Yaotang Li

Some new sufficient conditions ensuring that the $k$-subdirect sum of strictly diagonally dominant matrices and Nekrasov matrices is in the class of Nekrasov matrices are given. These sufficient conditions are different from those in [Electron. J. Linear Algebra, 38:339-346, 2022] and [Linear Multilinear Algebra, 64:208-218, 2016; 72:1044-1055, 2023]. In addition, some examples are given to illustrate the conditions presented.

NONNEGATIVE matrix factorization (NMF) is an effective technique for dimensionality reduction of high-dimensional data for tasks such as machine learning and data visualization. However, for practical clustering tasks, traditional NMF ignores the manifold information of both the data space and feature space, as well as the discriminative information of the data. In this paper, we propose a semisupervised NMF called dual-graph-regularization-constrained nonnegative matrix factorization with label discrimination (DCNMFLD). DCNMFLD combines dual graph regularization and prior label information as additional constraints, making full use of the intrinsic geometric and discriminative structures of the data, and can efficiently enhance the discriminative and exclusionary nature of clustering and improve the clustering performance. The evaluation of the clustering experimental results on four benchmark datasets demonstrates the effectiveness of our new algorithm.

One of the most common diseases among women of reproductive age is bacterial vaginosis (BV). However, the etiology of BV remains unknown. In this study, we modeled the temporal sample of the vaginal microbiome as a network and investigated the relationship between the network edges and BV. Furthermore, we used feature selection algorithms including decision tree (DT) and ReliefF (RF) to select the network feature edges associated with BV and subsequently validated these feature edges through logistic regression (LR) and support vector machine (SVM). The results show that: machine learning can distinguish vaginal community states (BV, ABV, SBV, and HEA) based on a few feature edges; selecting the top five feature edges of importance can achieve the best accuracy for the feature selection and classification model; the feature edges selected by DT outperform those selected by RF in terms of classification algorithm LR and SVM, and LR with DT feature edges is more suitable for diagnosing BV; two feature selection algorithms exhibit differences in the importance of ranking of edges; the feature edges selected by DT and RF cannot construct sub-network associated with BV. In short, the feature edges selected by our method can serve as indicators for personalized diagnosis of BV and aid in the clarification of a more mechanistic interpretation of its etiology.