simlr_interpretation
simlr_interpretation.RmdSimilarity-driven multi-view linear reconstruction
Introduction
Modern science generates data from multiple sources (e.g., genetics, imaging, behavior), yet integrating these ‘views’ to find a single, coherent underlying signal is a major statistical challenge. Similarity-driven multi-view linear reconstruction (SiMLR) addresses this by exploiting inter-modality relationships to transform large scientific datasets into a smaller joint space. The link between the original data () and the reduced embedding space is a sparse set of features ( ). Standard statistical tools may then be applied on the embeddings .
SiMLR may be used in a variety of other ways. We will cover a basic example and follow with different use cases. These examples are perhaps less involved than those given in the original publication’s cloud computing examples but illustrate new functionality.
Example: Applying SiMLR to Simulated Multi-View Data
In this section, we explore how SiMLR can be applied to multi-view datasets. We’ll generate synthetic data to simulate the application of SiMLR, compare the results to traditional methods like Singular Value Decomposition (SVD), and visualize the relationships between the views. This example derives from the simulation-based evaluation in the original paper.
Step 1: Simulate Multi-View Data
We begin by simulating three different views of data, each representing different modalities or datasets that share some underlying structure.
library(forcats)
library(ANTsR)
#> Warning: replacing previous import 'stats::filter' by 'dplyr::filter' when
#> loading 'ANTsR'
#> ANTsR 0.6.4
#>
#> Attaching package: 'ANTsR'
#> The following objects are masked from 'package:stats':
#>
#> sd, step, var
#> The following objects are masked from 'package:base':
#>
#> all, any, apply, max, min, prod, range, sum
library(reshape2)
set.seed(1500)
nsub <- 100 # Number of subjects/samples
npix <- c(100, 200, 133) # Number of features in each view
nk <- 5 # Number of latent factors
# Generating outcome matrices for each view
outcome <- matrix(rnorm(nsub * nk), ncol = nk)
outcome1 <- matrix(rnorm(nsub * nk), ncol = nk)
outcome2 <- matrix(rnorm(nsub * nk), ncol = nk)
outcome3 <- matrix(rnorm(nsub * nk), ncol = nk)
# Generating transformation matrices for each view
view1tx <- matrix(rnorm(npix[1] * nk), nrow = nk)
view2tx <- matrix(rnorm(npix[2] * nk), nrow = nk)
view3tx <- matrix(rnorm(npix[3] * nk), nrow = nk)
# Creating the multi-view data matrices
mat1 <- (outcome %*% t(outcome1) %*% (outcome1)) %*% view1tx
mat2 <- (outcome %*% t(outcome2) %*% (outcome2)) %*% view2tx
mat3 <- (outcome %*% t(outcome3) %*% (outcome3)) %*% view3tx
colnames(mat1)=paste0("m1.",1:ncol(mat1))
colnames(mat2)=paste0("m2.",1:ncol(mat2))
colnames(mat3)=paste0("m3.",1:ncol(mat3))
# Combine the matrices into a list
matlist <- list(m1 = mat1, m2 = mat2, m3 = mat3)
gsmd = generate_structured_multiview_data( nsub, npix,
k_shared=nk, k_specific=1, seed=0 )
matlist = gsmd$data_list
mat1 = gsmd$data_list[[1]]
mat2 = gsmd$data_list[[2]]
mat3 = gsmd$data_list[[3]]
outcome = gsmd$ground_truth[[1]]
outcome1 = gsmd$ground_truth[[2]]$View1In this code, mat1, mat2, and
mat3 represent three views of the data. Each view is
constructed to share a common underlying structure but with different
transformations applied.
A more complex data generation scheme is available in
generate_structured_multiview_data.
Step 2: Apply SiMLR
Now we apply the SiMLR algorithm to the simulated multi-view data to find a common representation across the views.
