Non-negative matrix factorization (NMF) has become one of the most powerful methods for clustering and feature selection. However, the performance of the traditional NMF method severely degrades when the data contain noises and outliers or the manifold structure of the data is not taken into account. In this article, a novel method called correntropy-based hypergraph regularized NMF (CHNMF) is proposed to solve the above problem. Specifically, we use the correntropy instead of the Euclidean norm in the loss term of CHNMF, which will improve the robustness of the algorithm. And the hypergraph regularization term is also applied to the objective function, which can explore the high-order geometric information in more sample points. Then, the half-quadratic (HQ) optimization technique is adopted to solve the complex optimization problem of CHNMF. Finally, extensive experimental results on multi-cancer integrated data indicate that the proposed CHNMF method is superior to other state-of-the-art methods for clustering and feature selection.

Non-negative Matrix Factorization (NMF) is a dimensionality reduction approach for learning a parts-based and linear representation of non-negative data. It has attracted more attention because of that. In practice, NMF not only neglects the manifold structure of data samples, but also overlooks the priori label information of different classes. In this paper, a novel matrix decomposition method called Hyper-graph regularized Constrained Non-negative Matrix Factorization (HCNMF) is proposed for selecting differentially expressed genes and tumor sample classification. The advantage of hyper-graph learning is to capture local spatial information in high dimensional data. This method incorporates a hyper-graph regularization constraint to consider the higher order data sample relationships. The application of hyper-graph theory can effectively find pathogenic genes in cancer datasets. Besides, the label information is further incorporated in the objective function to improve the discriminative ability of the decomposition matrix. Supervised learning with label information greatly improves the classification effect. We also provide the iterative update rules and convergence proofs for the optimization problems of HCNMF. Experiments under The Cancer Genome Atlas (TCGA) datasets confirm the superiority of HCNMF algorithm compared with other representative algorithms through a set of evaluations.

Cardamonin (CAD) is a member of the aromatic ketones family that is closely related to anti-bacterial, anti-inflammatory and anti-cancer effects. Nevertheless, the physiological function of cardamonin in chronic colitis and colon cancer has not been well verified. We found that cardamonin treatment alleviates intestinal disease, including recurring colitis and colitis-associated tumorigenesis, along with the reduced secretion of IL-1β and TNF-α. Further, cardamonin inhibits cell viability and inflammation factors of colorectal cancer cells in vitro. In tumor cells, the inhibitory effect of cardamonin on cell proliferation is closely related to decreased phosphorylation of signal transducers and activators of transcription (STAT) signals. This study reveals the crucial role of cardamonin in sustaining gastrointestinal homeostasis and offers a new strategy for colon cancer therapy.

Cancer genomic data contain views from different sources that provide complementary information about genetic activity. This provides a new way for cancer research. Feature selection and multi-view clustering are hot topics in bioinformatics, and they can make full use of complementary information to improve the effect. In this paper, a novel integrated model called Multi-view Non-negative Matrix Factorization (MvNMF) is proposed for the selection of common differential genes (co-differential genes) and multi-view clustering. In order to encode the geometric information in the multi-view genomic data, graph regularized MvNMF (GMvNMF) is further proposed by applying the graph regularization constraint in the objective function. GMvNMF can not only obtain the potential shared feature structure and shared cluster group structure, but also capture the manifold structure of multi-view data. The validity of the proposed GMvNMF method was tested in four multi-view genomic data. Experimental results showed that the GMvNMF method has better performance than other representative methods.

Background: Deciphering spatial domains using spatially resolved transcriptomics (SRT) is of great value for characterizing and understanding tissue architecture. However, the inherent heterogeneity and varying spatial resolutions present challenges in the joint analysis of multimodal SRT data. Results: We introduce a multimodal geometric deep learning method, named stMMR, to effectively integrate gene expression, spatial location, and histological information for accurate identifying spatial domains from SRT data. stMMR uses graph convolutional networks and a self-attention module for deep embedding of features within unimodality and incorporates similarity contrastive learning for integrating features across modalities. Conclusions: Comprehensive benchmark analysis on various types of spatial data shows superior performance of stMMR in multiple analyses, including spatial domain identification, pseudo-spatiotemporal analysis, and domain-specific gene discovery. In chicken heart development, stMMR reconstructed the spatiotemporal lineage structures, indicating an accurate developmental sequence. In breast cancer and lung cancer, stMMR clearly delineated the tumor microenvironment and identified marker genes associated with diagnosis and prognosis. Overall, stMMR is capable of effectively utilizing the multimodal information of various SRT data to explore and characterize tissue architectures of homeostasis, development, and tumor.

Background: As one of the most popular data representation methods, non-negative matrix decomposition (NMF) has been widely concerned in the tasks of clustering and feature selection. However, most of the previously proposed NMF-based methods do not adequately explore the hidden geometrical structure in the data. At the same time, noise and outliers are inevitably present in the data.Results: To alleviate these problems, we present a novel NMF framework named robust hypergraph regularized non-negative matrix factorization (RHNMF). In particular, the hypergraph Laplacian regularization is imposed to capture the geometric information of original data. Unlike graph Laplacian regularization which captures the relationship between pairwise sample points, it captures the high-order relationship among more sample points. Moreover, the robustness of the RHNMF is enhanced by using the L_2,1-norm constraint when estimating the residual. This is because the L_2,1-norm is insensitive to noise and outliers.Conclusions: Clustering and common abnormal expression gene (com-abnormal expression gene) selection are conducted to test the validity of the RHNMF model. Extensive experimental results on multi-view datasets reveal that our proposed model outperforms other state-of-the-art methods.