Functional Principal Component Analysis

Vertical and Horizontal Functional Principal Component Analysis using SRSF

moduleauthor:: Derek Tucker <dtucker@stat.fsu.edu>

fPCA.horizfPCA(gam, time, no, showplot=True)

This function calculates horizontal functional principal component analysis on aligned data

Parameters:

• gam – numpy ndarray of shape (M,N) of M warping functions
• time – vector of size N describing the sample points
• no (int) – number of components to extract (default = 1)
• showplot (bool) – Shows plots of results using matplotlib (default = T)

Return type:

tuple of numpy ndarray

Return q_pca:

srsf principal directions

Return f_pca:

functional principal directions

Return latent:

latent values

Return coef:

coefficients

Return U:

eigenvectors

fPCA.vertfPCA(fn, time, qn, no=1, showplot=True)

This function calculates vertical functional principal component analysis on aligned data

Parameters:

• fn – numpy ndarray of shape (M,N) of M aligned functions with N samples
• time – vector of size N describing the sample points
• qn – numpy ndarray of shape (M,N) of M aligned SRSF with N samples
• no (int) – number of components to extract (default = 1)
• showplot (bool) – Shows plots of results using matplotlib (default = T)

Return type:

tuple of numpy ndarray

Return q_pca:

srsf principal directions

Return f_pca:

functional principal directions

Return latent:

latent values

Return coef:

coefficients

Return U:

eigenvectors