Consider that matrix trace lasso regularized convex ℓ -norm with p= 1, 2 regression methods usually have the higher computational complexity due to the singular value decomposition (SVD) of larger size matrix in big data and information processing. By factoring the matrix trace lasso into the squared sum of two Frobenius-norm, this work studies the solutions of both adaptive sparse representation (ASR) and correlation adaptive subspace segmentation (CASS), respectively. Meanwhile, the derived models involve multi-variable nonconvex functions with at least two equality constraints. To solve them efficiently, we devise the nonconvex alternating direction multiplier methods (NADMM) with convergence analysis satisfying the Karush-Kuhn-Tucher (KKT) conditions. Finally, numerical experiments to the subspace clustering can show the less timing consumptions than CASS and the nearby performance of our proposed method when compared with the existing segmentation methods like SSC, LRR, LSR and CASS.