# Applying SiMLR
prepro=c( "centerAndScale","np")
constr='orthox0.02x1' # good default
result <- simlr(matlist,constraint=constr,scale=prepro,
mixAlg='pca', energyType='acc', # recommended
verbose=TRUE)
#>
#> --- Method Summary ---
#> • Mixer Algorithm : pca
#> • Energy Type : acc
#> • Sparseness Alg. : soft
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: bidirectional_lookahead
#> • domain-knowledge : 0
#> ----------------------
#>
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 0.9329915 0.8870375 0.7966900
#> Norm Weights: 0.933, 0.887, 0.797
#> Orth Weights: 0, 0, 0
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 2 | Energy: -0.3344 | Best.Energy: -0.3344 (at iter 2) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 3 | Energy: -0.5193 | Best.Energy: -0.5193 (at iter 3) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 8 | Energy: -0.5621 | Best.Energy: -0.5621 (at iter 8) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 10 | Energy: -0.6426 | Best.Energy: -0.6426 (at iter 10) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 12 | Energy: -0.6976 | Best.Energy: -0.6976 (at iter 12) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 17 | Energy: -0.7498 | Best.Energy: -0.7498 (at iter 17) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> ~~Convergence criteria met @ 68
#> No improvement over 10% of max iterations 50
#> ~~Converged at 16 iterations.
# Projecting data into the reduced space
p1 <- mat1 %*% (result$v[[1]])
p2 <- mat2 %*% (result$v[[2]])
p3 <- mat3 %*% (result$v[[3]])
# pheatmap::pheatmap( result$v[[1]], cluster_cols=F, cluster_rows=F )SiMLR identifies a sparse set of features that best reconstruct each
view, resulting in projections p1, p2, and
p3 for each view.
Step 3: Visualization and Comparison
To understand the effectiveness of the SiMLR projections, we can compare the correlations between the projections of different views. Additionally, we’ll compare the results to those obtained via Singular Value Decomposition (SVD).
# Calculate SVD for comparison
svd1 <- svd(mat1, nu = nk, nv = 0)$u
svd2 <- svd(mat2, nu = nk, nv = 0)$u
svd3 <- svd(mat3, nu = nk, nv = 0)$u
# Calculate correlations between the SiMLR projections
cor_p1_p2 <- range(cor(p1, p2))
cor_p1_p3 <- range(cor(p1, p3))
cor_p2_p3 <- range(cor(p2, p3))
# Compare with correlations from SVD
cor_svd1_svd2 <- range(cor(svd1, svd2))
# Print the results
cat("Correlation between p1 and p2:", cor_p1_p2, "\n")
#> Correlation between p1 and p2: -0.7029881 0.8777331
cat("Correlation between p1 and p3:", cor_p1_p3, "\n")
#> Correlation between p1 and p3: -0.53927 0.8316805
cat("Correlation between p2 and p3:", cor_p2_p3, "\n")
#> Correlation between p2 and p3: -0.3277606 0.8645039
cat("Correlation between SVD1 and SVD2:", cor_svd1_svd2, "\n")
#> Correlation between SVD1 and SVD2: -0.7306001 0.6777956Visualizing Correlations
Visualizing these correlations helps us understand the similarity between the views after the SiMLR transformation.
library(ggplot2)
# Function to plot correlation heatmaps
plot_cor_heatmap <- function(mat1, mat2, title) {
cor_mat <- abs(cor(mat1,mat2))
ggplot(melt(cor_mat), aes(Var1, Var2, fill = value)) +
geom_tile() +
scale_fill_gradient2(midpoint = 0.5, low = "blue", high = "red", mid = "white") +
theme_minimal() +
labs(title = title, x = "Variables", y = "Variables") +
coord_fixed()
}
# Plotting the correlations
plot_cor_heatmap(p1, p2, "Correlation Heatmap of p1-p2")
plot_cor_heatmap(p1, p3,"Correlation Heatmap of p1-p3")
plot_cor_heatmap(p2, p3, "Correlation Heatmap of p2-p3")
These heatmaps show how the reduced representations from SiMLR correlate within each view. Comparing these with similar plots for SVD will reveal whether SiMLR captures more meaningful relationships between the views.
Step 4: Permutation Test
A permutation test can assess whether the observed correlations are significant.
