Nonnegative Matrix Factorization (NMF), as a group representation learning model, produces part-based representation with interpretable features that can be applied to various problems, such as data clustering. The findings indicate that the NMF model with divergence ( -NMF) performs excellently in clustering different data types and noise assumptions. However, existing NMF-based data clustering methods are defined within a latent decoder model, lacking a verification mechanism. Recently, self-representation techniques have been applied to a wide range of tasks, empowering models to autonomously learn and verify representations that faithfully reflect the intricacies and nuances inherent in their input data. This paper proposes a self-representation factorization model for data clustering that incorporates local information into its learning process. The Regularized Encoder-Decoder NMF model based on divergence ( -REDNMF) integrates encoder and decoder factorizations into a cost function that mutually verify and refine each other, resulting in the formation of more distinct clusters. To incorporate the local information into the method, we add a graph regularization to the model. The -REDNMF, owing to its autoencoder-like architecture and utilization of local information, produces more informative word embeddings with generalization abilities that apply to various data types. We present an efficient and effective optimization algorithm based on multiplicative update rules to solve the proposed unified model. The experimental results on the ten well-known datasets show that the proposed -REDNMF model outperforms other state-of-the-art data clustering methods.
