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When utilising non-negative matrix factorisation (NMF) to decompose a data matrix into the product of two low-rank matrices with non-negative entries, the noisy components of data may be introduced into the matrix. Many approaches have been proposed to address the problem. Different from them, the authors consider the group sparsity and the geometric structure of data by introducing ℓ 2, 1-norm and local structure preserving regularisation in the formulated objective function. A graph regularised sparse NMF de-noising approach is proposed to learn discriminative representations for the original data. Since the non-differentiability of ℓ 2, 1-norm increases the computational cost, they propose an effective iterative multiplicative update algorithm to solve the objective function by using the Frobenius-norm of transpose coefficient matrix. Experimental results on facial image datasets demonstrate the superiority of the proposed approach over several state-of-the-art approaches.