s1 <- sample(1:nsub)
s2 <- sample(1:nsub)
permMats=list(vox = mat1, vox2 = mat2[s1, ], vox3 = mat3[s2, ])
resultp <- simlr(permMats,constraint=constr,scale=prepro,
mixAlg='pca', energyType='acc', # recommended
verbose=TRUE)
#>
#> --- Method Summary ---
#> • Mixer Algorithm : pca
#> • Energy Type : acc
#> • Sparseness Alg. : soft
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: bidirectional_lookahead
#> • domain-knowledge : 0
#> ----------------------
#>
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> vox vox2 vox3
#> 3.072983 1.177631 8.308016
#> Norm Weights: 3.073, 1.178, 8.308
#> Orth Weights: 0, 0, 0
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 2 | Energy: -0.3439 | Best.Energy: -0.3439 (at iter 2) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 3 | Energy: -0.6163 | Best.Energy: -0.6163 (at iter 3) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> It: 4 | Energy: -1.1187 | Best.Energy: -1.1187 (at iter 4) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> It: 8 | Energy: -1.2509 | Best.Energy: -1.2509 (at iter 8) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> It: 12 | Energy: -1.4077 | Best.Energy: -1.4077 (at iter 12) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 32 | Energy: -1.5345 | Best.Energy: -1.5345 (at iter 32) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 48 | Energy: -1.7944 | Best.Energy: -1.7944 (at iter 48) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> It: 57 | Energy: -1.8224 | Best.Energy: -1.8224 (at iter 57) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
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#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .bidirectional_linesearch(V_current = V_current, descent_direction =
#> search_direction, : Bidirectional line search failed to find a suitable step
#> size in either direction.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .bidirectional_linesearch(V_current = V_current, descent_direction =
#> search_direction, : Bidirectional line search failed to find a suitable step
#> size in either direction.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> It: 83 | Energy: -1.8894 | Best.Energy: -1.8894 (at iter 83) | Ortho: 0.0000
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> Warning in .robust_backtracking_linesearch(V_current = V_current,
#> descent_direction = -descent_direction, : Robust line search failed to find a
#> suitable step size; possibly at local minimum or numerical issue.
#> ~~Convergence criteria met @ 134
#> No improvement over 10% of max iterations 50
#> ~~Converged at 82 iterations.
p1p <- mat1 %*% (resultp$v[[1]])
p2p <- mat2[s1, ] %*% (resultp$v[[2]])
p3p <- mat3[s2, ] %*% (resultp$v[[3]])
# Compare the permuted correlations
cor_p1p_p2p <- range(cor(p1p, p2p))
cor_p1p_p3p <- range(cor(p1p, p3p))
cor_p2p_p3p <- range(cor(p2p, p3p))
# Print permuted results
cat("Permuted Correlation between p1p and p2p:", cor_p1p_p2p, "\n")
#> Permuted Correlation between p1p and p2p: -0.4449884 0.4524357
cat("Permuted Correlation between p1p and p3p:", cor_p1p_p3p, "\n")
#> Permuted Correlation between p1p and p3p: -0.4693403 0.4408695
cat("Permuted Correlation between p2p and p3p:", cor_p2p_p3p, "\n")
#> Permuted Correlation between p2p and p3p: -0.5197852 0.4801599The permutation test will show if the observed correlations are stronger than those expected by chance.
This introductory example demonstrates how SiMLR can uncover the shared structure across multiple views of data. The correlations between the projections indicate the degree to which the algorithm has captured this shared structure, and the permutation test serves as a validation step.
Integration of Multiple Data Types via Dimensionality Reduction
SiMLR is particularly useful when working with datasets from different modalities (e.g., genomics, proteomics, and imaging data). By finding a joint embedding space, SiMLR can integrate these diverse data types into a unified representation, facilitating downstream analyses such as clustering, classification, or regression.
When dealing with high-dimensional data, dimensionality reduction techniques are often required to make the data more manageable and to avoid issues like the curse of dimensionality. SiMLR provides an approach that not only reduces dimensionality but also maintains the relationships between different views of the data, making it a powerful tool for exploratory data analysis and visualization. Below, we illustrate reading, writing and exploratory integrated visualization.
library(fpc)
library(cluster)
library(gridExtra)
library(ggpubr)
sim2nm=tempfile()
write_simlr_data_frames( result$v, sim2nm )
simres2=read_simlr_data_frames( sim2nm, names(matlist) )
popdf = data.frame( age = outcome, cog=outcome1, mat1, mat2, mat3 )
temp2=apply_simlr_matrices( popdf, simres2, center=TRUE, scale=TRUE )
simnames=temp2[[2]]
zz=exploratory_visualization( temp2[[1]][,simnames[1:4]], dotsne=FALSE )
print( zz$plot )
Now we can icorporate the “modalities” in order to predict the simulated outcome matrix. Note that contributions exist from each modality in the regression (in some cases). This is one of the advantages of SiMLR: it provides systematic guidance for building these types of integrative models.
