Fig. 1

Flowchart of Capsule-LPI. a Multimodal feature extraction. The figure shows the feature extraction process of one LncRNA–protein pair. Firstly, sequence features, motif information, physicochemical properties and secondary structure features of the lncRNA and protein are extracted, respectively. The same groups of features of lncRNA and protein are concatenated respectively, yielding four feature vectors. \(F_1\)–\(F_4\) stands for sequence features, motif information, physicochemical properties and secondary structure features, respectively. Note that the dimensions of the four feature vectors are not the same. b The architecture of Capsule-LPI. The architecture of Capsule-LPI is divided into two parts, the first part is four different feature-learning subnetworks for four feature vectors, each subnetwork consists of fully connected layers. The second part is one capsule network. \(F_1\)–\(F_4\) are feature vectors, refer to sequence feature, motif information, physicochemical properties and secondary structure, respectively. First, each feature vector passes through its own feature learning subnetwork to get a three-dimensional output vector. Then the output vectors are treated as capsules and obtain \(U_1\)–\(U_4\). \(U_1\)–\(U_4\) include diversified information with prediction by each feature. \(W_1\)–\(W_4\) are transformation matrices. They are able to transform \(U_1\)–\(U_4\) into the same prediction space and they are the only parameters learned through backpropagation in the second part. \(U'_1\)–\(U'_4\) represent the predictions of different features in the same prediction space. Next, add \(U'_1\)–\(U'_4\) to get a new capsule. Using the “squashing” activation function to compress the length of the new capsule to a range from 0 to 1 to get the final Capsule V. Then take the length of V to represent the final prediction result, with lengths greater than 0.5 as interactions and lengths less than 0.5 as no interactions. Note that \(U_1\)–\(U_4\), \(U'_1\)–\(U'_4\) and V are essentially vectors; we call them “capsules” because they are the units of capsule network