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Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration.

Code ↔ Paper

5 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 5 matches
  1. [1] § Methods › Expectation-Maximization Algorithm for ProJIVE ↔ Simulations/FnRunProJIVE_Simulations_n1000_Feng.R, lines 1–67 · score 0.75 · pPCA, Cholesky decomposition, AJIVE solution, covariance matrix, square, MLE
  2. [2] § Methods › Expectation-Maximization Algorithm for ProJIVE ↔ Simulations/FnRunProJIVE_Simulations_n1000_GG.R, lines 1–64 · score 0.75 · pPCA, Cholesky decomposition, AJIVE solution, covariance matrix, square, MLE
  3. [3] § Methods › Model Identifiability › Theorem 1. ↔ R/GenerateToyData.R, lines 1–55 · score 0.71 · joint variation, individual variation, error variances, joint signal, individual components, variable
  4. [4] § Simulation Study › Simulation Design ↔ R/GenerateToyData.R, lines 1–55 · score 0.67 · individual variation explained, individual ranks, joint signal, attributable, model, blocks
  5. [5] § Methods › Model Identifiability ↔ ProblematicIdentifiabilityExample_v2.Rmd, lines 87–109 · score 0.55 · positive semidefinite, orthogonal transformations, linear, components, Model, matrix

Paper

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The authors' code

R · 204 lines · 9.6 KB · other · 2 matches

  1. #' Generates K Simulated Datasets that follow JIVE Model using binary subject scores
  2. #'
  3. #' @param n Sample size.
  4. #' @param p Number of features per block (input as a vector).
  5. #' @param JntVarEx Proportions of joint variation explained (input as a vector).
  6. #' @param IndVarEx Proportions of individual variation explained (input as a vector).
  7. #' @param jnt_rank Joint Rank.
  8. #' @param equal.eig Logical (TRUE/FALSE), which allows the user to specify whether components within a data-blocks joint (or individual) signal should be equally waited. The default is FALSE.
  9. #' @param ind_ranks Individual rank for each block (input as a vector).
  10. #' @param JntVarAdj Logical (TRUE/FALSE): Specify whether signal matrices should be weighted to achieve the desired proportions of variation attributable to the joint signal.
  11. #' @param mix.probs A numerical vector that specifies the number of individual components (ranks) for each data block. Each entry describes the probability in the Gaussian Mixture model for the score. Entries need to add to 1.
  12. #' @param SVD.plots Logical (TRUE/FALSE): Should plots of signal matrix singular values be produced to verify ranks?
  13. #' @param Error Logical (TRUE/FALSE): Should the data be noise-contaminated?
  14. #' @param print.cor logical (TRUE/FALSE), Print the correlation matrix for the scores? (Allows one to assess orthoganility between scores/compnents)
  15. #' @param Loads char: Toy data can be generated with loadings from 'Gaussian', 'Rademacher', or 'Double_Exp' (double exponential) distributions. Loadings can also be fixed at binary (0/1) values assigned to half of the variables with keyword 'Fixed'.
  16. #' @param Scores char: Joint subject scores can be randomly generated from 'Gaussian', 'Binomial', or 'Gaussian_Mixture' distributions. The last refers to a mixture of Gaussians with unit variance, where 20% have mean -4, 50% have mean 0, and 30% have mean 4. In all cases individual scores are standard Gaussian.
  17. #' @param error.variances A numeric vector specifying the variance of the noise for each dataset.
  18. #'
  19. #' @return K simulated datasets that follow JIVE Model.
  20. #' Contains four main elements:
  21. #' - Data Components: A list containing three sub-lists (each of length K), JointSignalMatrices, IndivSignalMatrices, and NoiseMatrices.
  22. #' - Data Blocks: A list of length K, where each element is the final observed dataset (joint + individual + noise) of dimension n x p(k).
