MOTIVATION: Integrating multi-omics data provides valuable insights into biological processes by capturing information across multiple molecular layers, enabling a comprehensive understanding of complex diseases and driving advancements in precision medicine. However, existing computational methods for multi-omics integration face significant challenges, such as low reliability and poor generalizability, due to the high dimensionality and low sample size nature of omics data. RESULTS: To address these challenges, we present PEARL (Pearson-Enhanced spectrAl gRaph convoLutional networks), a novel deep graph learning method for biomedical classification and functional important omics features identification. PEARL leverages a simple yet effective learning architecture to achieve superior and robust performance in high-dimensional, low-sample-size multi-omics settings. Our results demonstrate that PEARL significantly outperforms existing state-of-the-art methods on both synthetic and real biomedical datasets. Furthermore, applied to Alzheimer's disease (AD) brain multi-omics data, features prioritized by PEARL lead to functionally important genes that demonstrate significant enrichment in AD-related pathways. These findings highlight PEARL's practical utility in biomedical research and its potential to enhance biological interpretability in multi-omics studies. AVAILABILITY AND IMPLEMENTATION: The source code of our computational framework is available at https://github.com/zqq121017/PEARL.

Dynamic mode decomposition (DMD) has emerged as a powerful data-driven technique for extracting dominant spatiotemporal patterns from complex signals. However, conventional DMD methods are limited to matrix-based formulations, which might be inefficient or inadequate for modeling inherently multidimensional data including images, videos, and multiway sensor data. In this letter, we propose tensor dynamic mode decomposition (TDMD), a novel extension of DMD to third-order tensors using recently developed transform-based tensor products. By leveraging tensor factorization techniques, TDMD provides a compact and structure-preserving representation of multidimensional signals, enabling more accurate and efficient signal reconstruction and mode extraction compared to conventional DMD approaches that require data flattening. We demonstrate the effectiveness of TDMD using numerical examples.

Drug repositioning presents a compelling strategy to accelerate therapeutic development by uncovering new indications for existing compounds. However, current computational methods are often limited in their ability to integrate heterogeneous biomedical data and model the intricate, multiscale relationships underlying drug-disease associations, while large-scale experimental validation remains prohibitively resource-intensive. Here, we present DREAM-GNN (Dual-Route Embedding-Aware Model for Graph Neural Networks), a multiview deep graph learning framework that incorporates biomedical domain knowledge with two complementary graphs capturing both topological structure and feature similarity to enable accurate and biologically meaningful prediction of drug-disease associations. Extensive experiments on benchmark datasets demonstrate that DREAM-GNN significantly outperforms current state-of-the-art methods in recovering artificially removed repositioning candidates, including in scenarios involving unseen drugs and diseases. These results establish DREAM-GNN as a robust and generalizable computational framework with broad potential to streamline drug discovery and advance precision medicine.

MOTIVATION: Forecasting the synergistic effects of drug combinations facilitates drug discovery and development, especially regarding cancer therapeutics. While numerous computational methods have emerged, most of them fall short in fully modeling the relationships among clinical entities including drugs, cell lines, and diseases, which hampers their ability to generalize to drug combinations involving unseen drugs. These relationships are complex and multidimensional, requiring sophisticated modeling to capture nuanced interplay that can significantly influence therapeutic efficacy. RESULTS: We present a novel deep hypergraph learning method named Heterogeneous Entity Representation for MEdicinal Synergy (HERMES) prediction to predict the synergistic effects of anti-cancer drugs. Heterogeneous data sources, including drug chemical structures, gene expression profiles, and disease clinical semantics, are integrated into hypergraph neural networks equipped with a gated residual mechanism to enhance high-order relationship modeling. HERMES demonstrates state-of-the-art performance on two benchmark datasets, significantly outperforming existing methods in predicting the synergistic effects of drug combinations, particularly in cases involving unseen drugs. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/Christina327/HERMES.

As a natural extension of link prediction on graphs, hyperlink prediction aims for the inference of missing hyperlinks in hypergraphs, where a hyperlink can connect more than two nodes. Hyperlink prediction has applications in a wide range of systems, from chemical reaction networks and social communication networks to protein-protein interaction networks. In this article, we provide a systematic and comprehensive survey on hyperlink prediction. We adopt a classical taxonomy from link prediction to classify the existing hyperlink prediction methods into four categories: similarity-based, probability-based, matrix optimization-based, and deep learning-based methods. To compare the performance of methods from different categories, we perform a benchmark study on various hypergraph applications using representative methods from each category. Notably, deep learning-based methods prevail over other methods in hyperlink prediction.

MOTIVATION: Feature selection is a powerful dimension reduction technique which selects a subset of relevant features for model construction. Numerous feature selection methods have been proposed, but most of them fail under the high-dimensional and low-sample size (HDLSS) setting due to the challenge of overfitting. RESULTS: We present a deep learning-based method-GRAph Convolutional nEtwork feature Selector (GRACES)-to select important features for HDLSS data. GRACES exploits latent relations between samples with various overfitting-reducing techniques to iteratively find a set of optimal features which gives rise to the greatest decreases in the optimization loss. We demonstrate that GRACES significantly outperforms other feature selection methods on both synthetic and real-world datasets. AVAILABILITY AND IMPLEMENTATION: The source code is publicly available at https://github.com/canc1993/graces.

Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergraphs are mathematically tractable objects that can be utilized to precisely represent and analyze multi-way interactions. Here we present the Hypergraph Analysis Toolbox (HAT), a software package for visualization and analysis of multi-way interactions in complex systems.