We consider the problem of subspace clustering using the SSC (Sparse Subspace Clustering) approach, which has several desirable theoretical properties and has been shown to be effective in various computer vision applications.We develop a large scale distributed framework for the computation of SSC via an alternating direction method of multiplier (ADMM) algorithm. The proposed framework solves SSC in column blocks and only involves parallel multivariate Lasso regression subproblems and sample-wise operations. This appealing property allows us to allocate multiple cores/machines for the processing of individual column blocks.We evaluate our algorithm on a shared-memory architecture. Experimental results on real-world datasets confirm that the proposed block-wise ADMM framework is substantially more efficient than its matrix counterpart used by SSC,without sacrificing accuracy. Moreover, our approach is directly applicable to decentralized neighborhood selection for Gaussian graphical models structure estimation.