  23. #' - Scores: A list with two matrices, Joint (n x jnt_rank) and Indiv (n x sum(ind_ranks)).
  24. #' - Loadings: A list containing Joint and Indiv loadings.
  25. #' @export
  26. #'
  27. #' @examples
  28. #'r.J = 3
  29. #'r.I1 = 2
  30. #'r.I2 = 2
  31. #'n = 1000
  32. #'p1 = 20
  33. #'p2 = 200
  34. #'JntVarEx1 = 0.1
  35. #'JntVarEx2 = 0.1
  36. #'IndVarEx1 = 0.25
  37. #'IndVarEx2 = 0.25
  38. #'ToyDat = GenerateToyData(n = n, p = c(p1, p2), JntVarEx = c(0.1, 0.1),
  39. #'IndVarEx = c(0.25, 0.25), jnt_rank = r.J, ind_ranks = c(r.I1, r.I2))
  40. GenerateToyData <- function(n, p, JntVarEx, IndVarEx, jnt_rank = 1, equal.eig = FALSE, ind_ranks, JntVarAdj = TRUE, mix.probs = NULL,
  41. SVD.plots = TRUE, Error = TRUE, print.cor = TRUE, Loads = "Rademacher", Scores = "Gaussian_Mixture",
  42. error.variances = NULL){
  44. r.J = jnt_rank
  45. r.I = ind_ranks
  46. K = length(p)
  47. Scores.text = ifelse(is.numeric(Scores), "as defined by user", paste("from", Scores, "distributions"))
  48. Loads.text = ifelse(is.list(Loads), "as defined by user.", paste("from", Loads, "distributions."))
  49. cat(paste0("Generating Scores ", Scores.text, " and Loadings ", Loads.text, ". \n"))
  51. if(is.numeric(Scores)){
  52. JntScores = Scores[,1:r.J, drop = FALSE]
  53. IndivScores = Scores[,-(1:r.J), drop = FALSE]
  54. } else if(Scores=="Binomial"){
  55. JntScores = matrix(stats::rbinom(n*r.J, size=1, prob=0.2), nrow = n, ncol = r.J)
  57. b = stats::rbinom(n*sum(r.I), size=1, prob=0.4)
  58. b = 1 - 2*b
  59. IndivScores = matrix(b, nrow = n, ncol = sum(r.I))
  60. } else if (Scores=="Gaussian_Mixture"){
  61. if(is.null(mix.probs)){mix.probs = c(0.2, 0.5, 0.3)}
  62. n.groups = length(mix.probs)
  63. n.vals = (n.groups-1)/2
  64. if(is.integer(length(mix.probs)/2)){
  65. group.means = c(-4*(n.vals:1),4*(1:n.vals))
  66. } else {
  67. group.means = c(-4*(n.vals:1),0,4*(1:n.vals))
  68. }
  69. JointScores.groups = list()
  70. for(l in 1:length(mix.probs)){
  71. JointScores.groups[[l]] =
  72. matrix(stats::rnorm(n*mix.probs[l]*r.J, mean = group.means[l]),
  73. ncol = r.J)}
  74. JntScores = do.call(rbind, JointScores.groups)
  75. IndivScores = matrix(stats::rnorm(n*sum(r.I)), nrow = n, ncol = sum(r.I))
  76. } else if(Scores=="Gaussian"){
  77. JntScores = matrix(stats::rnorm(n*r.J), ncol = r.J)
  78. IndivScores = matrix(stats::rnorm(n*sum(r.I)), nrow = n, ncol = sum(r.I))
  79. } else if (is.numeric(Scores)){
  80. if(nrow(Scores == n) & ncol(Scores) == r.J+sum(r.I)){
  81. JntScores = Scores[,1:r.J]
  82. IndivScores = Scores[,-(1:r.J)]
  83. } else{
  84. cat("Matrix of subject scores must have n rows and jnt_rank+sum(ind_ranks) columns.")
  85. }
  86. } else {
  87. message("Please use one of the following three options to generate data with corresponding subject scores: 1) 'Gaussian' 2) 'Gaussian_Mixture' 3) Binomial.\n")
  88. message("Alternatively, the user can enter a matrix of subject scores with n rows and jnt_rank+sum(ind_ranks) columns.\n")
  89. }
  91. colnames(JntScores) = paste("Jnt Score", 1:r.J)
  92. IndivScores.names = NULL
  94. for(k in 1:K){
  95. IndivScores.names = c(IndivScores.names, paste0("Indiv X", k, " Score ", 1:r.I[k]))
  96. }
  97. colnames(IndivScores) = IndivScores.names
  99. if(print.cor){
  100. cat("The correlation between subject scores is given by")
  101. print(round(stats::cor(cbind(JntScores, IndivScores)),4))
  102. }
  104. Jnt.Loads.All = list()
  105. Indiv.Loads.All = list()
  106. D.I = list()
  107. Noise = Joint.Sigs = Indiv.Sigs = list()
  108. Sig.Mats = Data.Mats = list()
  109. temp.fcn = function(x){x[sample(round(length(x)/2))] = 1; x}
  112. if(is.null(error.variances)){
  113. error.variances = rep(1,K)
  114. } else if(is.numeric(error.variances) & length(error.variances) != K){
