  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.
