SiMLR Simulation Study: Demonstrate basic assumptions for SiMLR and compare to RGCCA
Brian B. Avants et al.
2020-10-11
Decode known latent signal distributed across 3 matrices with SiMLR and RGCCA. For each run, we:
- split the data matrices into train and test groups
- run SiMLR, RGCCA and SGCCA on the triad of matrices
- for SiMLR, we select a similarity measurement (via the
energyTypevariable, default CCA-like) - run SiMLR on permuted matrices as a reference null result
- predict the latent signal from the low-dimensional space given the embedding data from each method
- use the amount of variance explained as the outcome measurement.
Under the above simulation, a better method will more reliably explain the underlying true latent signal.
The key metrics will compare the ability to predict the known latent signal in testing data based on the embeddings derived in an unsupervised dimensionality reduction step. This is one of the primary ways in which SiMLR may be used to study high-dimensional datasets.
The main metric will be the R\(^2\) value between the model fit and the true latent signal in the test data. Higher values (averaged over simulations) are associated with better performance.
The simulation study has several parameter the user may explore to gain more insight. Default options corrupt each matrix by an amount drawn from a random uniform distribution. We also add modality-specific covariation via a smoothing operation. This operation also dampens signal.
Note: every run re-simulates the input data, re-runs SiMLR and RGCCA and compares the findings to the same applied to permuted data. In a real example, you would only run SiMLR and RGCCA on permuted data in each loop.
Result: Demonstrate well-above chance recovery of latent signal competitive with or better than RGCCA and its sparse counterpart, SGCCA.
Result: SiMLR demonstrates more consistent signal recovery than RGCCA (strongly) and SGCCA (smaller but still distinct advantage).
The reduced variance in performance in likely due in part to both graph-based regularization and the primal formulation i.e. that we directly optimize the smoothed and sparsified feature vectors instead of using the dual formulation.
set.seed( 808 )
library( ANTsR )
library( RGCCA )
# library( smoother )
doA = TRUE
smoothRows <- function( x ) {
window = sample( 25:150, 1 )
nr = nrow( x )
nc = ncol( x )
xout = x * 0
for ( k in 1:nr ) {
vex = x[k,]
xout[ k, ] = vex # smoother::smth.gaussian( vex, window=window, tails=TRUE )
}
antsrimpute( xout )
}
doCorruption = TRUE
if ( ! exists( "energyType" ) ) energyType = 'cca'
nComp = 4 # n components
if ( ! exists( "nsims" ) ) nsims = 120
nits = 100 # n-iterations
nz = 0 # simulated signal parameter - not sensitive to this choice
nzs = 1.5 # simulated signal parameter - not sensitive to this choice
nzs2 = 1 # simulated signal parameter - not sensitive to this choice
nna = rep( NA, nsims )
# this data frame will hold the results and allow us to answer questions about how noise impacts the outcome
simdatafrm = data.frame(
symRSQ = nna,
rgccaRSQ = nna,
sgccaRSQ = nna,
prmRSQ = nna,
corrupt1 = nna,
corrupt2 = nna,
corrupt3 = nna,
nTrueEmbeddings = nna,
nForSim = nna
)
################################################################################
for ( sim in c(1:nsims) ) {
set.seed( sim )
smaller = rnorm( 1, 0.8, 0.2 )
nsub = round( 400 * smaller ) # number of subjects
npix = c( nsub*4, nsub*2, nsub * 8 ) # size of matrices are wildly different
ntrain = 0.8 * round( nsub )
train = sample( c( rep(T, ntrain ) ,rep(F, nsub - ntrain )) ) # train and test split
test = !train
nEmbeddings = nk = sample( 5:25, 1 )# for latent signal
# the outcome's first column is the latent signal that we are seeking
mixmats = diag( nk )
outcome = scale( matrix(runif( nsub * nk, nz, nzs2 ),ncol=nk) )
# the 3 matrices below represent modality specific distributions
view1tx = scale(matrix( rnorm( npix[1] * nk, nz, nzs ), nrow=nk ))
view2tx = scale(matrix( rnorm( npix[2] * nk, nz, nzs*1.5 ), nrow=nk ))
view3tx = scale(matrix( rnorm( npix[3] * nk, nz, nzs*0.8 ), nrow=nk ))
# below we mix the independent basis matrices with the true signal
outcomex = outcome
# throw some difference in here - so really just the first column is the latent signal
reo=2:nk
outcomex[,reo]=sample(outcomex[,reo])
# here, we resample the diagonal matrix to provide some variability about
# where the signals appear across different modalities
# we also smooth to provide some modality specific covariation
smoosig = abs( rnorm( 3, 6, 1.5 ) ) # draw from a distribution of smoothing parameters
if ( doA ) mixmat = as.matrix( smoothImage( as.antsImage( mixmats[sample(1:nrow(mixmats)),] %*% view1tx) , smoosig[3] ) ) else mixmat = smoothRows( mixmats[sample(1:nrow(mixmats)),] %*% view1tx )
# mix in the real signal --- repeat the same procedures for all 3 views of data
mat1 = (outcomex %*% mixmat )
outcomex=outcome
outcomex[,reo]=sample(outcomex[,reo])
if ( doA ) mixmat = as.matrix( smoothImage( as.antsImage( mixmats[sample(1:nrow(mixmats)),] %*% view2tx), smoosig[2] ) ) else mixmat = smoothRows( mixmats[sample(1:nrow(mixmats)),] %*% view2tx )
mat2 = (outcomex %*% mixmat )
outcomex = outcome
outcomex[,reo] = sample(outcomex[,reo])
if ( doA ) mixmat = as.matrix( smoothImage( as.antsImage( mixmats[sample(1:nrow(mixmats)),] %*% view3tx), smoosig[1] ) ) else mixmat = smoothRows( mixmats[sample(1:nrow(mixmats)),] %*% view3tx )
mat3 = (outcomex %*% mixmat )
# small additive noise for each matrix
mat1 = mat1 + matrix( rnorm( prod(dim(mat1)), 0, 0.25 ), nrow=nsub)
mat2 = mat2 + matrix( rnorm( prod(dim(mat2)), 0, 0.25 ), nrow=nsub)
mat3 = mat3 + matrix( rnorm( prod(dim(mat3)), 0, 0.25 ), nrow=nsub)
if ( doCorruption ) {
# corrupt a portion of matrices - with random amounts of corruption each simulation
ruinRate = runif(3,0.1,0.9)
corrSDs = abs( rnorm( 3, 10, 10 ) )
corrMNs = rnorm( 3, 0, 10 )
corrInds = round(npix[3] * ruinRate[3] ):npix[3]
mat3[ ,corrInds] = matrix( rnorm( prod(dim(mat3[ , corrInds])), corrMNs[3], corrSDs[3] ), nrow=nsub)
corrInds = round(npix[2] * ruinRate[2] ):npix[2]
mat2[ ,corrInds] = matrix( rnorm( prod(dim(mat2[ , corrInds])), corrMNs[2], corrSDs[2] ), nrow=nsub)
corrInds = round(npix[1] * ruinRate[1] ):npix[1]
mat1[ ,corrInds] = matrix( rnorm( prod(dim(mat1[ , corrInds])), corrMNs[1], corrSDs[1] ), nrow=nsub)
}