# multi-view regression
summary( lm( age.1 ~ View1PC1 + View2PC1 + View3PC1, data=temp2[[1]] ))
#>
#> Call:
#> lm(formula = age.1 ~ View1PC1 + View2PC1 + View3PC1, data = temp2[[1]])
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.209548 -0.055564 -0.005481 0.064010 0.233397
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.002580 0.008185 -0.315 0.75326
#> View1PC1 -0.107701 0.039207 -2.747 0.00718 **
#> View2PC1 -0.327959 0.052230 -6.279 9.87e-09 ***
#> View3PC1 0.269772 0.065353 4.128 7.80e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.08185 on 96 degrees of freedom
#> Multiple R-squared: 0.3564, Adjusted R-squared: 0.3363
#> F-statistic: 17.72 on 3 and 96 DF, p-value: 3.113e-09
summary( lm( age.2 ~ View1PC1 + View2PC1 + View3PC1, data=temp2[[1]] ))
#>
#> Call:
#> lm(formula = age.2 ~ View1PC1 + View2PC1 + View3PC1, data = temp2[[1]])
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.14289 -0.05913 0.00078 0.04666 0.19685
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.005101 0.007391 -0.690 0.492
#> View1PC1 0.170772 0.035406 4.823 5.30e-06 ***
#> View2PC1 -0.219208 0.047166 -4.648 1.07e-05 ***
#> View3PC1 -0.042624 0.059016 -0.722 0.472
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.07391 on 96 degrees of freedom
#> Multiple R-squared: 0.4742, Adjusted R-squared: 0.4577
#> F-statistic: 28.85 on 3 and 96 DF, p-value: 2.19e-13
summary( lm( age.3 ~ View1PC1 + View2PC1 + View3PC1, data=temp2[[1]] ))
#>
#> Call:
#> lm(formula = age.3 ~ View1PC1 + View2PC1 + View3PC1, data = temp2[[1]])
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.276583 -0.049161 0.005662 0.051539 0.233027
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.006146 0.008204 -0.749 0.456
#> View1PC1 0.243021 0.039297 6.184 1.52e-08 ***
#> View2PC1 0.035423 0.052350 0.677 0.500
#> View3PC1 -0.301835 0.065503 -4.608 1.25e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.08204 on 96 degrees of freedom
#> Multiple R-squared: 0.3514, Adjusted R-squared: 0.3312
#> F-statistic: 17.34 on 3 and 96 DF, p-value: 4.479e-09
summary( lm( age.4 ~ View1PC1 + View2PC1 + View3PC1, data=temp2[[1]] ))
#>
#> Call:
#> lm(formula = age.4 ~ View1PC1 + View2PC1 + View3PC1, data = temp2[[1]])
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.130174 -0.029903 0.003014 0.027864 0.107905
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.0002726 0.0045419 0.060 0.95226
#> View1PC1 -0.1382882 0.0217562 -6.356 6.94e-09 ***
#> View2PC1 0.0369849 0.0289825 1.276 0.20500
#> View3PC1 -0.1187168 0.0362646 -3.274 0.00148 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.04542 on 96 degrees of freedom
#> Multiple R-squared: 0.802, Adjusted R-squared: 0.7958
#> F-statistic: 129.6 on 3 and 96 DF, p-value: < 2.2e-16
summary( lm( age.5 ~ View1PC1 + View2PC1 + View3PC1, data=temp2[[1]] ))
#>
#> Call:
#> lm(formula = age.5 ~ View1PC1 + View2PC1 + View3PC1, data = temp2[[1]])
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.183167 -0.062915 0.002871 0.052293 0.233107
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.005220 0.009028 0.578 0.5645
#> View1PC1 0.074145 0.043246 1.715 0.0897 .
#> View2PC1 -0.185996 0.057610 -3.229 0.0017 **
#> View3PC1 0.132766 0.072084 1.842 0.0686 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.09028 on 96 degrees of freedom
#> Multiple R-squared: 0.2154, Adjusted R-squared: 0.1909
#> F-statistic: 8.784 on 3 and 96 DF, p-value: 3.326e-05Sparse Feature Selection
SiMLR incorporates sparse feature selection, allowing users to identify a minimal subset of features that contribute most to the joint embedding space. This can be particularly advantageous in settings where interpretability is crucial, such as biomarker discovery in biological datasets.
pp=plot_features( simres2 )
grid.arrange( grobs=pp, nrow=3, top='Joint features' )
Improved Model Interpretability
By projecting the data into a joint space, SiMLR helps improve the interpretability of machine learning models. The sparse feature selection ensures that only the most informative features are retained, making it easier to understand the relationships between the input data and the model’s predictions.
