•In this study, we propose a learning framework to identify the interactive genes based on multi-omics data, which is important to explore multiple related genes within the same co-expression network influences the manifestation of a phenotype.•We integrate different omics based on their similarities and apply spectral clustering to identify cancer subtypes. We measure the similarity in different omics based on shared neighbors, which is more comparable between omics since different omics have different data distributions.•The interactive genes for each cancer subtype are detected by learning the dense subgraphs embedded in the gene co-expression networks. The results by systematic gene ontology enrichment analysis show that different cancer subtypes exhibit distinct gene co-expression networks and interactive gene groups with different functional enrichment. Recent advances in multi-omics databases offer the opportunity to explore complex systems of cancers across hierarchical biological levels. Some methods have been proposed to identify the genes that play a vital role in disease development by integrating multi-omics. However, the existing methods identify the related genes separately, neglecting the gene interactions that are related to the multigenic disease. In this study, we develop a learning framework to identify the interactive genes based on multi-omics data including gene expression. Firstly, we integrate different omics based on their similarities and apply spectral clustering for cancer subtype identification. Then, a gene co-expression network is construct for each cancer subtype. Finally, we detect the interactive genes in the co-expression network by learning the dense subgraphs based on the L1 prosperities of eigenvectors in the modularity matrix. We apply the proposed learning framework on a multi-omics cancer dataset to identify the interactive genes for each cancer subtype. The detected genes are examined by DAVID and KEGG tools for systematic gene ontology enrichment analysis. The analysis results show that the detected genes have relationships to cancer development and the genes in different cancer subtypes are related to different biological processes and pathways, which are expected to yield important references for understanding tumor heterogeneity and improving patient survival.