# automate the regularization selection using up to 50 neighbors for each matrix
inmats = list( vox = mat1[train,], vox2 = mat2[train,], vox3 = mat3[train,] )
regs = regularizeSimlr( list( mat1[train,], mat2[train,], mat3[train,] ),
rep( 50, 3 ), sigma = rep( 10.0, 3 ) )
result = simlr(
inmats,
smoothingMatrices = regs,
energyType = energyType,
initialUMatrix = nComp,
verbose = FALSE,
iterations = nits,
mixAlg = mixingMethod ) # allows different methods to be compared
p1 = mat1 %*% abs(result$v[[1]]); colnames(p1) = paste0("PC",1:ncol(p1))
p2 = mat2 %*% abs(result$v[[2]]); colnames(p2) = paste0("PC",1:ncol(p1))
p3 = mat3 %*% abs(result$v[[3]]); colnames(p3) = paste0("PC",1:ncol(p1))
nnn = 1:nComp
temp=data.frame( outc = outcome[,1], sym1=p1[,nnn], sym2=p2[,nnn], sym3=p3[,nnn] )
mdlsym=lm( outc~.,data=temp[train,])
dfPred = data.frame( true_test_outcome = temp$outc[test], predicted_outcome = predict(mdlsym,newdata=temp[test,]))
mdlsymPred = lm( true_test_outcome ~ predicted_outcome, data=dfPred )
rsqsym = cor( temp$outc[test], predict(mdlsym,newdata=temp[test,]) )^2
rsqsym
if ( sim == 1 ) {
library( rtemis )
rtlayout(1, 3, byrow = TRUE, autolabel = TRUE)
rtemis::mplot3.xy( temp[test,]$sym1.PC1, temp[test,]$sym2.PC1, main='SiMLR: PC1_1 vs PC2_1', se.fit = TRUE, fit='lm' )
# rtemis::mplot3.xy( temp[test,]$sym2.PC1, temp[test,]$sym3.PC1, main='SiMLR: PC2_1 vs PC3_1', se.fit = TRUE, fit='lm' )
rtemis::mplot3.xy( temp[test,]$sym3.PC1, temp[test,]$sym3.PC3, main='SiMLR: PC3_1 vs PC3_3', se.fit = TRUE, fit='lm' )
# rtemis::mplot3.xy( temp[test,]$sym2.PC3, temp[test,]$sym1.PC4, main='SiMLR: PC2_3 vs PC1_4', se.fit = TRUE, fit='lm' )
rtemis::mplot3.xy( dfPred$true_test_outcome, dfPred$predicted_outcome, main='SiMLR: Test Data', se.fit = TRUE, fit='lm' )
}
# compare to permuted data
s1 = sample( 1:nsub)
s2 = sample( 1:nsub)
s3 = sample( 1:nsub)
pmat1=mat1[s1,]
pmat2=mat2[s2,]
pmat3=mat3[s3,]
inmats = list( vox = pmat1[train,], vox2 = pmat2[train,], vox3 = pmat3[train,] )
resultp = simlr(
inmats,
smoothingMatrices = regs,
energyType = energyType,
initialUMatrix = nComp,
verbose = F, iterations=5, mixAlg=mixingMethod )
p1p = pmat1 %*% abs(resultp$v[[1]])
p2p = pmat2 %*% abs(resultp$v[[2]])
p3p = pmat3 %*% abs(resultp$v[[3]])
temp=data.frame( outc = outcome[,1], p1p[,nnn], p2p[,nnn], p3p[,nnn] )
mdlprm=lm( outc~.,data=temp[train,])
rsqprm = cor( temp$outc[test], predict(mdlprm,newdata=temp[test,]) )^2
# compare to RGCCA - follow the recommended SABSCOV formulation
myrgcca = rgcca( # this initializes with SVD
A = list( mat1[train,],mat2[train,],mat3[train,]),
C = 1 - diag( 3 ),
tau = rep( 1, 3 ), # for rgcca
scheme = 'centroid',
ncomp = rep( nComp, 3 ),
scale = TRUE,
verbose = FALSE )
prgcca = cbind(
mat1 %*% myrgcca$a[[1]][,nnn],
mat2 %*% myrgcca$a[[2]][,nnn],
mat3 %*% myrgcca$a[[3]][,nnn] )
temp=data.frame( outc = outcome[,1], prgcca[,1:(max(nnn)*3)] )
mdlrgcca=lm( outc~.,data=temp[train,])
rsqrgcca = cor( temp$outc[test], predict(mdlrgcca,newdata=temp[test,]) )^2
# compare to SGCCA - follow suggested glioma example in documentation
myrgcca = sgcca( # this initializes with SVD
A = list( mat1[train,],mat2[train,],mat3[train,]),
scheme = "centroid",
ncomp = rep( nComp, 3 ),
scale = TRUE,
c1 = rep( 0.5, 3 ), # use something like simlr
verbose = FALSE )
prgcca = cbind(
mat1 %*% myrgcca$a[[1]][,nnn],
mat2 %*% myrgcca$a[[2]][,nnn],
mat3 %*% myrgcca$a[[3]][,nnn] )
temp=data.frame( outc = outcome[,1], prgcca[,1:(max(nnn)*3)] )
mdlrgcca=lm( outc~.,data=temp[train,])
rsqsgcca = cor( temp$outc[test], predict(mdlrgcca,newdata=temp[test,]) )^2
simdatafrm[sim,] = c(
rsqsym,
rsqrgcca,
rsqsgcca,
rsqprm, ruinRate, nk, nsub )
print( paste("Simulation:",sim,"rsqsym",rsqsym, "rsqsgcca", rsqsgcca))
print( simdatafrm[sim,] )
cat("<<<<********>>>>\n")
}## [1] "Simulation: 1 rsqsym 0.202856720935524 rsqsgcca 0.018726097942524"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 1 0.2028567 0.08271954 0.0187261 0.01437723 0.6097639 0.1657645 0.2102564
## nTrueEmbeddings nForSim
## 1 18 270
## <<<<********>>>>
## [1] "Simulation: 2 rsqsym 0.575525752182748 rsqsgcca 0.595573100376879"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 2 0.5755258 0.1663712 0.5955731 0.04996832 0.4274195 0.8341307 0.503782
## nTrueEmbeddings nForSim
## 2 7 248
## <<<<********>>>>
## [1] "Simulation: 3 rsqsym 0.510498864728684 rsqsgcca 0.449030498392422"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 3 0.5104989 0.3909184 0.4490305 0.06680795 0.3815088 0.8738479 0.3846142
## nTrueEmbeddings nForSim
## 3 23 243
## <<<<********>>>>
## [1] "Simulation: 4 rsqsym 0.359807619453061 rsqsgcca 0.504529295978701"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 4 0.3598076 0.2380919 0.5045293 0.01155261 0.3743984 0.2930968 0.7249775
## nTrueEmbeddings nForSim
## 4 21 337
## <<<<********>>>>
## [1] "Simulation: 5 rsqsym 0.554356456728195 rsqsgcca 0.553934741260822"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 5 0.5543565 0.4183328 0.5539347 0.002639123 0.4553291 0.5243792 0.7343283
## nTrueEmbeddings nForSim
## 5 14 253
## <<<<********>>>>
## [1] "Simulation: 6 rsqsym 0.543351442261847 rsqsgcca 0.566153587511158"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 6 0.5433514 0.5761825 0.5661536 0.03951137 0.6356254 0.5923085 0.7961964
## nTrueEmbeddings nForSim
## 6 20 342
## <<<<********>>>>
## [1] "Simulation: 7 rsqsym 0.568273357324806 rsqsgcca 0.655560290093703"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 7 0.5682734 0.5894104 0.6555603 4.089757e-07 0.5721252 0.4228447 0.64963
## nTrueEmbeddings nForSim
## 7 20 503
## <<<<********>>>>
## [1] "Simulation: 8 rsqsym 0.648204055466001 rsqsgcca 0.641991566398773"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 8 0.6482041 0.5973998 0.6419916 0.02776197 0.850412 0.5317252 0.3854239
## nTrueEmbeddings nForSim
## 8 16 313
## <<<<********>>>>
## [1] "Simulation: 9 rsqsym 0.647349551325274 rsqsgcca 0.709779240852967"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 9 0.6473496 0.5016047 0.7097792 0.007461439 0.2962562 0.5647676 0.3991453
## nTrueEmbeddings nForSim
## 9 6 259
## <<<<********>>>>
## [1] "Simulation: 10 rsqsym 0.69144463443665 rsqsgcca 0.647042973433406"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 10 0.6914446 0.6591293 0.647043 0.001320208 0.8285033 0.1398677 0.2981007
## nTrueEmbeddings nForSim
## 10 5 321
## <<<<********>>>>
## [1] "Simulation: 11 rsqsym 0.635899873833549 rsqsgcca 