As the amount of information in the actual application increases, security has become a crucial problem for people. Since security requirements continue to improve, biometrics has been widely studied in recent years. Consider the limitation of traditional security authentication such as performance degradation and system vulnerabilities, an unsupervised model may be more suitable for practical applications. In this paper, we proposed a novel elasticity network-based subspace clustering model for security authentication. Our approach combines ridge regression model with representation coefficient sparsity to construct an elasticity network. Then, we design an iterative numerical scheme with augmented Lagrangian multiplier to solve the objective function, and all variables are alternately solved to satisfy optimization. We evaluate our proposed security authentication model on two public face and handwriting datasets. The experimental results demonstrate that our approach outperforms other comparison methods.