Clustering is an active research topic in the field of machine learning. Weakly supervised learning is an important research direction in semi-supervised learning, which has wide range of application scenarios. In the research of clustering and weakly supervised learning, it is proposed that a framework of weakly supervised learning is based on k labeled samples. Firstly, the framework expands labeled samples by clustering and clustering confidence level. Secondly, the energy function of the restricted Boltzmann machine is improved, and a learning model of the restricted Boltzmann machine based on k labeled samples is proposed. Finally, the model of ratiocination and algorithm are proposed. In order to test the framework and the model, a series of public data sets are chosen for comparative experiments. The experimental results show that the proposed weakly supervised learning framework based on k labeled samples is more effective.