysis on aligned data

• fn array of shape (M,N) of N aligned functions with M samples
• timet vector of size M describing the sample points
• qn array of shape (M,N) of N aligned SRSF with M samples
• no number of components to extract (default = 1)

Returns Dict containing:

• q_pca srsf principal directions
• f_pca functional principal directions
• latent latent values
• coef coefficients
• U eigenvectors

horiz_fPCA(gam, timet; no=1)

Calculates horizontal functional principal component analysis on aligned data

• gam array of shape (M,N) of N warping functions with M samples
• timet vector of size M describing the sample points
• no number of components to extract (default = 1)

Returns Dict containing:

• gam_pca warping principal directions
• psi_pca srsf functional principal directions
• latent latent values
• U eigenvectors
• gam_mu mean warping function
• vec1 shooting vectors

gauss_model(fn, timet, qn, gam; n=1, sort_samples=false)

Computes random samples of functions from aligned data using Gaussian model

• fn aligned functions (M,N)
• timet vector (M) describing time
• qn aligned srvfs (M,N)
• gam warping functions (M,N)
• n number of samples
• sort_samples sort samples

Returns Dict containing:

• fs random aligned functions
• gams random warping functions
• ft random functions