Researchers are regularly interested in interpreting the multipartite structure of data entities according to their functional relationships. Data is often heterogeneous with intricately hidden inner structure. With limited prior knowledge, researchers are likely to confront the problem of transforming this data into knowledge. We develop a new framework, called heat-passing, which exploits intrinsic similarity relationships within noisy and incomplete raw data, and constructs a meaningful map of the data. The proposed framework is able to rank, cluster, and visualize the data all at once. The novelty of this framework is derived from an analogy between the process of data interpretation and that of heat transfer, in which all data points contribute simultaneously and globally to reveal intrinsic similarities between regions of data, meaningful coordinates for embedding the data, and exemplar data points that lie at optimal positions for heat transfer. We demonstrate the effectiveness of the heat-passing framework for robustly partitioning the complex networks, analyzing the globin family of proteins and determining conformational states of macromolecules in the presence of high levels of noise. The results indicate that the methodology is able to reveal functionally consistent relationships in a robust fashion with no reference to prior knowledge. The heat-passing framework is very general and has the potential for applications to a broad range of research fields, for example, biological networks, social networks and semantic analysis of documents.