Semi-supervised non-negative matrix factorization with weighted label propagation for data representation

Label propagation has been widely used to enhance performance for clustering. Many semi-supervised non-negative matrix factorization (NMF) methods based on label propagation have been proposed. However, these methods mainly pay attention to learning a label prediction matrix, neglecting the efficient learning of a low-dimensional representation of original data. Additionally, they lead to inconsistent structures with NMF when leveraging label constraints, compromising the learning performance for low-dimensional representation and basis matrix. To address these problems, this paper proposes a novel semi-supervised NMF method named semi-supervised non-negative matrix factorization with weighted label propagation (SNMFWLP). Firstly, SNMFWLP considers an orthogonal constraint on basis matrix to minimize the redundancy in the process of decomposition in NMF. Secondly, SNMFWLP introduces a weighted label propagation model into NMF to learn an efficient low-dimensional representation used as label prediction matrix. The weighted label propagation model not only propagates label information but also maintains the structures consistent with structures of NMF, beneficial to a consistent low-dimensional representation. Additionally, effective algorithm and convergence analysis are also presented. Finally, numerous experiments on real-world data sets are conducted to demonstrate the superiority of the proposed method in comparison to several state-of-the-art unsupervised and semi-supervised NMF methods. • A weighted label propagation is introduced, preserving consistent structures with NMF. • A semi-supervised NMF model is proposed for consistent low-dimensional representation. • Numerous experimental results demonstrate the superiority of the proposed method.