Cross-Modal Prediction or Imputation
In scenarios where you have multiple data modalities but missing information scattered across some of the views, SiMLR can be used to impute the missing data by leveraging the relationships between the available modalities. This cross-modal prediction capability is particularly useful in multi-omics studies and other fields where complete data is often unavailable.
popdfi=popdf
proportion <- 0.25
num_NAs <- ceiling(proportion * nrow(popdfi) * ncol(popdfi))
indices <- arrayInd(sample(1:(nrow(popdfi) * ncol(popdfi)), num_NAs), .dim = dim(popdfi))
popdfi[indices] <- NA
nms=names(simres2)
nsimx=3
sep='.'
imputedcols=c()
for ( n in nms ) {
for ( v in 1:nsimx ) {
thiscol=paste0(n,sep,v)
if ( any( is.na( popdfi[,thiscol] ) )) {
imputedcols=c(imputedcols,thiscol)
popdfi = simlr_impute( popdfi, nms, v, n, separator=sep )
}
}
}
impresult=data.frame( og=popdf[,imputedcols[1]], imp=popdfi[,imputedcols[1]])
ggscatter( impresult, 'og', 'imp' ) + ggtitle(paste("Imputed vs original data",imputedcols[1]))
#> Warning: Removed 5 rows containing missing values or values outside the scale range
#> (`geom_point()`).
Testing Significance of Joint Relationships
We use a metric (rvcoef) that is not directly optimized
to assess the significance of the simlr result versus permuted data. The
RV coefficient is analogous to the Pearson correlation coefficient but
is used for comparing two matrices (or datasets) rather than two
variables. It measures the similarity of the column spaces (subspaces)
spanned by the columns of two matrices. We compute the
rvcoef across all pairs of data at each permutation and
compare to the original values. Another alternative
(diagcorr) is also possible.
diagcorr = function( X,Y ) mean(abs(diag(cor(X,Y))))
initu = initializeSimlr( matlist, 3, jointReduction = TRUE )
np=40
myperm = simlr.perm( matlist,
energyType='regression',
constraint=constr,scale=prepro,
initialUMatrix=initu,
iterations=500,
nperms=np, FUN=adjusted_rvcoef, verbose=TRUE )
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.119373 7.110481 4.533551
#> Norm Weights: 3.119, 7.11, 4.534
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.605873 6.779412 4.728773
#> Norm Weights: 3.606, 6.779, 4.729
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3338 | Best.Energy: 0.3338 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.353512 7.632748 4.766009
#> Norm Weights: 3.354, 7.633, 4.766
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3338 | Best.Energy: 0.3338 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.410867 6.940708 4.881424
#> Norm Weights: 3.411, 6.941, 4.881
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.341475 7.113242 4.824803
#> Norm Weights: 3.341, 7.113, 4.825
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.380806 7.024959 4.455000
#> Norm Weights: 3.381, 7.025, 4.455
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3338 | Best.Energy: 0.3338 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.388814 6.750244 4.824568
#> Norm Weights: 3.389, 6.75, 4.825
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.410218 7.498827 4.221164
#> Norm Weights: 3.41, 7.499, 4.221
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.309547 7.008600 4.136867
#> Norm Weights: 3.31, 7.009, 4.137
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.413913 6.734840 4.554724
#> Norm Weights: 3.414, 6.735, 4.555
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.412406 6.629812 4.469787
#> Norm Weights: 3.412, 6.63, 4.47
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.454967 6.794718 4.806324
#> Norm Weights: 3.455, 6.795, 4.806
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.516603 7.188520 4.269432
#> Norm Weights: 3.517, 7.189, 4.269
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3337 | Best.Energy: 0.3337 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.795535 7.276929 4.988741
#> Norm Weights: 3.796, 7.277, 4.989
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.258633 7.093432 4.817820
#> Norm Weights: 3.259, 7.093, 4.818
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3336 | Best.Energy: 0.3336 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.538885 6.698644 4.981111
