Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace clustering algorithm that seeks to represent each point as a sparse convex combination of a few nearby points. We then extend the algorithm to constrained clustering and active learning settings. Our motivation for developing such a framework stems from the fact that typically either a small amount of labelled data is available in advance; or it is possible to label some points at a cost. The latter scenario is typically encountered in the process of validating a cluster assignment. Extensive experiments on simulated and real data sets show that the proposed approach is effective and competitive with state-of-the-art methods.