Clustering is a fundamental and important step in many image processing tasks, such as face recognition and image segmentation. The performance of clustering can be largely enhanced if relevant weak supervision information is appropriately exploited. To achieve this goal, in this paper, we propose the Compound Weakly Supervised Clustering (CSWC) method. Concretely, CSWC incorporates two types of widely available and easily accessed weak supervision information from the label and feature aspects, respectively. To be specific, at the label level, the pairwise constraints are utilized as a kind of typical weak label supervision information. At the feature level, the partial instances collected from multiple perspectives have internal consistency and they are regarded as weak structure supervision information. To achieve a more confident clustering partition, we learn a unified graph with its similarity matrix to incorporate the above two types of weak supervision. On one hand, this similarity matrix is constructed by self-expression across the partial instances collected from multiple perspectives. On the other hand, the pairwise constraints, i.e., must-links and cannot-links, are considered by formulating a regularizer on the similarity matrix. Finally, the clustering results can be directly obtained according to the learned graph, without performing additional clustering techniques. Besides evaluating CSWC on 7 benchmark datasets, we also apply it to the application of face clustering in video data since it has vast application potentiality. Experimental results demonstrate the effectiveness of our algorithm in both incorporating compound weak supervision and identifying faces in real applications.