#> Norm Weights: 3.539, 6.699, 4.981
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.474009 7.101863 4.404884
#> Norm Weights: 3.474, 7.102, 4.405
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.294782 7.213067 4.652329
#> Norm Weights: 3.295, 7.213, 4.652
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.310270 7.213983 4.204553
#> Norm Weights: 3.31, 7.214, 4.205
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.828284 6.933832 4.567220
#> Norm Weights: 3.828, 6.934, 4.567
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3341 | Best.Energy: 0.3341 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.286339 6.814044 4.566057
#> Norm Weights: 3.286, 6.814, 4.566
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.612617 7.127943 4.629671
#> Norm Weights: 3.613, 7.128, 4.63
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.796653 7.260534 4.189594
#> Norm Weights: 3.797, 7.261, 4.19
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3337 | Best.Energy: 0.3337 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.235175 7.772221 4.534052
#> Norm Weights: 3.235, 7.772, 4.534
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.245054 7.019586 4.219374
#> Norm Weights: 3.245, 7.02, 4.219
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.358093 7.260168 4.647634
#> Norm Weights: 3.358, 7.26, 4.648
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.142433 6.790014 4.688565
#> Norm Weights: 3.142, 6.79, 4.689
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.118724 7.227603 4.536603
#> Norm Weights: 3.119, 7.228, 4.537
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.567306 6.719840 4.518456
#> Norm Weights: 3.567, 6.72, 4.518
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 2.952451 6.593536 4.711115
#> Norm Weights: 2.952, 6.594, 4.711
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.484742 7.161973 4.377775
#> Norm Weights: 3.485, 7.162, 4.378
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.689624 6.922378 4.391847
#> Norm Weights: 3.69, 6.922, 4.392
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.281339 6.625239 4.658988
#> Norm Weights: 3.281, 6.625, 4.659
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.778171 7.041370 4.535378
#> Norm Weights: 3.778, 7.041, 4.535
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3338 | Best.Energy: 0.3338 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.505156 7.056561 4.030072
#> Norm Weights: 3.505, 7.057, 4.03
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3334 | Best.Energy: 0.3334 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.798113 6.909903 4.452740
#> Norm Weights: 3.798, 6.91, 4.453
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3336 | Best.Energy: 0.3336 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.687441 7.024452 4.316078
#> Norm Weights: 3.687, 7.024, 4.316
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.404762 6.801764 4.879154
#> Norm Weights: 3.405, 6.802, 4.879
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.459896 7.185760 4.710103
#> Norm Weights: 3.46, 7.186, 4.71
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3333 | Best.Energy: 0.3333 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.530403 7.037199 4.103779
#> Norm Weights: 3.53, 7.037, 4.104
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3338 | Best.Energy: 0.3338 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
#>
#> --- Method Summary ---
#> • Mixer Algorithm : svd
#> • Energy Type : regression
#> • Sparseness Alg. : NA
#> • expBeta : 0
#> • constraint : ortho
#> • constraint-it : 1
#> • constraint-wt : 0.02
#> • optimizationStyle: adam
#> • domain-knowledge : 0
#> ----------------------
#>
#> Setting adaptive orthogonality/energy weights based on first few iterations...
#> [1] "Setting adaptive orthogonality/energy weights based on first few iterations..."
#> Domain Weights: 1, 1, 1
#> View1 View2 View3
#> 3.694944 7.026537 4.801269
#> Norm Weights: 3.695, 7.027, 4.801
#> Orth Weights: 0, 0, 0
#> It: 2 | Energy: 0.3335 | Best.Energy: 0.3335 (at iter 2) | Ortho: 0.0000
#> ~~Convergence criteria met @ 53
#> No improvement over 10% of max iterations 50
#> --Did not converge after 53 iterations.
