Complex networks play an important role in a plethora of disciplines in natural sciences. Cleaning up noisy observed networks, poses an important challenge in network analysis Existing methods utilize labeled data to alleviate the noise effect in the network. However, labeled data is usually expensive to collect while unlabeled data can be gathered cheaply. In this paper, we propose an optimization framework to mine useful structures from noisy networks in an unsupervised manner. The key feature of our optimization framework is its ability to utilize local structures as well as global patterns in the network. We extend our method to incorporate multi-resolution networks in order to add further resistance to high-levels of noise. We also generalize our framework to utilize partial labels to enhance the performance. We specifically focus our method on multi-resolution Hi-C data by recovering clusters of genomic regions that co-localize in 3D space. Additionally, we use Capture-C-generated partial labels to further denoise the Hi-C network. We empirically demonstrate the effectiveness of our framework in denoising the network and improving community detection results.