  115. cat("The parameter 'error.variances' can be entered as 1) a numeric vector with the same length as 'p' (homoscedastic option) or 2) a list of length 'p' whose kth entry is a numeric vector of length 'p_k'.\n")
  116. } else if(is.list(error.variances) & length(error.variances) != K){
  117. cat("The parameter 'error.variances' can be entered as 1) a numeric vector with the same length as 'p' (homoscedastic option) or 2) a list of length 'p' whose kth entry is a numeric vector of length 'p_k'.\n")
  118. }
  120. for(k in 1:K){
  121. if(length(Loads)==1){
  122. if(Loads == "Gaussian"){
  123. Jnt.Loads.All[[k]] = matrix(stats::rnorm(r.J*p[k]), nrow = r.J, ncol = p[k])
  124. } else if (Loads == "Fixed"){
  125. Jnt.Loads.All[[k]] = matrix(apply(matrix(0, nrow = r.J, ncol = p[k]), 1, temp.fcn), nrow = r.J)
  126. } else if (Loads == "Double_Exp"){
  127. Jnt.Loads.All[[k]] = matrix(extraDistr::rlaplace(p[k]*(r.J)), nrow = r.J)
  128. } else if (Loads == "Rademacher"){
  129. Jnt.Loads.All[[k]] = matrix(extraDistr::rsign(p[k]*(r.J)), nrow = r.J)
  130. }
  131. } else if (is.list(Loads)){
  132. Jnt.Loads.All[[k]] = t(Loads[[1]][[k]])
  133. }
  134. D.J = (1 - equal.eig)*diag(r.J:1) + equal.eig*diag(rep(1,r.J))
  136. # Joint.Sigs[[k]] = JntScores%*%sqrt(D.J[[k]])%*%Jnt.Loads.All[[k]]
  137. Joint.Sigs[[k]] = JntScores%*%D.J%*%Jnt.Loads.All[[k]]
  139. if(SVD.plots){
  140. plot(svd(Joint.Sigs[[k]])$d, ylab = "Singular Values",
  141. main = paste0("SVD of Joint Signal from X", k))
  142. }
  143. temp.IndScores = IndivScores[,(k>1)*sum(r.I[1:(k-1)])+(1:r.I[k])]
  145. if(length(Loads)==1){
  146. if(Loads == "Gaussian"){
  147. Indiv.Loads.All[[k]] = matrix(stats::rnorm(n = p[k]*r.I[k]), nrow = r.I[k], ncol = p[k])
  148. } else if (Loads == "Fixed"){
  149. temp.fcn = function(x){x[sample(round(length(x)/4))] = 1; x}
  150. Indiv.Loads.All[[k]] = matrix(apply(matrix(-1, nrow = r.I[k], ncol = p[k]), 1, temp.fcn), nrow = r.I[k])
  151. } else if (Loads == "Double_Exp"){
  152. Indiv.Loads.All[[k]] = matrix(extraDistr::rlaplace(p[k]*(r.I[k])), nrow = r.I[k])
  153. } else if (Loads == "Rademacher"){
  154. Indiv.Loads.All[[k]] = matrix(extraDistr::rsign(p[k]*(r.I[k])), nrow = r.I[k])
  155. }
  156. } else if (is.list(Loads)){
  157. Indiv.Loads.All[[k]] = t(Loads[[2]][[k]])
  158. }
  160. D.I[[k]] = (1 - equal.eig)*diag(r.I[k]:1) + equal.eig*diag(rep(1,r.I[k]))
  162. Indiv.Sigs[[k]] = temp.IndScores%*%D.I[[k]]%*%Indiv.Loads.All[[k]]
  164. if(SVD.plots){
  165. plot(svd(Indiv.Sigs[[k]])$d, ylab = "Singular Values",
  166. main = paste0("SVD of Individual Signal from X", k))
  167. }
  169. Sig.Mats[[k]] = Joint.Sigs[[k]] + Indiv.Sigs[[k]]
  171. if(is.vector(error.variances) & !is.list(error.variances)){
  172. Noise[[k]] = matrix(stats::rnorm(n*p[k], sd = sqrt(error.variances[k])), nrow = n)
  173. } else if(is.list(error.variances)){
  174. Noise[[k]] = matrix(mvtnorm::rmvnorm(n, sigma = diag(error.variances[[k]])), nrow = n)
  175. }
  178. Data.Mats[[k]] = CJIVE::AdjSigVarExp(Joint.Sigs[[k]], Indiv.Sigs[[k]], Noise[[k]],
  179. JntVarEx[k], IndVarEx[k])
  181. Joint.Sigs[[k]] = Data.Mats[[k]]$J
  182. Indiv.Sigs[[k]] = Data.Mats[[k]]$I
  183. }
  185. Blocks = lapply(Data.Mats, function(x) x[["Data"]])
  187. Dat.Comps = list(Joint.Sigs, Indiv.Sigs, Noise)
  188. names(Dat.Comps) = c("JointSignalMatrices", "IndivSignalMatrices", "NoiseMatrices")
  190. Scores = list(JntScores, IndivScores)
  191. names(Scores) = c("Joint", "Indiv")
  193. Loadings = list(list(),list())
  194. names(Loadings) = c("Joint", "Indiv")
  195. for(k in 1:K){
  196. Loadings[["Joint"]][[k]] = D.J%*%Jnt.Loads.All[[k]]
  197. Loadings[["Indiv"]][[k]] = D.I[[k]]%*%Indiv.Loads.All[[k]]
  198. }
  200. out = list(Dat.Comps, Blocks, Scores, Loadings)
  201. names(out) = c("Data Components", "Data Blocks", "Scores", "Loadings")
  203. return(out)
  204. }

