Nowadays, enormous amounts of data are continuously generated not only in massive scale, but also from different, sometimes conflicting, views. Therefore, it is important to consolidate different concepts for intelligent decision making. For example, to predict the research areas of some people, the best results are usually achieved by combining and consolidating predictions obtained from the publication network, co-authorship network and the textual content of their publications. Multiple supervised and unsupervised hypotheses can be drawn from these information sources, and negotiating their differences and consolidating decisions usually yields a much more accurate model due to the diversity and heterogeneity of these models. In this paper, we address the problem of "consensus learning" among competing hypotheses, which either rely on outside knowledge (supervised learning) or internal structure (unsupervised clustering). We argue that consensus learning is an NP-hard problem and thus propose to solve it by an efficient heuristic method. We construct a belief graph to first propagate predictions from supervised models to the unsupervised, and then negotiate and reach consensus among them. Their final decision is further consolidated by calculating each model's weight based on its degree of consistency with other models. Experiments are conducted on 20 Newsgroups data, Cora research papers, DBLP author-conference network, and Yahoo! Movies datasets, and the results show that the proposed method improves the classification accuracy and the clustering quality measure (NMI) over the best base model by up to 10%. Furthermore, it runs in time proportional to the number of instances, which is very efficient for large scale data sets.