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.