Fig. 1

a Schematic overview of PathExpSurv. The basic architecture of the neural network consists 3 layers (gene layer, pathway layer and output layer). The connection between the gene layer and the pathway layer is determined by the pathway mask matrix, in which number 1 (black) means a non-penalized link representing a fixed relationship between gene and pathway in prior information, number 1 (grey) means a penalized link representing a possible relationship to be explored, and number 0 (white) means no link. The training scheme of PathExpSurv includes two phases, namely pre-training phase and training phase. In the pre-training phase, the prior pathway mask (M) is used to pre-train the model to achieve a relatively high and stable performance. In the training phase, a specific fully connected mask (\(\textbf{E}\)) with prior links and \(L_1\)-penalized non-prior links is used to train the model to explore the unknown space and obtain the expanded pathways. b Pipeline of pathway expansion. We first randomly chose 90% samples from the dataset to train the PathExpSurv model, and repeated 100 times to obtain the weight matrices between the gene layer and the pathway layer \(\textbf{W}_1^{(k)}\) \((k=1,\ldots ,100)\). Then we transformed these matrices into binary matrices \(\textbf{O}^{(k)}\) \((k=1,\ldots ,100)\), and calculated the occurrence probability matrix \(\textbf{S}\) based on these binary matrices. Finally we obtained the expanded pathways matrix \(\textbf{R}\) by filtering out the gene-pathway pairs with small occurrence probabilities