print( tail( myperm$significance, 2 ) )
#> n perm rvcoef_View1_View2 rvcoef_View1_View3 rvcoef_View2_View3
#> 42 3 ttest 223.4201 168.7521 150.6077
#> 43 3 pvalue 0.0000 0.0000 0.0000
gglist = list()
simlrmaps=colnames(myperm$significance)[-c(1:2)]
for ( xxx in simlrmaps ) {
pvec=myperm$significance[ myperm$significance$perm %in% as.character(1:np),xxx]
original_tstat <- myperm$significance[1,xxx] # replace with actual value
gglist[[length(gglist)+1]]=( visualize_permutation_test( pvec, original_tstat, xxx ) )
}
grid.arrange( grobs=gglist, top='Cross-modality relationships: permutation tested')
# display simlr results
gglist2=list()
for ( i in 1:(length(matlist)-1)) {
for ( j in ((i+1):length(matlist))) {
toviz1=data.matrix(simres2[[i]])
toviz2=data.matrix(simres2[[j]])
temp=visualize_lowrank_relationships( matlist[[i]], matlist[[j]],
toviz1, toviz2,
nm1=names(matlist)[i], nm2=names(matlist)[j] )$plot
gglist2[[length(gglist2)+1]]=temp
}
}
grid.arrange(grobs=(gglist2),nrow=1, top='Low-rank correlations: SiMLR')
Evaluating Machine Learning Objective Functions
This section of the tutorial vignette provides an example of how to
set up and run a parameter search using the simlr.search function. Here,
csearch contains a list of constraint options that include
“none” and different options for enforcing orthogonality in the
feature space. This list will be used to explore different
constraint options during the parameter search.
In this step, the simlr.parameters function is called to create a
parameter list (simparms) that will control the grid
search. Each parameter category (e.g., nsimlr_options,
prescaling_options, etc.) is provided with options as a
list. These parameters specify the settings and constraints that will be
explored during the optimization process.
nsimlr_options: The number of latent factors to consider.prescaling_options: Methods for data scaling/preprocessing (robust, whiten, np).objectiver_options: The objective function used (eg regression or cca).mixer_options: The mixing technique (ica or pca).sparval_options: Sparseness settings.expBeta_options: Exponential smoothing parameter beta values. e.g. 0.0, 0.9, 0.99, 0.999.positivities_options: Positivity constraints.optimus_options: The optimization strategy (lineSearch, mixed, greedy).constraint_options: Feature space orthogonality constraints to apply.search_type: The type of search to perform (full indicates a full grid search).num_samples: The number of samples to evaluate during the search.
paster <- function(vec1, vec2) {
paste0(rep(vec1, each = length(vec2)), vec2)
}
csearch = list( "orthox0x0", "orthox0.002x1")
# the 10x10 are weights on the optimization term of the energy
simparms = simlr.parameters(
nsimlr_options = list( 2 ),
prescaling_options = list(
c( "centerAndScale", "np"), c( "center", "np") ),
objectiver_options = list('acc','normalized_correlation','lrr',"regression"),
mixer_options=list( 'pca' , 'ica'),
sparval_options=list( c(0.5,0.5,0.5) ), # less relevant if orthowt > 0
expBeta_options = list( c(0.0) ),
positivities_options = list(
c("positive","positive","positive")),
optimus_options=list( "adam", 'adagrad', 'nadam' ),
constraint_options=csearch,
search_type="full", # full or random
num_samples=5
)The regularizeSimlr function is used to apply
regularization to the input matrices matlist. Regularization can help
prevent overfitting by penalizing complexity. The fraction and sigma
parameters control the extent and type of regularization.
regs = regularizeSimlr(matlist, fraction=0.05,
sigma=rep(1.5,length(matlist)))
plot( image( regs[[1]] ) )
The simlr.search function performs the grid search over
the parameter space defined in simparms. It takes the
matrices matlist and regs as input. The nperms specifies
the number of permutations to evaluate for robustness. The
verbose parameter controls the level of detail in the
output during the search process.
simlrXs=simlr.search(
matlist,
regs=regs,
simparms,
maxits=500,
nperms=10, # just fast for vignette
verbose=1
)
#> Running 96 parameter sets sequentially...
# simlrXs$paramsearchFinally, simlrXs$paramsearch retrieves the results of
the parameter search. This will show the performance of different
parameter combinations, helping to identify the optimal settings for the
SiMLR algorithm. The “best” result here will have the highest value for
final_energy and its parameters are stored in the
parameters slot.
#>
#> Attaching package: 'dplyr'
#> The following object is masked from 'package:gridExtra':
#>
#> combine
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
Path modeling
SIMLR has a path modeling variant that lets you build the graph of connections however you like. Call the matrices A, B and C. If you build: A=>A, B=>B, C=>C then you will learn within-modality feature sets. If you build A=>(B,C), B=>A, C=>A then you will “focus” on A. The default graph is A=>(B,C), B=>(A,C), C=>(A,B) ]