0.487634845631952"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 11 0.6358999 0.463435 0.4876348 0.003318125 0.2858025 0.4138801 0.465193
## nTrueEmbeddings nForSim
## 11 6 273
## <<<<********>>>>
## [1] "Simulation: 12 rsqsym 0.395343407365176 rsqsgcca 0.556552317212778"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 12 0.3953434 0.4937726 0.5565523 0.0010043 0.6473258 0.397628 0.646168
## nTrueEmbeddings nForSim
## 12 15 202
## <<<<********>>>>
## [1] "Simulation: 13 rsqsym 0.452262816888679 rsqsgcca 0.187849234612155"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 13 0.4522628 0.08321715 0.1878492 0.02104285 0.6888443 0.1847571 0.2689542
## nTrueEmbeddings nForSim
## 13 24 364
## <<<<********>>>>
## [1] "Simulation: 14 rsqsym 0.542463499126587 rsqsgcca 0.547674808826771"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 14 0.5424635 0.4086983 0.5476748 0.0004746701 0.6714665 0.8571574 0.6680247
## nTrueEmbeddings nForSim
## 14 9 267
## <<<<********>>>>
## [1] "Simulation: 15 rsqsym 0.531842994983515 rsqsgcca 0.633558410137305"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 15 0.531843 0.5900965 0.6335584 0.006772317 0.2550545 0.8027444 0.2884029
## nTrueEmbeddings nForSim
## 15 23 341
## <<<<********>>>>
## [1] "Simulation: 16 rsqsym 0.439368750636714 rsqsgcca 0.378181848044538"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 16 0.4393688 0.300542 0.3781818 0.01488231 0.8224056 0.2788775 0.3789082
## nTrueEmbeddings nForSim
## 16 20 358
## <<<<********>>>>
## [1] "Simulation: 17 rsqsym 0.505979023297046 rsqsgcca 0.325216816997708"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 17 0.505979 0.2446114 0.3252168 0.01695063 0.3827463 0.1016975 0.498994
## nTrueEmbeddings nForSim
## 17 16 239
## <<<<********>>>>
## [1] "Simulation: 18 rsqsym 0.448821138556339 rsqsgcca 0.487545156122575"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 18 0.4488211 0.4760749 0.4875452 0.001080676 0.5939755 0.8541631 0.8179487
## nTrueEmbeddings nForSim
## 18 21 394
## <<<<********>>>>
## [1] "Simulation: 19 rsqsym 0.629652155658994 rsqsgcca 0.610320351851101"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 19 0.6296522 0.5842467 0.6103204 0.02569567 0.5315619 0.8480022 0.8151635
## nTrueEmbeddings nForSim
## 19 15 225
## <<<<********>>>>
## [1] "Simulation: 20 rsqsym 0.589364031474132 rsqsgcca 0.631717335166447"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 20 0.589364 0.5748232 0.6317173 0.002688741 0.894567 0.3830734 0.7762652
## nTrueEmbeddings nForSim
## 20 20 413
## <<<<********>>>>
## [1] "Simulation: 21 rsqsym 0.481744511326206 rsqsgcca 0.424489898976203"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 21 0.4817445 0.4008263 0.4244899 0.0004808662 0.5307914 0.6875179 0.4006813
## nTrueEmbeddings nForSim
## 21 12 383
## <<<<********>>>>
## [1] "Simulation: 22 rsqsym 0.467783620434676 rsqsgcca 0.494342717311942"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 22 0.4677836 0.5103097 0.4943427 0.0337345 0.8267991 0.8716003 0.1569747
## nTrueEmbeddings nForSim
## 22 21 279
## <<<<********>>>>
## [1] "Simulation: 23 rsqsym 0.436913198343056 rsqsgcca 0.393342607460417"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 23 0.4369132 0.4023419 0.3933426 0.01039347 0.1604842 0.6603718 0.6257906
## nTrueEmbeddings nForSim
## 23 18 335
## <<<<********>>>>
## [1] "Simulation: 24 rsqsym 0.554522752677056 rsqsgcca 0.540257822588242"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 24 0.5545228 0.5114599 0.5402578 0.04053957 0.1296695 0.1695853 0.1227204
## nTrueEmbeddings nForSim
## 24 25 276
## <<<<********>>>>
## [1] "Simulation: 25 rsqsym 0.409693621879637 rsqsgcca 0.380594555044674"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 25 0.4096936 0.2873388 0.3805946 0.006115338 0.8768807 0.6860525 0.1169671
## nTrueEmbeddings nForSim
## 25 6 303
## <<<<********>>>>
## [1] "Simulation: 26 rsqsym 0.417833234579801 rsqsgcca 0.192686681356382"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 26 0.4178332 0.2956608 0.1926867 0.001731067 0.6882603 0.6693866 0.2517785
## nTrueEmbeddings nForSim
## 26 19 150
## <<<<********>>>>
## [1] "Simulation: 27 rsqsym 0.474148500570386 rsqsgcca 0.446730557125625"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 27 0.4741485 0.3633363 0.4467306 0.0003835995 0.6904371 0.3571471 0.5333443
## nTrueEmbeddings nForSim
## 27 19 473
## <<<<********>>>>
## [1] "Simulation: 28 rsqsym 0.62370347552732 rsqsgcca 0.694456226136815"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 28 0.6237035 0.6131814 0.6944562 0.03162872 0.620296 0.8436519 0.458144
## nTrueEmbeddings nForSim
## 28 6 168
## <<<<********>>>>
## [1] "Simulation: 29 rsqsym 0.636009105803206 rsqsgcca 0.687258593145159"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 29 0.6360091 0.5377198 0.6872586 0.06222598 0.5194642 0.8266058 0.6277783
## nTrueEmbeddings nForSim
## 29 11 217
## <<<<********>>>>
## [1] "Simulation: 30 rsqsym 0.54768435213864 rsqsgcca 0.361962147639716"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 30 0.5476844 0.2458016 0.3619621 0.05350086 0.3032608 0.7383811 0.5852181
## nTrueEmbeddings nForSim
## 30 20 217
## <<<<********>>>>
## [1] "Simulation: 31 rsqsym 0.465656920222987 rsqsgcca 0.526921066150372"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 31 0.4656569 0.4618586 0.5269211 0.006254274 0.7282429 0.2031838 0.4044328
## nTrueEmbeddings nForSim
## 31 18 324
## <<<<********>>>>
## [1] "Simulation: 32 rsqsym 0.418908109615615 rsqsgcca 0.524980373796632"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 32 0.4189081 0.3883998 0.5249804 8.5009e-05 0.3501221 0.5624648 0.4493418
## nTrueEmbeddings nForSim
## 32 8 321
## <<<<********>>>>
## [1] "Simulation: 33 rsqsym 0.251999335077914 rsqsgcca 0.268563043104229"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 33 0.2519993 0.08773133 0.268563 1.382864e-05 0.436592 0.1385706 0.3680125
## nTrueEmbeddings nForSim
## 33 22 309
## <<<<********>>>>
## [1] "Simulation: 34 rsqsym 0.334529570450818 rsqsgcca 0.392154570116717"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 34 0.3345296 0.2082791 0.3921546 0.04103443 0.1544002 0.8155863 0.2192953
## nTrueEmbeddings nForSim
## 34 15 309
## <<<<********>>>>## Warning in sgccak(R, C, c1 = c1, scheme = scheme, init = init, bias = bias, :
## The SGCCA algorithm did not converge after 1000 iterations.