Fig. 1

MMGAT method. (A) The first layer of MMGAT initializes embeddings \({h}_{sim}\left(k\left(\cdot \right)\right)\) and \({h}_{co}\left(k\left(\cdot \right)\right)\) for k-mer nodes \({\text{k}}\left(\cdot \right)\) in similarity and coexisting subgraphs, respectively. It employs an attention mechanism to independently learn k-mer embeddings \({E}_{sim}\left(k\left(\cdot \right)\right)\) and \({E}_{co}\left(k\left(\cdot \right)\right)\) in both subgraphs. Subsequently these two kinds of k-mer embeddings are input to the second layer to learn inclusive-similarity and inclusive-coexisting attention coefficients in inclusive subgraphs respectively. Then these two types of attention coefficients and two types of k-mer embeddings are aggregated as the embedding of sequence nodes. Finally, the sequence embeddings are input to the fully connected layer to predict TFBSs. (B) MMGAT finds k-mer seeds based on inclusive-similarity and inclusive-coexisting attention coefficients learned in the second layer, and then finds TFBSs of multiple lengths based on coexisting probabilities