GenerateToyData.R at commit 4b1fbc5, under other · at the source

Overview

Authors: Raphiel J. Murden1, Ganzhong Tian1, Deqiang Qiu2, Benjamin B. Risk1
ORCID iDs: Raphiel J. Murden
  1. Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, GA
  2. Department of Radiology and Imaging Sciences, Emory University School of Medicine, Atlanta, GA
Institutions: Emory University (United States)
Journal: Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America, article 10.1080/10618600.2026.2639081
Dates: published online 15 June 2026; in print June 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1080/10618600.2026.2639081 · PMID 42368974 · PMCID PMC13308631 · OpenAlex W7135078391
Open access: hybrid, a free copy (OpenAlex)
Preprint: arxiv:2603.12351
Status: code verified
Categories: human (organism), Alzheimer's / dementia (population), methods / tools (subfield)
Methods: Statistics, Smoothing, state filtering, decompositions, Machine learning, fMRI & imaging, Preprocessing
Keywords: ADNI, Alzheimer’s Disease, JIVE, Multi-block data analysis, Multimodal data analysis, Probabilistic PCA
Topic: Time Series Analysis and Forecasting (Signal Processing, Computer Science), according to OpenAlex
Funding: NIA NIH HHS (R21 AG064405, R21 AG066970, R01 AG072603, P30 AG066511); NIMH NIH HHS (R01 MH129855)
Citations: not cited yet (Europe PMC); 41 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repository