## [1] "Simulation: 35 rsqsym 0.696461566826266 rsqsgcca 0.692674333583416"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 35 0.6964616 0.4506672 0.6926743 0.0005701815 0.5851936 0.3427513 0.5000881
## nTrueEmbeddings nForSim
## 35 7 405
## <<<<********>>>>
## [1] "Simulation: 36 rsqsym 0.586154512307116 rsqsgcca 0.349633394596894"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 36 0.5861545 0.405382 0.3496334 0.001031353 0.2522588 0.7206225 0.8813692
## nTrueEmbeddings nForSim
## 36 24 345
## <<<<********>>>>
## [1] "Simulation: 37 rsqsym 0.500895107968697 rsqsgcca 0.34229890230554"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 37 0.5008951 0.1316114 0.3422989 0.02355264 0.4398332 0.4602104 0.250888
## nTrueEmbeddings nForSim
## 37 7 330
## <<<<********>>>>
## [1] "Simulation: 38 rsqsym 0.0870134877821341 rsqsgcca 0.118994380725365"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 38 0.08701349 0.01403716 0.1189944 0.03046258 0.1679595 0.7741895 0.2491769
## nTrueEmbeddings nForSim
## 38 25 300
## <<<<********>>>>
## [1] "Simulation: 39 rsqsym 0.608686398109982 rsqsgcca 0.454043440551608"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 39 0.6086864 0.337834 0.4540434 0.0004240518 0.2791145 0.640759 0.8329312
## nTrueEmbeddings nForSim
## 39 25 305
## <<<<********>>>>
## [1] "Simulation: 40 rsqsym 0.482688700650622 rsqsgcca 0.36697276127582"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 40 0.4826887 0.2389479 0.3669728 0.005312991 0.1590437 0.833552 0.4547524
## nTrueEmbeddings nForSim
## 40 24 358
## <<<<********>>>>
## [1] "Simulation: 41 rsqsym 0.51199622995669 rsqsgcca 0.503186954954368"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 41 0.5119962 0.3828291 0.503187 0.008403915 0.4847883 0.291713 0.8222376
## nTrueEmbeddings nForSim
## 41 20 256
## <<<<********>>>>
## [1] "Simulation: 42 rsqsym 0.556410135042568 rsqsgcca 0.511858027221582"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 42 0.5564101 0.3585077 0.511858 0.02191264 0.3012763 0.627033 0.3951814
## nTrueEmbeddings nForSim
## 42 20 430
## <<<<********>>>>
## [1] "Simulation: 43 rsqsym 0.65792937498457 rsqsgcca 0.574131284356983"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 43 0.6579294 0.5780918 0.5741313 5.521392e-05 0.7214112 0.8823007 0.3360352
## nTrueEmbeddings nForSim
## 43 17 317
## <<<<********>>>>
## [1] "Simulation: 44 rsqsym 0.633708318629736 rsqsgcca 0.584978389409612"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 44 0.6337083 0.4620259 0.5849784 0.0009523041 0.6155342 0.8495107 0.1289159
## nTrueEmbeddings nForSim
## 44 9 372
## <<<<********>>>>
## [1] "Simulation: 45 rsqsym 0.61313402515677 rsqsgcca 0.588719287021426"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 45 0.613134 0.5227885 0.5887193 0.007486326 0.1410228 0.289673 0.356922
## nTrueEmbeddings nForSim
## 45 12 347
## <<<<********>>>>
## [1] "Simulation: 46 rsqsym 0.351405565235849 rsqsgcca 0.422803589835628"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 46 0.3514056 0.2128069 0.4228036 0.000707703 0.3769051 0.5152114 0.2799855
## nTrueEmbeddings nForSim
## 46 19 248
## <<<<********>>>>
## [1] "Simulation: 47 rsqsym 0.428165807612968 rsqsgcca 0.517948539126346"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 47 0.4281658 0.5015011 0.5179485 0.04041243 0.8738161 0.1229469 0.30533
## nTrueEmbeddings nForSim
## 47 12 480
## <<<<********>>>>
## [1] "Simulation: 48 rsqsym 0.535343053258258 rsqsgcca 0.562433880394532"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 48 0.5353431 0.5915697 0.5624339 0.002735931 0.471881 0.522434 0.8014456
## nTrueEmbeddings nForSim
## 48 19 336
## <<<<********>>>>
## [1] "Simulation: 49 rsqsym 0.725596711813013 rsqsgcca 0.704244400642284"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 49 0.7255967 0.6370647 0.7042444 0.01075836 0.6656333 0.6198922 0.866629
## nTrueEmbeddings nForSim
## 49 13 293
## <<<<********>>>>
## [1] "Simulation: 50 rsqsym 0.587834137342566 rsqsgcca 0.56595396091291"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 50 0.5878341 0.3452818 0.565954 0.01046475 0.4344102 0.6799204 0.4099741
## nTrueEmbeddings nForSim
## 50 16 364
## <<<<********>>>>
## [1] "Simulation: 51 rsqsym 0.508581689984302 rsqsgcca 0.475377230043224"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 51 0.5085817 0.3566666 0.4753772 9.912991e-05 0.3476936 0.8587498 0.486094
## nTrueEmbeddings nForSim
## 51 18 381
## <<<<********>>>>
## [1] "Simulation: 52 rsqsym 0.438369462954532 rsqsgcca 0.136185908409598"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 52 0.4383695 0.06545324 0.1361859 0.0002085117 0.1569439 0.2231528 0.1094279
## nTrueEmbeddings nForSim
## 52 18 241
## <<<<********>>>>
## [1] "Simulation: 53 rsqsym 0.392503100692882 rsqsgcca 0.36556762450566"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 53 0.3925031 0.3179103 0.3655676 0.007368847 0.4425242 0.1883126 0.5680132
## nTrueEmbeddings nForSim
## 53 17 336
## <<<<********>>>>
## [1] "Simulation: 54 rsqsym 0.553761033666771 rsqsgcca 0.312845185739914"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 54 0.553761 0.07820099 0.3128452 0.0001934515 0.8272887 0.4393381 0.2237687
## nTrueEmbeddings nForSim
## 54 15 471
## <<<<********>>>>
## [1] "Simulation: 55 rsqsym 0.410488174405146 rsqsgcca 0.338546044894568"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 55 0.4104882 0.1876889 0.338546 0.002430318 0.2681519 0.3353227 0.4164188
## nTrueEmbeddings nForSim
## 55 12 330
## <<<<********>>>>
## [1] "Simulation: 56 rsqsym 0.522743544262301 rsqsgcca 0.561318650609173"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 56 0.5227435 0.5374709 0.5613187 0.01373336 0.2937456 0.8149369 0.8739436
## nTrueEmbeddings nForSim
## 56 12 301
## <<<<********>>>>
## [1] "Simulation: 57 rsqsym 0.577820764193399 rsqsgcca 0.540933641683108"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 57 0.5778208 0.4067728 0.5409336 0.003914938 0.1002266 0.4612999 0.2636267
## nTrueEmbeddings nForSim
## 57 7 264
## <<<<********>>>>
## [1] "Simulation: 58 rsqsym 0.492289391023667 rsqsgcca 0.433578117219692"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 58 0.4922894 0.3645029 0.4335781 0.0001359366 0.7507904 0.3868264 0.6326859
## nTrueEmbeddings nForSim
## 58 17 284
## <<<<********>>>>
## [1] "Simulation: 59 rsqsym 0.611949746795321 rsqsgcca 0.45002137921813"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 