In the oncogenomics domain, there is an increasing interest and need for computational methodologies that harness multidimensional patient characterizations. These methods aim to decipher the growing availability and heterogeneity of omics and annotation data at our disposal. In this study, we propose a two-phase workflow designed for data integration and knowledge extraction, applied to the hot clinical topic of breast cancer subtyping and employing Non-negative Matrix Tri-Factorization (NMTF). This technique decomposes a non-negative data matrix into three lower-rank matrices for exploration and pattern discovery. Our NMTF-based innovative strategy jointly analysed association matrices of a multi-partite network including different omics data of breast cancer patients and their corresponding subtypes, and found a network reconstruction able to maximize correct patient-subtype predictions. Based on this optimized reconstruction, the workflow second stage builds subtype-specific subnetworks and latent representations of all their nodes to establish associations also between subtypes and involved omics data. Our approach can delve into latent patterns and intricate relationships spanning various input data within a multidimensional framework. Thus, it not only sheds fresh light on BRCA subtypes but also offers adaptability for analogous classification efforts on similar clinical issues.