fpc_wsvd: Eigenfunctions via weighted, regularized SVD

In tf: S3 Classes and Methods for Tidy Functional Data

Eigenfunctions via weighted, regularized SVD

Description

Compute (truncated) orthonormal eigenfunctions and scores for (partially missing) data on a common (potentially non-equidistant) grid.

Usage

fpc_wsvd(data, arg, pve = 0.995)

## S3 method for class 'matrix'
fpc_wsvd(data, arg, pve = 0.995)

## S3 method for class 'data.frame'
fpc_wsvd(data, arg, pve = 0.995)

Arguments

data	numeric matrix of function evaluations (each row is one curve, no NAs)
arg	numeric vector of argument values
pve	percentage of variance explained

Details

Performs a weighted SVD with trapezoidal quadrature weights s.t. returned vectors represent (evaluations of) orthonormal eigenfunctions \phi_j(t), not eigenvectors \phi_j = (\phi_j(t_1), \dots, \phi_j(t_n)), specifically:
\int_T \phi_j(t)^2 dt \approx \sum_i \Delta_i \phi_j(t_i)^2 = 1 given quadrature weights \Delta_i, not \phi_j'\phi_j = \sum_i \phi_j(t_i)^2 = 1;
\int_T \phi_j(t) \phi_k(t) dt = 0 not \phi_j'\phi_k = \sum_i \phi_j(t_i)\phi_k(t_i) = 0, c.f. mogsa::wsvd().
For incomplete data, this uses an adaptation of softImpute::softImpute(), see references. Note that will not work well for data on a common grid if more than a few percent of data points are missing, and it breaks down completely for truly irregular data with no/few common timepoints, even if observed very densely. For such data, either re-evaluate on a common grid first or use more advanced FPCA approaches like refund::fpca_sc(), see last example for tfb_fpc()

Value

a list with entries

• mu estimated mean function (numeric vector)

• efunctions estimated FPCs (numeric matrix, columns represent FPCs)

• scores estimated FPC scores (one row per observed curve)

• npc how many FPCs were returned for the given pve (integer)

• scoring_function a function that returns FPC scores for new data and given eigenfunctions, see tf:::.fpc_wsvd_scores for an example.

Author(s)

Trevor Hastie, Rahul Mazumder, Cheng Meng, Fabian Scheipl

References

code adapted from / inspired by mogsa::wsvd() by Cheng Meng and softImpute::softImpute() by Trevor Hastie and Rahul Mazumder.
Meng C (2023). mogsa: Multiple omics data integrative clustering and gene set analysis. https://bioconductor.org/packages/mogsa.
Mazumder, Rahul, Hastie, Trevor, Tibshirani, Robert (2010). “Spectral regularization algorithms for learning large incomplete matrices.” The Journal of Machine Learning Research, 11, 2287-2322.
Hastie T, Mazumder R (2021). softImpute: Matrix Completion via Iterative Soft-Thresholded SVD. R package version 1.4-1, https://CRAN.R-project.org/package=softImpute.

See Also

Other tfb-class: tfb, tfb_fpc(), tfb_spline()

Other tfb_fpc-class: tfb_fpc()

tf documentation built on May 29, 2024, 5:28 a.m.