OnlineFPCA

A compact, reproducible codebase for the OnlineFPCA project used in the associated paper.

This repository contains R code to run online stochastic-gradient FPCA, baseline batch methods, simulation studies, and real-data analyses for the paper. The README below explains the project structure, how to set up the environment, and how to reproduce tables and figures from the paper.

NOTE: data//output/ directory contains a large number of data/result files, which may slow down repo cloning.

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📦 Repository structure

Top-level layout (important files/directories):

• R/ – Core R implementation files
  • onlineFPCA.R: OnlineFPCA algorithm
  • onlineFDAlocalpoly.R: OnlineCov algorithm (adapted from the code for Yang & Yao (2023))
  • fpcaReg.R: SOAP algorithm, a batch FPCA method
  • Other helper utilities.
• experiments/ – Simulation scripts and analysis helpers (e.g. fpca1d.R, fpca2d.R). run_reps.sh is a helper for submitting repeated (seeded) simulation jobs on an HPC cluster.
• test/ – demo-fpca1d.R and demo-fpca2d.R are also for 1D and 2D simulation studies, but also easier to be run interactively.
• application/ – Real-data pipelines and plotting scripts (e.g. gfr.R, aqi.R).
• data/ – Data required to reproduce the application results. For this project the subfolders of interest are data/gfr/ and data/epa-aqs/.
• data_generation/ – Data simulators used by the simulation studies.
• external_codes/ – Third-party algorithms: mOpCov and REML.
• install_pkgs.R – Script to install required R packages in a fresh environment.
• output/ – Include our result files from simulation studies and real-data analysis. Large files are removed due to size limits.

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🧪 Reproduce tables and figures

Note: Plain numbers (1,2,...) are in the main article. Numbers with "S" (S1, S2, ...) are in the supplementary materials.

• Table 1, 2, S4: Main simulation studies for 1D and 2D data under different noise levels. In experiments/, Run fpca1d.R and fpca2d.R for --seed across 1~100. Then, run analyze_fpca1d.R and analyze_fpca2d.R to obtain results from knitr::kable(). Table 1 and 2 are part of Table S4.

• Figure 3: FPC plot for AQI data. First run application/aqi.R to obtain fit_aqi_*.Rdata. Then, run application/analyze_aqi.R to produce the plot simu-aqi-fpc.pdf.

• Figure S1: Use Matrix::image() to plot the matrix B, G and S in the 1D simulation.

• Figure S2: CI plot for 1D simulation. In experiments/, run ci-simu1d.R for --seed across 1~100. Then, run analyze_ci1d.R to produce the plot ci1d-ci.pdf.

• Figure S3: CI plot for 2D simulation. In experiments/, run ci-simu2d.R for --seed across 1~100. Then, run analyze_ci2d.R to produce the plot ci2d-ci.pdf.

• Table S1: RMSEs for different $(C,W,B)$. Run check_bwc.R for --seed across 1~100. Then, analyze_bwc.R will produce the table.

• Figure S4, Table S2: RMSEs for different $\omega$ and block sizes. Run check_abv.R for --seed across 1~100. Then, run analyze_abv.R to produce the figure abv_paths.pdf and the table.

• Table S3: RMSEs for different mini-batch sizes. Run check_nbatch.R for --seed across 1~100. Then, run analyze_nbatch.R to produce the table.

• Figure S5, S6: RMSEs of FPCs in simulation studies under different sample sizes. Run size1d.R and size2d.R for --seed across 1~100. Then, run analyze_size1d.R and analyze_size2d.R to produce the figures size1d_rmse.pdf and size2d_rmse.pdf, respectively.

• Figures S7: RMSEs in simulation studies where the true FPCs are obtained from real data. Run simu_gfr.R and simu_aqi.R for --seed across 1~100. Then, run analyze_simu_gfr.R and analyze_simu_aqi.R to produce the figures simu-gfr-fpc.pdf and simu-aqi-fpc.pdf, respectively.

• Figure S9: FPC plot for news clicks data. First run application/news/news.R to obtain result_news_*.Rdata. Then, run application/news/analyze_news.R to produce the plot news_eigfun.pdf.

• Figure S9 and S10: Dynamic tuning path in 1D/2D simulation. The script fpca1d.R will produce the dynamic tuning path taupath-sim*d-sgd.pdf when the seed is 1234. You can set simple to 1 and compare to 0 to simplify the workflow and focus on figure plotting.

Rscript experiments/fpca1d.R --seed 1234 --compare 0 --simple 1
Rscript experiments/fpca2d.R --seed 1234 --compare 0 --simple 1

• Figure S11: Subject examples from the AQI data. The script application/aqi/aqi-eda.R provides a complete walk-through of the exploratory data analysis of the AQI data, and the command to generate Figure 4 (aqi-sample.pdf).

• Figure S12: FPC plot for GFR data. First run application/gfr/gfr.R to obtain result_gfr_*.Rdata. Then, run application/gfr/analyze_gfr.R to produce the plot gfr_eigfun.pdf.

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🧰 Environment setup

1. R (tested): R 4.5.0 (or a recent patch release).

2. Install the packages used in the analyses:

Rscript install_pkgs.R

3. Make sure data/ contains the required inputs. The (large) application datasets are not stored in the repo; if needed, place the original data files in data/gfr/ and data/epa-aqs/ as used by application/gfr.R and application/aqi.R.

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Tested Package Versions

Package	Version
argparse	2.3.1
cowplot	1.2.0
doFuture	1.1.3
dplyr	1.1.4
face	0.1-8
fastmatrix	0.6-4
fda	6.3.0
fdapace	0.6.0
foreach	1.5.2
giscoR	1.0.0
gslnls	1.4.2
lubridate	1.9.4
ManifoldOptim	1.0.1
Metrics	0.1.4
mgcv	1.9-4
Rcpp	1.1.0
Rdimtools	1.1.3
readr	2.1.6
readxl	1.4.5
remotes	2.5.0
RSpectra	0.16-2
rTensor	1.4.9
sf	1.0-23
sm	2.2-6.0
spData	2.3.4
stringr	1.6.0
tidyr	1.3.2