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Comparing the Heatmaps for Original and Knockoff Sample Taxa Matrices

We demonstrate the ability of zinck to capture the compositional and highly sparse nature of microbiome count data by comparing the heatmaps of the original sample taxa matrix \(\mathbf{X}\) with its high quality knockoff copy, \(\tilde{\mathbf{X}}\).

The CRC dataset contain \(574\) subjects (\(290\) CRC cases and \(284\) controls) and \(849\) gut bacterial species. Our analysis focuses on \(401\) species with an average relative abundance greater than \(0.2\) across all subjects. Then, we consider a toy setting with \(20\) randomly selected samples and \(30\) randomly selected CRC taxa at the species level. The sample library sizes vary between \(17\) and \(4588\), within an average library size of \(1329\). The zero-inflation level in the original sample taxa matrix is \(0.51\).


load("/Users/Patron/Documents/zinck research/count.RData") 
norm_count <- count/rowSums(count)
col_means <- colMeans(norm_count > 0)
indices <- which(col_means > 0.2)
sorted_indices <- indices[order(col_means[indices], decreasing=TRUE)]
dcount <- count[,sorted_indices][,1:400]

set.seed(123) 
selected_rows <- sample(1:nrow(dcount), 20)     ## Randomly select 20 subjects
selected_cols <- sample(1:ncol(dcount),30)      ## Randomly select 30 taxa
X <- dcount[selected_rows,selected_cols]      ## Resulting OTU matrix of dimensions 20*30

Next, we fit the ZIGD-augmented LDA model which is inbuilt within the fit.zinck function of the zinck package, and then use the posterior estimates of the latent parameters to generate the knockoff copy.


model_zinck <- fit.zinck(X, num_clusters=13, method="ADVI", seed=2, boundary_correction = TRUE,prior_ZIGD = TRUE)
Theta <- model_zinck$theta
Beta <- model_zinck$beta
X_zinck <- generateKnockoff(X,Theta,Beta,seed=2)

We will now visualize the heatmaps of the original matrix and its corresponding knockoff copy. The draw.heatmap function applies an arcsinh transformation to the data for normalization and better visualization of abundance patterns and zero inflation within the sample taxa matrix. Note that, before displaying the heatmaps, we sort the taxa in decreasing order of average sparsity among all the subjects.

rownames(X_zinck) <- rownames(X)
draw.heatmap <- function(X, title = "") {
  reshape2::melt(asinh(X)) %>%
    dplyr::rename(sample = Var1, taxa = Var2, asinh.abun = value) %>%
    ggplot2::ggplot(., aes(x = taxa, y = sample, fill = asinh.abun)) +
    ggplot2::geom_tile() +
    ggplot2::theme_bw() +
    ggplot2::ggtitle(title) +
    ggplot2::labs(fill = "arcsinh\nabundance") +
    ggplot2::theme(
      plot.title = element_text(hjust = 0.5, size = 24),  # Increase font size here
      axis.title.x = element_blank(),
      axis.title.y = element_blank(),
      axis.text.x = element_text(size = 3, angle = 90),
      axis.text.y = element_text(size = 4)
    ) +
    viridis::scale_fill_viridis(discrete = FALSE, direction = -1, na.value = "grey") +
    theme(
      axis.title.x = element_blank(),
      axis.text.x = element_blank(),
      axis.ticks.x = element_blank(),
      axis.title.y = element_blank(),
      axis.text.y = element_blank(),
      axis.ticks.y = element_blank(),
      panel.grid.major = element_blank(),
      panel.grid.minor = element_blank(),
      panel.background = element_blank(),
      panel.border = element_blank(),
      legend.position = "none"
    ) +
    ggplot2::coord_fixed(ratio = 1)  # Fixing the aspect ratio
}

# Calculate the sparsity of each column for the Original OTU matrix
sparsity1 <- apply(X, 2, function(col) 1 - mean(col > 0))
sparsity2 <- apply(X_zinck, 2, function(col) 1 - mean(col > 0))

# Order the matrices by decreasing sparsity
X <- X[, order(sparsity1, decreasing = FALSE)]
X_zinck <- X_zinck[, order(sparsity2, decreasing = FALSE)]

heat1 <- draw.heatmap(X, "Original taxon count matrix")
heat2 <- draw.heatmap(X_zinck, "Zinck knockoff copy")
plot_grid(heat1, heat2, ncol = 2, align="v")

Version Author Date
d4297f5 ghoshstats 2024-12-12
22a846b Patron 2024-06-19
51a584c Patron 2024-06-18

It is evident from the above heatmaps that the knockoff copy depicts most of the features corresponding to the original matrix, in terms of zero-inflation and compositionality. This underscores the fact that the knockoff copy preserves the underlying structure of the observed sample taxa count matrix.


sessionInfo()
R version 4.1.3 (2022-03-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur/Monterey 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] cowplot_1.1.1        randomForest_4.7-1.1 gridExtra_2.3       
 [4] glmnet_4.1-7         Matrix_1.5-1         reshape2_1.4.4      
 [7] ggplot2_3.4.2        zinLDA_0.0.0.9000    dplyr_1.1.2         
[10] knockoff_0.3.6       zinck_0.0.0.9000    

loaded via a namespace (and not attached):
 [1] viridis_0.6.5        sass_0.4.6           jsonlite_1.8.5      
 [4] viridisLite_0.4.2    splines_4.1.3        foreach_1.5.2       
 [7] bslib_0.5.0          RcppParallel_5.1.7   StanHeaders_2.21.0-7
[10] highr_0.10           stats4_4.1.3         yaml_2.3.7          
[13] pillar_1.9.0         lattice_0.21-8       glue_1.6.2          
[16] digest_0.6.31        promises_1.2.0.1     colorspace_2.1-0    
[19] htmltools_0.5.5      httpuv_1.6.11        plyr_1.8.8          
[22] pkgconfig_2.0.3      rstan_2.21.8         scales_1.2.1        
[25] processx_3.8.1       whisker_0.4.1        later_1.3.1         
[28] git2r_0.32.0         tibble_3.2.1         generics_0.1.3      
[31] farver_2.1.1         cachem_1.0.8         withr_2.5.0         
[34] cli_3.6.1            survival_3.5-5       magrittr_2.0.3      
[37] crayon_1.5.2         evaluate_0.21        ps_1.7.5            
[40] fs_1.6.2             fansi_1.0.4          pkgbuild_1.4.2      
[43] tools_4.1.3          loo_2.6.0            prettyunits_1.1.1   
[46] lifecycle_1.0.3      matrixStats_0.63.0   stringr_1.5.0       
[49] munsell_0.5.0        callr_3.7.3          compiler_4.1.3      
[52] jquerylib_0.1.4      rlang_1.1.1          grid_4.1.3          
[55] iterators_1.0.14     rstudioapi_0.14      rmarkdown_2.22      
[58] gtable_0.3.3         codetools_0.2-19     inline_0.3.19       
[61] DBI_1.1.3            R6_2.5.1             knitr_1.43          
[64] fastmap_1.1.1        utf8_1.2.3           workflowr_1.7.1     
[67] rprojroot_2.0.3      shape_1.4.6          stringi_1.7.12      
[70] parallel_4.1.3       Rcpp_1.0.10          vctrs_0.6.5         
[73] tidyselect_1.2.0     xfun_0.39