59 0.6119497 0.2612097 0.4500214 0.02538561 0.5269512 0.8585265 0.2362692
## nTrueEmbeddings nForSim
## 59 5 171
## <<<<********>>>>
## [1] "Simulation: 60 rsqsym 0.241047524720244 rsqsgcca 0.154954811568022"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 60 0.2410475 0.06798344 0.1549548 0.02107654 0.1368409 0.4308373 0.1536706
## nTrueEmbeddings nForSim
## 60 5 378
## <<<<********>>>>
## [1] "Simulation: 61 rsqsym 0.518071641251794 rsqsgcca 0.478090567151587"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 61 0.5180716 0.3877688 0.4780906 0.0003069895 0.7889965 0.2945368 0.5370012
## nTrueEmbeddings nForSim
## 61 20 290
## <<<<********>>>>
## [1] "Simulation: 62 rsqsym 0.557764321435361 rsqsgcca 0.10709024086297"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 62 0.5577643 5.971027e-05 0.1070902 0.00227918 0.2928243 0.8788607 0.1882851
## nTrueEmbeddings nForSim
## 62 13 384
## <<<<********>>>>
## [1] "Simulation: 63 rsqsym 0.648632041269752 rsqsgcca 0.72597409027156"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 63 0.648632 0.631906 0.7259741 0.0003751725 0.7306326 0.4942561 0.4960944
## nTrueEmbeddings nForSim
## 63 21 426
## <<<<********>>>>
## [1] "Simulation: 64 rsqsym 0.261629099150799 rsqsgcca 0.0510543583554501"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 64 0.2616291 0.1212347 0.05105436 0.1689841 0.3259776 0.2503945 0.4200655
## nTrueEmbeddings nForSim
## 64 21 183
## <<<<********>>>>
## [1] "Simulation: 65 rsqsym 0.33514630699484 rsqsgcca 0.391080548520454"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 65 0.3351463 0.1598126 0.3910805 0.02243095 0.8581586 0.3279982 0.4257686
## nTrueEmbeddings nForSim
## 65 16 224
## <<<<********>>>>
## [1] "Simulation: 66 rsqsym 0.452828433636637 rsqsgcca 0.400317684596816"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 66 0.4528284 0.2112562 0.4003177 0.01879933 0.4530189 0.640667 0.4527265
## nTrueEmbeddings nForSim
## 66 17 506
## <<<<********>>>>
## [1] "Simulation: 67 rsqsym 0.499855707430381 rsqsgcca 0.543582395303469"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 67 0.4998557 0.3941403 0.5435824 4.119169e-06 0.1862677 0.5875123 0.4180602
## nTrueEmbeddings nForSim
## 67 24 418
## <<<<********>>>>
## [1] "Simulation: 68 rsqsym 0.520717639253581 rsqsgcca 0.393353301220279"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 68 0.5207176 0.4409409 0.3933533 0.01812426 0.4696518 0.2779817 0.2467748
## nTrueEmbeddings nForSim
## 68 19 435
## <<<<********>>>>
## [1] "Simulation: 69 rsqsym 0.512832801721864 rsqsgcca 0.428005383535426"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 69 0.5128328 0.3811938 0.4280054 0.007619002 0.1099845 0.5348248 0.5275168
## nTrueEmbeddings nForSim
## 69 8 326
## <<<<********>>>>
## [1] "Simulation: 70 rsqsym 0.434879113070005 rsqsgcca 0.52241607460703"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 70 0.4348791 0.2601868 0.5224161 0.06328212 0.6776801 0.647109 0.8815156
## nTrueEmbeddings nForSim
## 70 17 197
## <<<<********>>>>
## [1] "Simulation: 71 rsqsym 0.713879019022198 rsqsgcca 0.682346119437703"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 71 0.713879 0.6673374 0.6823461 0.01726109 0.3003894 0.2379569 0.2127435
## nTrueEmbeddings nForSim
## 71 25 285
## <<<<********>>>>
## [1] "Simulation: 72 rsqsym 0.464818367936637 rsqsgcca 0.330786782282328"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 72 0.4648184 0.0443791 0.3307868 0.004171204 0.3011837 0.4871177 0.6970519
## nTrueEmbeddings nForSim
## 72 15 430
## <<<<********>>>>
## [1] "Simulation: 73 rsqsym 0.556099477533113 rsqsgcca 0.534509309466627"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 73 0.5560995 0.2497581 0.5345093 0.003254804 0.8569064 0.3947365 0.4396441
## nTrueEmbeddings nForSim
## 73 8 308
## <<<<********>>>>
## [1] "Simulation: 74 rsqsym 0.468897181246393 rsqsgcca 0.384064993077656"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 74 0.4688972 0.2561163 0.384065 0.01297155 0.6702812 0.2161957 0.5101028
## nTrueEmbeddings nForSim
## 74 20 363
## <<<<********>>>>
## [1] "Simulation: 75 rsqsym 0.47657560341125 rsqsgcca 0.512149963257713"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 75 0.4765756 0.4724307 0.51215 0.003208978 0.7490435 0.7985777 0.1631237
## nTrueEmbeddings nForSim
## 75 19 257
## <<<<********>>>>
## [1] "Simulation: 76 rsqsym 0.484740753966208 rsqsgcca 0.581772650422497"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 76 0.4847408 0.3706199 0.5817727 0.001486698 0.6437605 0.4883076 0.4903955
## nTrueEmbeddings nForSim
## 76 18 345
## <<<<********>>>>
## [1] "Simulation: 77 rsqsym 0.274660577979467 rsqsgcca 0.0886396795793668"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 77 0.2746606 0.04884299 0.08863968 0.02827622 0.4233497 0.5933021 0.1258496
## nTrueEmbeddings nForSim
## 77 8 276
## <<<<********>>>>
## [1] "Simulation: 78 rsqsym 0.337247729840773 rsqsgcca 0.240153541495727"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 78 0.3372477 0.1660221 0.2401535 0.0006594788 0.1547818 0.1775583 0.4993309
## nTrueEmbeddings nForSim
## 78 13 377
## <<<<********>>>>
## [1] "Simulation: 79 rsqsym 0.534902291583144 rsqsgcca 0.531540284135714"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 79 0.5349023 0.3364088 0.5315403 0.0002734066 0.5654484 0.5645001 0.7428239
## nTrueEmbeddings nForSim
## 79 12 409
## <<<<********>>>>
## [1] "Simulation: 80 rsqsym 0.469426476485691 rsqsgcca 0.259295257499687"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 80 0.4694265 0.0290133 0.2592953 0.003683866 0.4462618 0.7851674 0.2694984
## nTrueEmbeddings nForSim
## 80 15 308
## <<<<********>>>>
## [1] "Simulation: 81 rsqsym 0.602546413922538 rsqsgcca 0.6270887366707"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 81 0.6025464 0.5587883 0.6270887 0.01644433 0.2400547 0.3223464 0.2583558
## nTrueEmbeddings nForSim
## 81 14 237
## <<<<********>>>>
## [1] "Simulation: 82 rsqsym 0.465727554022581 rsqsgcca 0.281301104245019"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 82 0.4657276 0.2911373 0.2813011 0.003478853 0.2712748 0.7504076 0.3170967
## nTrueEmbeddings nForSim
## 82 13 222
## <<<<********>>>>
## [1] "Simulation: 83 rsqsym 0.267359586921645 rsqsgcca 0.27749133701365"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 83 0.2673596 0.2636826 0.2774913 0.02320815 0.6055685 0.6917729 0.7518633
## nTrueEmbeddings nForSim
## 83 21 130
## <<<<********>>>>## Warning in sgccak(R, C, c1 = c1, scheme = scheme, init = init, bias = bias, :
## The SGCCA algorithm did not converge after 1000 iterations.