Gegenbauer Graph Neural Networks for Time-Varying Signal Reconstruction.

Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series forecasting. Accurately capturing the spatio-temporal information inherent in these signals is crucial for effectively addressing these tasks. However, existing approaches relying on smoothness assumptions of temporal differences and simple convex optimization techniques that have inherent limitations. To address these challenges, we propose a novel approach that incorporates a learning module to enhance the accuracy of the downstream task. To this end, we introduce the Gegenbauer-based graph convolutional (GegenConv) operator, which is a generalization of the conventional Chebyshev graph convolution by leveraging the theory of Gegenbauer polynomials. By deviating from traditional convex problems, we expand the complexity of the model and offer a more accurate solution for recovering time-varying graph signals. Building upon GegenConv, we design the Gegenbauer-based time graph neural network (GegenGNN) architecture, which adopts an encoder-decoder structure. Likewise, our approach also uses a dedicated loss function that incorporates a mean squared error (MSE) component alongside Sobolev smoothness regularization. This combination enables GegenGNN to capture both the fidelity to ground truth and the underlying smoothness properties of the signals, enhancing the reconstruction performance. We conduct extensive experiments on real datasets to evaluate the effectiveness of our proposed approach. The experimental results demonstrate that GegenGNN outperforms state-of-the-art methods, showcasing its superior capability in recovering time-varying graph signals.

BraneMF: integration of biological networks for functional analysis of proteins.

MOTIVATION: The cellular system of a living organism is composed of interacting bio-molecules that control cellular processes at multiple levels. Their correspondences are represented by tightly regulated molecular networks. The increase of omics technologies has favored the generation of large-scale disparate data and the consequent demand for simultaneously using molecular and functional interaction networks: gene co-expression, protein-protein interaction (PPI), genetic interaction and metabolic networks. They are rich sources of information at different molecular levels, and their effective integration is essential to understand cell functioning and their building blocks (proteins). Therefore, it is necessary to obtain informative representations of proteins and their proximity, that are not fully captured by features extracted directly from a single informational level. We propose BraneMF, a novel random walk-based matrix factorization method for learning node representation in a multilayer network, with application to omics data integration. RESULTS: We test BraneMF with PPI networks of Saccharomyces cerevisiae, a well-studied yeast model organism. We demonstrate the applicability of the learned features for essential multi-omics inference tasks: clustering, function and PPI prediction. We compare it to the state-of-the-art integration methods for multilayer networks. BraneMF outperforms baseline methods by achieving high prediction scores for a variety of downstream tasks. The robustness of results is assessed by an extensive parameter sensitivity analysis. AVAILABILITY AND IMPLEMENTATION: BraneMF's code is freely available at: https://github.com/Surabhivj/BraneMF, along with datasets, embeddings and result files. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BRANEnet: embedding multilayer networks for omics data integration.

BACKGROUND: Gene expression is regulated at different molecular levels, including chromatin accessibility, transcription, RNA maturation, and transport. These regulatory mechanisms have strong connections with cellular metabolism. In order to study the cellular system and its functioning, omics data at each molecular level can be generated and efficiently integrated. Here, we propose BRANENET, a novel multi-omics integration framework for multilayer heterogeneous networks. BRANENET is an expressive, scalable, and versatile method to learn node embeddings, leveraging random walk information within a matrix factorization framework. Our goal is to efficiently integrate multi-omics data to study different regulatory aspects of multilayered processes that occur in organisms. We evaluate our framework using multi-omics data of Saccharomyces cerevisiae, a well-studied yeast model organism. RESULTS: We test BRANENET on transcriptomics (RNA-seq) and targeted metabolomics (NMR) data for wild-type yeast strain during a heat-shock time course of 0, 20, and 120 min. Our framework learns features for differentially expressed bio-molecules showing heat stress response. We demonstrate the applicability of the learned features for targeted omics inference tasks: transcription factor (TF)-target prediction, integrated omics network (ION) inference, and module identification. The performance of BRANENET is compared to existing network integration methods. Our model outperforms baseline methods by achieving high prediction scores for a variety of downstream tasks.

Multiple similarity drug-target interaction prediction with random walks and matrix factorization.

The discovery of drug-target interactions (DTIs) is a very promising area of research with great potential. The accurate identification of reliable interactions among drugs and proteins via computational methods, which typically leverage heterogeneous information retrieved from diverse data sources, can boost the development of effective pharmaceuticals. Although random walk and matrix factorization techniques are widely used in DTI prediction, they have several limitations. Random walk-based embedding generation is usually conducted in an unsupervised manner, while the linear similarity combination in matrix factorization distorts individual insights offered by different views. To tackle these issues, we take a multi-layered network approach to handle diverse drug and target similarities, and propose a novel optimization framework, called Multiple similarity DeepWalk-based Matrix Factorization (MDMF), for DTI prediction. The framework unifies embedding generation and interaction prediction, learning vector representations of drugs and targets that not only retain higher order proximity across all hyper-layers and layer-specific local invariance, but also approximate the interactions with their inner product. Furthermore, we develop an ensemble method (MDMF2A) that integrates two instantiations of the MDMF model, optimizing the area under the precision-recall curve (AUPR) and the area under the receiver operating characteristic curve (AUC), respectively. The empirical study on real-world DTI datasets shows that our method achieves statistically significant improvement over current state-of-the-art approaches in four different settings. Moreover, the validation of highly ranked non-interacting pairs also demonstrates the potential of MDMF2A to discover novel DTIs.

MATI: An efficient algorithm for influence maximization in social networks.

Influence maximization has attracted a lot of attention due to its numerous applications, including diffusion of social movements, the spread of news, viral marketing and outbreak of diseases. The objective is to discover a group of users that are able to maximize the spread of influence across a network. The greedy algorithm gives a solution to the Influence Maximization problem while having a good approximation ratio. Nevertheless it does not scale well for large scale datasets. In this paper, we propose Matrix Influence, MATI, an efficient algorithm that can be used under both the Linear Threshold and Independent Cascade diffusion models. MATI is based on the precalculation of the influence by taking advantage of the simple paths in the node's neighborhood. An extensive empirical analysis has been performed on multiple real-world datasets showing that MATI has competitive performance when compared to other well-known algorithms with regards to running time and expected influence spread.

Locating influential nodes in complex networks.

Understanding and controlling spreading processes in networks is an important topic with many diverse applications, including information dissemination, disease propagation and viral marketing. It is of crucial importance to identify which entities act as influential spreaders that can propagate information to a large portion of the network, in order to ensure efficient information diffusion, optimize available resources or even control the spreading. In this work, we capitalize on the properties of the K-truss decomposition, a triangle-based extension of the core decomposition of graphs, to locate individual influential nodes. Our analysis on real networks indicates that the nodes belonging to the maximal K-truss subgraph show better spreading behavior compared to previously used importance criteria, including node degree and k-core index, leading to faster and wider epidemic spreading. We further show that nodes belonging to such dense subgraphs, dominate the small set of nodes that achieve the optimal spreading in the network.