Its files are read in the Code ↔ Paper reader above, with 5 matches between paragraphs and lines of code.

thebrisklab/ProJIVE

License: other
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 4b1fbc556bcc37ab4072a44c1fe9618abc7eb903, 12 August 2026
Languages: R (118), MATLAB (44), Python (31), C++ (1)
Size: 268 files, 194 scripts
Software Heritage: not archived
Found in: the text, “Theorem 1.”
Holds: README, license file, environment (DESCRIPTION, ARCHIVE/DESCRIPTION), tests, documentation, 5 notebooks
Not found: CITATION.cff, continuous integration
Tools: NumPy (31 files), ggplot2 (21 files), tidyverse (21 files), SciPy (19 files), reshape2 (16 files), reticulate (13 files), cowplot (12 files), scikit-learn (5 files), Statistics and Machine Learning Toolbox (3 files), mgcv (1 file), psych (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
197 files
At the source: github.com/thebrisklab/ProJIVE

Tracing map

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What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
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  • 5 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Versions

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Version 2, 28 September 2026

  • Publisher: n/a → Taylor & Francis

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, pages, dates, 4 authors, 6 keywords, 2 funders, 37 references.

Cite

This paper

Murden, R. J., Tian, G., Qiu, D., & Risk, B. B. (2026). Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration. Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America, 10.1080/10618600.2026.2639081. https://doi.org/10.1080/10618600.2026.2639081

BibTeX

@article{murden2026probabilistic,
author = {Murden, Raphiel J. and Tian, Ganzhong and Qiu, Deqiang and Risk, Benjamin B.},
title = {{Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration}},
journal = {Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America},
year = {2026},
month = jun,
pages = {10.1080/10618600.2026.2639081},
publisher = {Taylor \& Francis},
issn = {1061-8600},
doi = {10.1080/10618600.2026.2639081},
url = {https://doi.org/10.1080/10618600.2026.2639081},
pmid = {42368974},
pmcid = {PMC13308631}
}

RIS

TY - JOUR
AU - Murden, Raphiel J.
AU - Tian, Ganzhong
AU - Qiu, Deqiang
AU - Risk, Benjamin B.
TI - Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration
T2 - Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
J2 - J Comput Graph Stat
PY - 2026
DA - 2026/06/15
SP - 10.1080/10618600.2026.2639081
SN - 1061-8600
PB - Taylor & Francis
DO - 10.1080/10618600.2026.2639081
UR - https://doi.org/10.1080/10618600.2026.2639081
LA - en
ER -

CSL-JSON

{
"id": "10.1080/10618600.2026.2639081",
"type": "article-journal",
"title": "Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration",
"container-title": "Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America",
"author": [
{
"family": "Murden",
"given": "Raphiel J."
},
{
"family": "Tian",
"given": "Ganzhong"
},
{
"family": "Qiu",
"given": "Deqiang"
},
{
"family": "Risk",
"given": "Benjamin B."
}
],
"container-title-short": "J Comput Graph Stat",
"page": "10.1080/10618600.2026.2639081",
"DOI": "10.1080/10618600.2026.2639081",
"PMID": "42368974",
"PMCID": "PMC13308631",
"ISSN": "1061-8600",
"publisher": "Taylor & Francis",
"URL": "https://doi.org/10.1080/10618600.2026.2639081",
"language": "en",
"issued": {
"date-parts": [
[
2026,
6,
15
]
]
}
}

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