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.

Examining potential drug-target interactions (DTIs) is a pivotal component of drug discovery and repurposing. Recently, there has been a significant rise in the use of computational techniques to predict DTIs. Nevertheless, previous investigations have predominantly concentrated on assessing either the connections between nodes or the consistency of the network's topological structure in isolation. Such one-sided approaches could severely hinder the accuracy of DTI predictions. In this study, we propose a novel method called TTGCN, which combines heterogeneous graph convolutional neural networks (GCN) and graph attention networks (GAT) to address the task of DTI prediction. TTGCN employs a two-tiered feature learning strategy, utilizing GAT and residual GCN (R-GCN) to extract drug and target embeddings from the diverse network, respectively. These drug and target embeddings are then fused through a mean-pooling layer. Finally, we employ an inductive matrix completion technique to forecast DTIs while preserving the network's node connectivity and topological structure. Our approach demonstrates superior performance in terms of area under the curve and area under the precision-recall curve in experimental comparisons, highlighting its significant advantages in predicting DTIs. Furthermore, case studies provide additional evidence of its ability to identify potential DTIs.

In this correspondence, we study the minimal eigenvalues of a class of block-tridiagonal matrices from telecommunication system analysis. We present an eigenvalue analysis for two-user systems and efficient estimates for m-user systems.