## [1] "Simulation: 84 rsqsym 0.579423688488084 rsqsgcca 0.562166202930219"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 84 0.5794237 0.5869723 0.5621662 0.008638274 0.5766139 0.5075706 0.1269817
## nTrueEmbeddings nForSim
## 84 14 378
## <<<<********>>>>## Warning in sgccak(R, C, c1 = c1, scheme = scheme, init = init, bias = bias, :
## The SGCCA algorithm did not converge after 1000 iterations.## [1] "Simulation: 85 rsqsym 0.44064389897939 rsqsgcca 0.441601070309138"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 85 0.4406439 0.2444986 0.4416011 0.0009420033 0.609813 0.1514781 0.6292061
## nTrueEmbeddings nForSim
## 85 12 319
## <<<<********>>>>
## [1] "Simulation: 86 rsqsym 0.582115318301818 rsqsgcca 0.503980519434783"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 86 0.5821153 0.4446583 0.5039805 0.01902831 0.3358441 0.3240853 0.8426786
## nTrueEmbeddings nForSim
## 86 24 377
## <<<<********>>>>
## [1] "Simulation: 87 rsqsym 0.358174020368868 rsqsgcca 0.237756026328088"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 87 0.358174 0.1965243 0.237756 0.02127478 0.4697052 0.4237337 0.2751579
## nTrueEmbeddings nForSim
## 87 17 149
## <<<<********>>>>
## [1] "Simulation: 88 rsqsym 0.681483686714053 rsqsgcca 0.719837366483992"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 88 0.6814837 0.7052217 0.7198374 0.007010515 0.1529857 0.2631594 0.2922959
## nTrueEmbeddings nForSim
## 88 9 302
## <<<<********>>>>
## [1] "Simulation: 89 rsqsym 0.632347242931029 rsqsgcca 0.723562265811417"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 89 0.6323472 0.2954773 0.7235623 0.01481974 0.6562259 0.1322438 0.6857676
## nTrueEmbeddings nForSim
## 89 7 204
## <<<<********>>>>
## [1] "Simulation: 90 rsqsym 0.614529944164972 rsqsgcca 0.592271123229641"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 90 0.6145299 0.4240334 0.5922711 0.04900129 0.6310118 0.6484033 0.6847723
## nTrueEmbeddings nForSim
## 90 15 326
## <<<<********>>>>
## [1] "Simulation: 91 rsqsym 0.481029162474233 rsqsgcca 0.47162886101363"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 91 0.4810292 0.3279079 0.4716289 0.003818642 0.1137693 0.8786272 0.5353798
## nTrueEmbeddings nForSim
## 91 22 324
## <<<<********>>>>
## [1] "Simulation: 92 rsqsym 0.457007232072974 rsqsgcca 0.476281754919686"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 92 0.4570072 0.06712833 0.4762818 0.00131653 0.5576644 0.3941734 0.5302135
## nTrueEmbeddings nForSim
## 92 25 202
## <<<<********>>>>
## [1] "Simulation: 93 rsqsym 0.276010337516033 rsqsgcca 0.433679248222673"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 93 0.2760103 0.2630624 0.4336792 0.03900894 0.3560441 0.226927 0.5352436
## nTrueEmbeddings nForSim
## 93 13 294
## <<<<********>>>>
## [1] "Simulation: 94 rsqsym 0.624916032476443 rsqsgcca 0.668982247356921"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 94 0.624916 0.5782863 0.6689822 0.004602964 0.5291184 0.7492544 0.5367249
## nTrueEmbeddings nForSim
## 94 17 412
## <<<<********>>>>
## [1] "Simulation: 95 rsqsym 0.44396584676084 rsqsgcca 0.436839440780205"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 95 0.4439658 0.2711107 0.4368394 8.94108e-06 0.1295026 0.7203477 0.4332235
## nTrueEmbeddings nForSim
## 95 10 238
## <<<<********>>>>
## [1] "Simulation: 96 rsqsym 0.43938447159489 rsqsgcca 0.398062109699398"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 96 0.4393845 0.2148298 0.3980621 0.01016323 0.3888925 0.2550032 0.2558169
## nTrueEmbeddings nForSim
## 96 11 326
## <<<<********>>>>
## [1] "Simulation: 97 rsqsym 0.368261099338391 rsqsgcca 0.301835992177041"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 97 0.3682611 0.2737499 0.301836 0.01133582 0.2608804 0.2873599 0.7119718
## nTrueEmbeddings nForSim
## 97 13 181
## <<<<********>>>>
## [1] "Simulation: 98 rsqsym 0.560438879103046 rsqsgcca 0.566754553822022"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 98 0.5604389 0.4599721 0.5667546 0.01012596 0.4428944 0.2541065 0.3347575
## nTrueEmbeddings nForSim
## 98 10 313
## <<<<********>>>>
## [1] "Simulation: 99 rsqsym 0.706405169485256 rsqsgcca 0.494021558546621"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 99 0.7064052 0.5275812 0.4940216 0.05421854 0.5520611 0.6440624 0.1254326
## nTrueEmbeddings nForSim
## 99 10 337
## <<<<********>>>>
## [1] "Simulation: 100 rsqsym 0.609575699254108 rsqsgcca 0.393888924231565"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 100 0.6095757 0.2019161 0.3938889 0.00292468 0.5527685 0.856266 0.3965549
## nTrueEmbeddings nForSim
## 100 23 280
## <<<<********>>>>
## [1] "Simulation: 101 rsqsym 0.630187817439025 rsqsgcca 0.548861671617379"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 101 0.6301878 0.4970487 0.5488617 0.02163316 0.4105611 0.8063324 0.6630487
## nTrueEmbeddings nForSim
## 101 25 294
## <<<<********>>>>
## [1] "Simulation: 102 rsqsym 0.554808525578762 rsqsgcca 0.639175816961478"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 102 0.5548085 0.6054637 0.6391758 0.004152944 0.8525122 0.6505218 0.8316572
## nTrueEmbeddings nForSim
## 102 15 334
## <<<<********>>>>
## [1] "Simulation: 103 rsqsym 0.592739075146689 rsqsgcca 0.554842218037964"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 103 0.5927391 0.425402 0.5548422 0.05760645 0.5954883 0.6062012 0.8316034
## nTrueEmbeddings nForSim
## 103 20 257
## <<<<********>>>>
## [1] "Simulation: 104 rsqsym 0.315541504880694 rsqsgcca 0.395347060438571"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 104 0.3155415 0.2594474 0.3953471 0.002916099 0.4997567 0.4452579 0.4073715
## nTrueEmbeddings nForSim
## 104 24 292
## <<<<********>>>>
## [1] "Simulation: 105 rsqsym 0.523541079917334 rsqsgcca 0.501156946708329"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 105 0.5235411 0.2121226 0.5011569 0.02681065 0.5225104 0.3544439 0.8036832
## nTrueEmbeddings nForSim
## 105 14 217
## <<<<********>>>>
## [1] "Simulation: 106 rsqsym 0.415254757564255 rsqsgcca 0.454916790089812"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 106 0.4152548 0.213753 0.4549168 0.002384616 0.822649 0.43779 0.8917009
## nTrueEmbeddings nForSim
## 106 21 245
