<p>Non-negative matrix factorization (NMF) is a dimensionality reduction technique based on matrix factorization used to find linear representations of non-negative data based on latent features. Because NMF ignores the local geometric structure between the original objects, the latent feature representation obtained by NMF cannot represent the distance relationship between objects in the observable feature space. In this paper, we propose the maximum entropy non-negative matrix factorization (MENMF) to adjust the distance relationship of latent feature representation extracted by NMF from two aspects of enhancing the correlation of neighboring points and reducing the correlation of separated points, so as to restore the local geometric structure of the data. In addition, we add a sparse constraint to MENMF and propose the maximum entropy non-negative matrix factorization under sparse constraint (MENMFSC), which enhances the ability of latent features to represent the original objects. Finally, the proposed method is applied to clustering, and the applicability and effectiveness of the proposed method are proved by experiments.</p>