Algorithm 3: Reordering algorithm, REA

1 Input: $R\in {\mathbb{R}}^{8\times N}$, $l$ level of taxonomy 2 Output: $\hat{R}$, rearranged matrix $R$ 3 $\hat{R}$ $\leftarrow \varphi$ 4 Annotate: R in level l: $b_1,b_2,\dots ,b_N$ 5 $C_{l,1},\dots ,C_{l,k}$ $\leftarrow Dendrogram(b_1,b_2,\dots ,b_N)$ 6 Temp $\leftarrow \varphi$ 7 for Cluster in $C_{l,1},\dots ,C_{l,k}$ do 8 for taxa in Cluster do 9 Append taxa column to Temp if $l<8$ then 10 Temp $\leftarrow REA(Temp,l+1)$ 11 Append Temp to $\hat{R}$ 12 return $\hat{R}$