## <<<<********>>>>
## [1] "Simulation: 107 rsqsym 0.43444048653616 rsqsgcca 0.613984947392843"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 107 0.4344405 0.3700447 0.6139849 0.01098696 0.2662422 0.85 0.6465484
## nTrueEmbeddings nForSim
## 107 7 321
## <<<<********>>>>
## [1] "Simulation: 108 rsqsym 0.647637524135569 rsqsgcca 0.725311962828203"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 108 0.6476375 0.6252097 0.725312 0.003876096 0.5178112 0.7085239 0.686261
## nTrueEmbeddings nForSim
## 108 22 311
## <<<<********>>>>
## [1] "Simulation: 109 rsqsym 0.171822870681969 rsqsgcca 0.135051397560783"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 109 0.1718229 0.01966475 0.1350514 0.01571631 0.4445034 0.7832479 0.6515661
## nTrueEmbeddings nForSim
## 109 19 163
## <<<<********>>>>
## [1] "Simulation: 110 rsqsym 0.411885246266706 rsqsgcca 0.288982317370882"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 110 0.4118852 0.1305512 0.2889823 0.0001468147 0.635658 0.5320764 0.4454202
## nTrueEmbeddings nForSim
## 110 24 343
## <<<<********>>>>
## [1] "Simulation: 111 rsqsym 0.34924913486609 rsqsgcca 0.378644405525776"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 111 0.3492491 0.2684032 0.3786444 0.004289429 0.284206 0.150226 0.5085848
## nTrueEmbeddings nForSim
## 111 15 339
## <<<<********>>>>
## [1] "Simulation: 112 rsqsym 0.634579807399846 rsqsgcca 0.626592559497463"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 112 0.6345798 0.5214905 0.6265926 0.000298673 0.5591724 0.6889736 0.6090539
## nTrueEmbeddings nForSim
## 112 22 295
## <<<<********>>>>
## [1] "Simulation: 113 rsqsym 0.354559261029595 rsqsgcca 0.494927911559694"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 113 0.3545593 0.3148347 0.4949279 0.0007430371 0.1964909 0.5260146 0.4824141
## nTrueEmbeddings nForSim
## 113 15 331
## <<<<********>>>>
## [1] "Simulation: 114 rsqsym 0.237900155827878 rsqsgcca 0.315416751242309"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 114 0.2379002 0.2541153 0.3154168 0.02674227 0.5806778 0.2772731 0.357151
## nTrueEmbeddings nForSim
## 114 21 333
## <<<<********>>>>
## [1] "Simulation: 115 rsqsym 0.444482191722554 rsqsgcca 0.127296733404578"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 115 0.4444822 0.1861737 0.1272967 0.01287703 0.1475666 0.488095 0.5905698
## nTrueEmbeddings nForSim
## 115 7 371
## <<<<********>>>>## Warning in sgccak(R, C, c1 = c1, scheme = scheme, init = init, bias = bias, :
## The SGCCA algorithm did not converge after 1000 iterations.
## [1] "Simulation: 116 rsqsym 0.618043030090702 rsqsgcca 0.561956930511183"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 116 0.618043 0.5634997 0.5619569 0.03228521 0.6726812 0.6481071 0.2589203
## nTrueEmbeddings nForSim
## 116 16 372
## <<<<********>>>>
## [1] "Simulation: 117 rsqsym 0.495225633879678 rsqsgcca 0.509535722094019"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 117 0.4952256 0.5094449 0.5095357 0.02280156 0.1696539 0.5466123 0.5343067
## nTrueEmbeddings nForSim
## 117 20 366
## <<<<********>>>>
## [1] "Simulation: 118 rsqsym 0.0812364978925622 rsqsgcca 0.0132858716526127"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 118 0.0812365 0.01691603 0.01328587 0.05652837 0.3567169 0.2287202 0.388297
## nTrueEmbeddings nForSim
## 118 8 186
## <<<<********>>>>
## [1] "Simulation: 119 rsqsym 0.530636657395345 rsqsgcca 0.155943686123964"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 119 0.5306367 0.05070594 0.1559437 0.0001830088 0.2709615 0.2207935 0.3327085
## nTrueEmbeddings nForSim
## 119 25 149
## <<<<********>>>>
## [1] "Simulation: 120 rsqsym 0.476280990862383 rsqsgcca 0.596779951451762"
## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1 corrupt2 corrupt3
## 120 0.476281 0.3613531 0.59678 0.002363752 0.452771 0.7688931 0.8894699
## nTrueEmbeddings nForSim
## 120 14 298
## <<<<********>>>>Look over results, statistically
The r-squared value is most informative as it tells us how well the omnibus model predicts the known latent signal.
Compare SiMLR R\(^2\) vs. rgcca R\(^2\) with paired t-test.
print(t.test(simdatafrm[,"symRSQ"],simdatafrm[,"rgccaRSQ"],paired=T))##
## Paired t-test
##
## data: simdatafrm[, "symRSQ"] and simdatafrm[, "rgccaRSQ"]
## t = 12.008, df = 119, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.1192900 0.1664006
## sample estimates:
## mean of the differences
## 0.1428453Compare SiMLR R\(^2\) vs. sgcca R\(^2\) with paired t-test.
print(t.test(simdatafrm[,"symRSQ"],simdatafrm[,"sgccaRSQ"],paired=T))##
## Paired t-test
##
## data: simdatafrm[, "symRSQ"] and simdatafrm[, "sgccaRSQ"]
## t = 3.5184, df = 119, p-value = 0.0006158
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.01588906 0.05679416
## sample estimates:
## mean of the differences
## 0.03634161Compare SiMLR R\(^2\) vs. permuted SiMLR R\(^2\) with paired t-test.
print(t.test(simdatafrm[,"symRSQ"],simdatafrm[,"prmRSQ"],paired=T))##
## Paired t-test
##
## data: simdatafrm[, "symRSQ"] and simdatafrm[, "prmRSQ"]
## t = 38.655, df = 119, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.4515725 0.5003340
## sample estimates:
## mean of the differences
## 0.4759532Compare rgcca R\(^2\) vs. permuted SiMLR R\(^2\) with paired t-test.
print(t.test(simdatafrm[,"sgccaRSQ"],simdatafrm[,"prmRSQ"],paired=T))##
## Paired t-test
##
## data: simdatafrm[, "sgccaRSQ"] and simdatafrm[, "prmRSQ"]
## t = 27.9, df = 119, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.4084121 0.4708111
## sample estimates:
## mean of the differences
## 0.4396116mean performance
print( colMeans( simdatafrm ) )## symRSQ rgccaRSQ sgccaRSQ prmRSQ corrupt1
## 0.49118147 0.34833618 0.45483986 0.01522823 0.47281595
## corrupt2 corrupt3 nTrueEmbeddings nForSim
## 0.51951530 0.48067451 15.97500000 308.22500000Visualize overall results
simdatafrm = na.omit( simdatafrm )
myline = 1:nrow( simdatafrm )
plot( myline/max(myline), myline/max(myline), type='l', lty=5, main='Signal recovery comparison (r-squared): \n SiMLR vs RGCCA (blue triangle) and SGCCA (red x)', xlab='R-squared RGCCA and SGCCA', ylab='R-squared SiMLR' )
points( simdatafrm[,"rgccaRSQ"], simdatafrm[,"symRSQ"], col='blue', ylab='Rsq - SiMLR', xlab='Rsq - RGCCA', pch=2 )
points( simdatafrm[,"sgccaRSQ"], simdatafrm[,"symRSQ"], col='red', ylab='Rsq - SiMLR', xlab='Rsq - SGCCA', pch=4 )
Look at the effect of the corruption on the outcomes.
