diff --git a/articles/neocortex.html b/articles/neocortex.html index 66b5fb3..888a0c5 100644 --- a/articles/neocortex.html +++ b/articles/neocortex.html @@ -201,7 +201,10 @@

Spatial and temporal dynamics# Visualization of F(.) p <- ggplot( data = FX_long, - aes(x = `Time period`, y = F, linetype = `Neocortex area`, colour = `Neocortex area`, group = `Neocortex area`) + aes( + x = `Time period`, y = F, + linetype = `Neocortex area`, colour = `Neocortex area`, group = `Neocortex area` + ) ) + geom_line(linewidth = 0.5) + ylab(NULL) + @@ -228,12 +231,12 @@

Spatial and temporal dynamicsGene set enrichment analysis 

-# Inferred gene factors (corresponding to the W matrix in the MFAI paper)
-gene_factors <- mfairObject@W
-rownames(gene_factors) <- colnames(mfairObject@Y) # Assign gene symbols
-colnames(gene_factors) <- paste("Factor", c(1:3))
-head(gene_factors)
-#>           Factor 1   Factor 2   Factor 3
+# Inferred gene loadings (corresponding to the W matrix in the MFAI paper)
+gene_loadings <- mfairObject@W
+rownames(gene_loadings) <- colnames(mfairObject@Y) # Assign gene symbols
+colnames(gene_loadings) <- paste("Loading", c(1:3))
+head(gene_loadings)
+#>          Loading 1  Loading 2  Loading 3
 #> DCUN1D2 -1.0973545  0.4754917 -0.4656467
 #> ARRB1    3.7897678  0.5357535  0.3688403
 #> PDE1B    0.1807732  3.1537712 -0.5730507
@@ -241,8 +244,8 @@ 
Gene set enrichment analysis#> TOX      1.6022312 -1.6211514 -1.7326521
 #> LOXHD1  -3.4764620  0.1372484  0.1020414
-# Heatmap of the inferred gene factors
-pheatmap::pheatmap(t(gene_factors),
+# Heatmap of the inferred gene loadings
+pheatmap::pheatmap(t(gene_loadings),
   scale = "column",
   clustering_method = "complete",
   cluster_row = FALSE, cluster_col = TRUE,
@@ -253,14 +256,14 @@ 
Gene set enrichment analysis= 12
 )

-

We first calculated the relative weight of the \(k\)-th factor for the \(m\)-th gene by \(\left| W_{mk} \right| / \sum_{k^{\prime}=1}^{3} +

We first calculated the relative weight of the \(k\)-th loading for the \(m\)-th gene by \(\left| W_{mk} \right| / \sum_{k^{\prime}=1}^{3} \left| W_{mk^{\prime}} \right|\), where \(W_{m \cdot} \in \mathbb{R}^{3 \times 1}\) -is the \(m\)-th row of gene factors, -and then selected the top 300 weighted genes in each factor to form the +is the \(m\)-th row of gene loadings, +and then selected the top 300 weighted genes in each loading to form the gene sets.

-# Normalize each factor to have l2-norm equal one
-gene_factors <- apply(gene_factors,
+# Normalize each loading to have l2-norm equal one
+gene_loadings <- apply(gene_loadings,
   MARGIN = 2,
   FUN = function(x) {
     x / sqrt(sum(x^2))
@@ -268,14 +271,14 @@ 
Gene set enrichment analysis)
 
 # Relative weight
-gene_factors <- abs(gene_factors)
-gene_factors <- gene_factors / rowSums(gene_factors)
+gene_loadings <- abs(gene_loadings)
+gene_loadings <- gene_loadings / rowSums(gene_loadings)
 
-M <- nrow(gene_factors)[1] # Total number of genes M = 2,000
-ntop <- M * 0.15 # We use the top 300 weighted genes in each factor to form the gene sets
+M <- nrow(gene_loadings)[1] # Total number of genes M = 2,000
+ntop <- M * 0.15 # We use the top 300 weighted genes in each loading to form the gene sets
 
 # Index of top genes
-top_gene_idx <- apply(gene_factors,
+top_gene_idx <- apply(gene_loadings,
   MARGIN = 2,
   FUN = function(x) {
     which(rank(-x) <= ntop)
@@ -285,18 +288,18 @@ 
Gene set enrichment analysistop_genes <- apply(top_gene_idx,
   MARGIN = 2,
   FUN = function(x) {
-    rownames(gene_factors)[x]
+    rownames(gene_loadings)[x]
   }
 )
-colnames(top_genes) <- paste("Factor", c(1:3))
+colnames(top_genes) <- paste("Loading", c(1:3))
 head(top_genes)
-#>      Factor 1  Factor 2 Factor 3
-#> [1,] "ARRB1"   "PDE1B"  "AJAP1" 
-#> [2,] "LOXHD1"  "PDE7B"  "KCNA3" 
-#> [3,] "TYRP1"   "KCNA2"  "ASTN2" 
-#> [4,] "PRKG1"   "PMP22"  "EMID1" 
-#> [5,] "MS4A8B"  "GPR155" "GPR52" 
-#> [6,] "FAM131B" "SMAD2"  "SEC24D"
+#> Loading 1 Loading 2 Loading 3 +#> [1,] "ARRB1" "PDE1B" "AJAP1" +#> [2,] "LOXHD1" "PDE7B" "KCNA3" +#> [3,] "TYRP1" "KCNA2" "ASTN2" +#> [4,] "PRKG1" "PMP22" "EMID1" +#> [5,] "MS4A8B" "GPR155" "GPR52" +#> [6,] "FAM131B" "SMAD2" "SEC24D"

Then we can conduct the gene set enrichment analysis based on Gene Ontology for each factor.