  Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering
high-dimensional data points lying in a union of low-dimensional subspaces.
However, while $\ell_1$ optimization-based SSC algorithms suffer from high
computational complexity, other variants of SSC, such as Orthogonal Matching
Pursuit-based SSC (OMP-SSC), lose clustering accuracy in pursuit of improving
time efficiency. In this letter, we propose a novel Active OMP-SSC, which
improves clustering accuracy of OMP-SSC by adaptively updating data points and
randomly dropping data points in the OMP process, while still enjoying the low
computational complexity of greedy pursuit algorithms. We provide heuristic
analysis of our approach, and explain how these two active steps achieve a
better tradeoff between connectivity and separation. Numerical results on both
synthetic data and real-world data validate our analyses and show the
advantages of the proposed active algorithm.
