More details of the encoder, generator, and discriminator

Encoder In the similarity eigenvectors, each lncRNA contains the similarity information and position information of all other lncRNAs. Likewise, each disease contains information about the similarity and position of all the other diseases. As mentioned above, the BiGAN encoder is one of the two parts of an auto-encoder. The main functions of the encoder are to compress data, eliminate noise, and learn the features of the latent space. We take the similarity feature vectors of the samples as input so that the encoder can fully learn the parameters of the similarity vectors. In this way, the encoder can effectively map the data points into the latent feature space. The structure of BiGAN encoder is shown in Fig. ​Fig.7A.7A. The encoder is composed of three fully connected layers of the neural network. We can compute the output of each layer with the following formula:

where x denotes the similarity features of lncRNA-disease pairs. WE and bE represent the encoder weights and bias, respectively.

The structure of encoder, generator, and discriminator

The dimension of the similarity eigenvectors between the lncRNA and disease will be compressed into a low-dimensional vector after passing through each layer in the encoder. A trained encoder can predict the feature representations of data by capturing semantic attributes. The dense information of compressed low-dimensional vectors is more conducive to learning the mapping relationship of the latent space. To mine the representation of latent space more effectively, we decided to set the number of neurons in the final layer to 100. We employed ReLU as the activation function in the BiGAN model, and it can be defined as follows:

In addition, the encoder will randomly sample noise z in distribution PE(Z|X)=σ(Z-E(X)) and output latent features E(x) during training. Ultimately, we can obtain many data pairs (x, E(x)).

Generator In most generative adversarial network(GAN) models, the role of the generator is to learn the features of the original data and generate new data based on the learned characteristics. However, in the BiGAN model, the generator takes randomly sampled noise as input. As shown in Fig. ​Fig.7B,7B, the generator is similar to the encoder in that it has the same network structure. The output of the generator is calculated as follows:

where z is the feature of the latent space. WG and bG denote the weights and bias of the generator, respectively.

However, each layer in the generator increases the dimension of the potential representation and the final output dimension is the same as the original similarity feature vector dimension. Next, the representation with noise is decoded by the generator, and new lncRNA-disease associations are generated. Then, we can obtain a series of data pairs(G(z),z).

Discriminator The two data pairs mentioned above are taken as inputs to fool the discriminator. The discriminator discrimines whether the input data are real. If the discriminator thinks the data pairs come from the encoder, will be set as 1. If the discriminator thinks data pairs come from the generator, it will be set as 0. The structure of the discriminator is shown in Fig. ​Fig.7C,7C, where the sigmoid function is defined as follows:

where θ is the input of the sigmoid function.

The BiGAN encoder has a strong representation learning ability to learn the latent association between lncRNAs and diseases. The BiGAN generator will extract the features of the joint data and latent space to generate new lncRNA—disease associations. Finally, z=E(G(z)) and x=G(E(x)) are determined through a union probability distribution to arrive at a bidirectional structure. And you can see the concrete proof in the study of Jeff et al. According to our experiment, the BiGAN is an unsupervised feature learning model with strong robustness and representational learning ability. Compared with other computing models, the BiGAN performs remarkably well.