summary( lm( symRSQ ~ corrupt1 + corrupt2 + corrupt3 , data=simdatafrm))##
## Call:
## lm(formula = symRSQ ~ corrupt1 + corrupt2 + corrupt3, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39243 -0.06824 -0.00355 0.08362 0.28520
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.36171 0.04371 8.275 2.47e-13 ***
## corrupt1 0.09597 0.05346 1.795 0.0752 .
## corrupt2 0.11493 0.04955 2.319 0.0221 *
## corrupt3 0.05074 0.05373 0.944 0.3469
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1262 on 116 degrees of freedom
## Multiple R-squared: 0.0791, Adjusted R-squared: 0.05528
## F-statistic: 3.321 on 3 and 116 DF, p-value: 0.0223summary( lm( rgccaRSQ ~ corrupt1 + corrupt2 + corrupt3 , data=simdatafrm))##
## Call:
## lm(formula = rgccaRSQ ~ corrupt1 + corrupt2 + corrupt3, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37581 -0.10611 -0.00673 0.13422 0.45979
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.15431 0.05979 2.581 0.0111 *
## corrupt1 0.15602 0.07313 2.134 0.0350 *
## corrupt2 0.11140 0.06778 1.644 0.1030
## corrupt3 0.12979 0.07349 1.766 0.0800 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1726 on 116 degrees of freedom
## Multiple R-squared: 0.09001, Adjusted R-squared: 0.06648
## F-statistic: 3.825 on 3 and 116 DF, p-value: 0.01179summary( lm( sgccaRSQ ~ corrupt1 + corrupt2 + corrupt3 , data=simdatafrm))##
## Call:
## lm(formula = sgccaRSQ ~ corrupt1 + corrupt2 + corrupt3, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37958 -0.08963 0.01138 0.09209 0.38645
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.21803 0.05398 4.039 9.68e-05 ***
## corrupt1 0.16918 0.06602 2.562 0.01168 *
## corrupt2 0.11166 0.06120 1.825 0.07062 .
## corrupt3 0.20556 0.06635 3.098 0.00244 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1558 on 116 degrees of freedom
## Multiple R-squared: 0.1594, Adjusted R-squared: 0.1376
## F-statistic: 7.331 on 3 and 116 DF, p-value: 0.0001525Look at the effect of the number of subjects for the simulation on the outcomes.
summary( lm( symRSQ ~ nForSim, data=simdatafrm))##
## Call:
## lm(formula = symRSQ ~ nForSim, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.40165 -0.06715 0.00206 0.09119 0.23908
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3968428 0.0476503 8.328 1.69e-13 ***
## nForSim 0.0003061 0.0001499 2.042 0.0434 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1281 on 118 degrees of freedom
## Multiple R-squared: 0.03414, Adjusted R-squared: 0.02595
## F-statistic: 4.171 on 1 and 118 DF, p-value: 0.04335summary( lm( rgccaRSQ ~ nForSim, data=simdatafrm))##
## Call:
## lm(formula = rgccaRSQ ~ nForSim, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.38101 -0.11110 -0.00464 0.14838 0.35957
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.215177 0.065505 3.285 0.00134 **
## nForSim 0.000432 0.000206 2.097 0.03814 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1761 on 118 degrees of freedom
## Multiple R-squared: 0.03592, Adjusted R-squared: 0.02775
## F-statistic: 4.397 on 1 and 118 DF, p-value: 0.03814summary( lm( sgccaRSQ ~ nForSim, data=simdatafrm))##
## Call:
## lm(formula = sgccaRSQ ~ nForSim, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.42140 -0.10325 0.02626 0.11098 0.30883
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3362184 0.0616501 5.454 2.75e-07 ***
## nForSim 0.0003849 0.0001939 1.985 0.0495 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1657 on 118 degrees of freedom
## Multiple R-squared: 0.03231, Adjusted R-squared: 0.02411
## F-statistic: 3.939 on 1 and 118 DF, p-value: 0.04949Look at the effect of the number of bases for the simulation on the outcomes.
summary( lm( symRSQ ~ nTrueEmbeddings, data=simdatafrm))##
## Call:
## lm(formula = symRSQ ~ nTrueEmbeddings, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43070 -0.06493 0.01469 0.09909 0.24618
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.532748 0.035060 15.195 <2e-16 ***
## nTrueEmbeddings -0.002602 0.002066 -1.259 0.21
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1295 on 118 degrees of freedom
## Multiple R-squared: 0.01326, Adjusted R-squared: 0.004899
## F-statistic: 1.586 on 1 and 118 DF, p-value: 0.2104summary( lm( rgccaRSQ ~ nTrueEmbeddings, data=simdatafrm))##
## Call:
## lm(formula = rgccaRSQ ~ nTrueEmbeddings, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.35051 -0.13142 0.01237 0.14687 0.35164
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3603512 0.0485512 7.422 1.95e-11 ***
## nTrueEmbeddings -0.0007521 0.0028613 -0.263 0.793
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1793 on 118 degrees of freedom
## Multiple R-squared: 0.0005852, Adjusted R-squared: -0.007884
## F-statistic: 0.06909 on 1 and 118 DF, p-value: 0.7931summary( lm( sgccaRSQ ~ nTrueEmbeddings, data=simdatafrm))##
## Call:
## lm(formula = sgccaRSQ ~ nTrueEmbeddings, data = simdatafrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.46815 -0.07945 0.03686 0.11551 0.29056
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.508115 0.045323 11.211 <2e-16 ***
## nTrueEmbeddings -0.003335 0.002671 -1.249 0.214
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1674 on 118 degrees of freedom
## Multiple R-squared: 0.01304, Adjusted R-squared: 0.004674
## F-statistic: 1.559 on 1 and 118 DF, p-value: 0.2143Look at results via histogram
library( rtemis )
myMeth = paste0("SiMLR-mix-",mixingMethod,'-E-',energyType)
# Build dataset with different distributions
mdata <- data.frame(
method = rep( c(myMeth, "RGCCA", "SGCCA" ), each = nsims ),
value = c( simdatafrm[,1], simdatafrm[,2], simdatafrm[,3] )
)
mplot3.x( split( mdata$value, mdata$method ) )
ofn = paste0( '/results/simulation_energy', energyType, "_mix", mixingMethod, '.csv' )
if ( dir.exists( "/results/" ) ) write.csv( simdatafrm, ofn )library(viridis)
library(ggplot2)
library(dplyr)
library( psych )
opts <- options() # save old options
options(ggplot2.continuous.colour="viridis")
options(ggplot2.continuous.fill = "viridis")
theme_set(theme_minimal())
myMeth = paste0("SiMLR-mix-",mixingMethod,'-E-',energyType)
# Build dataset with different distributions
mdata <- data.frame(
method = rep( c(myMeth, "RGCCA", "SGCCA" ), each = nsims ),
value = c( simdatafrm[,1], simdatafrm[,2], simdatafrm[,3] )
)
histBy(mdata,"value","method",main='Signal Recovery Results: \n SiMLR (blue) vs rgcca (red) vs sgcca (green)' , xlab='RSQ')
viridis_qualitative_pal7 <- c("#440154FF", "#FDE725FF", "#443A83FF",
"#8FD744FF", "#31688EFF", "#35B779FF",
"#21908CFF")
p <- mdata %>%
ggplot( aes(x=value, fill=method, color = method )) +
geom_density( alpha=0.6, position = 'identity' ) +
theme(text = element_text(size = 20 )) + theme(legend.position="top") + scale_fill_manual( values = c("#440154FF","#FDE725FF", "#21908CFF"))
print( p )