Details of our Motif Clustering Procedure 1 Bayesian Hierarchical Clustering Model

The data for each discovered motif is a count matrix Ni which can have different widths and number of counts compared to other TF motifs. Our clustering will be based on a motif matrices with a fixed width w, so we assume each of these n raw motif matrices should contain a submatrixYi, i = 1,..., n of dimension w×4 that will be considered the ”central motif ” upon which the clustering will be based. We include components for both within-motif and between-motif variability of the nucleotide countsYijk where i indexes the motif, j indexes the w columns within each motif, and k indexes the four possible nucleotides within each column. Within-motif level: Count matrices p(Yi|Θi) = w∏ j=1 p(Yij|θij) Yij = (yija,..., yijt) ∼ Multinomial(ni, θij = (θija,..., θijt)) Between-motif level: Frequency matrices p(Θi