Hierarchical structure and the prediction of missing links in networks

A hierarchy index for networks in the brain reveals a complex entangled organizational structure

Networks involved in information processing often have their nodes arranged hierarchically, with the majority of connections occurring in adjacent levels. However, despite being an intuitively appealing concept, the hierarchical organization of large networks, such as those in the brain, is difficult to identify, especially in absence of additional information beyond that provided by the connectome. In this paper, we propose a framework to uncover the hierarchical structure of a given network, that identifies the nodes occupying each level as well as the sequential order of the levels. It involves optimizing a metric that we use to quantify the extent of hierarchy present in a network. Applying this measure to various brain networks, ranging from the nervous system of the nematode Caenorhabditis elegans to the human connectome, we unexpectedly find that they exhibit a common network architectural motif intertwining hierarchy and modularity. This suggests that brain networks may have evolved to simultaneously exploit the functional advantages of these two types of organizations, viz., relatively independent modules performing distributed processing in parallel and a hierarchical structure that allows sequential pooling of these multiple processing streams. An intriguing possibility is that this property we report may be common to information processing networks in general.

Power law of path multiplicity in complex networks

Complex networks describe a wide range of systems in nature and society. As a fundamental concept of graph theory, the path connecting nodes and edges plays a vital role in network science. Rather than focusing on the path length or path centrality, here we draw attention to the path multiplicity related to decision-making efficiency, which is defined as the number of shortest paths between node pairs and thus characterizes the routing choice diversity. Notably, through extensive empirical investigations from this new perspective, we surprisingly observe a "hesitant-world" feature along with the "small-world" feature and find a universal power-law of the path multiplicity, meaning that a small number of node pairs possess high path multiplicity. We demonstrate that the power-law of path multiplicity is much stronger than the power-law of node degree, which is known as the scale-free property. Then, we show that these phenomena cannot be captured by existing classical network models. Furthermore, we explore the relationship between the path multiplicity and existing typical network metrics, such as average shortest path length, clustering coefficient, assortativity coefficient, and node centralities. We demonstrate that the path multiplicity is a distinctive network metric. These results expand our knowledge of network structure and provide a novel viewpoint for network design and optimization with significant potential applications in biological, social, and man-made networks.

Link Prediction in Complex Networks Using Average Centrality-Based Similarity Score

Link prediction plays a crucial role in identifying future connections within complex networks, facilitating the analysis of network evolution across various domains such as biological networks, social networks, recommender systems, and more. Researchers have proposed various centrality measures, such as degree, clustering coefficient, betweenness, and closeness centralities, to compute similarity scores for predicting links in these networks. These centrality measures leverage both the local and global information of nodes within the network. In this study, we present a novel approach to link prediction using similarity score by utilizing average centrality measures based on local and global centralities, namely Similarity based on Average Degree (SACD), Similarity based on Average Betweenness (SACB), Similarity based on Average Closeness (SACC), and Similarity based on Average Clustering Coefficient (SACCC). Our approach involved determining centrality scores for each node, calculating the average centrality for the entire graph, and deriving similarity scores through common neighbors. We then applied centrality scores to these common neighbors and identified nodes with above average centrality. To evaluate our approach, we compared proposed measures with existing local similarity-based link prediction measures, including common neighbors, the Jaccard coefficient, Adamic-Adar, resource allocation, preferential attachment, as well as recent measures like common neighbor and the Centrality-based Parameterized Algorithm (CCPA), and keyword network link prediction (KNLP). We conducted experiments on four real-world datasets. The proposed similarity scores based on average centralities demonstrate significant improvements. We observed an average enhancement of 24% in terms of Area Under the Receiver Operating Characteristic (AUROC) compared to existing local similarity measures, and a 31% improvement over recent measures. Furthermore, we witnessed an average improvement of 49% and 51% in the Area Under Precision-Recall (AUPR) compared to existing and recent measures. Our comprehensive experiments highlight the superior performance of the proposed method.

Predictability of cortico-cortical connections in the mammalian brain

Despite a five order of magnitude range in size, the brains of mammals share many anatomical and functional characteristics that translate into cortical network commonalities. Here we develop a machine learning framework to quantify the degree of predictability of the weighted interareal cortical matrix. Partial network connectivity data were obtained with retrograde tract-tracing experiments generated with a consistent methodology, supplemented by projection length measurements in a nonhuman primate (macaque) and a rodent (mouse). We show that there is a significant level of predictability embedded in the interareal cortical networks of both species. At the binary level, links are predictable with an area under the ROC curve of at least 0.8 for the macaque. Weighted medium and strong links are predictable with an 85%-90% accuracy (mouse) and 70%-80% (macaque), whereas weak links are not predictable in either species. These observations reinforce earlier observations that the formation and evolution of the cortical network at the mesoscale is, to a large extent, rule based. Using the methodology presented here, we performed imputations on all area pairs, generating samples for the complete interareal network in both species. These are necessary for comparative studies of the connectome with minimal bias, both within and across species.

Deep-learning reconstruction of complex dynamical networks from incomplete data

Reconstructing complex networks and predicting the dynamics are particularly challenging in real-world applications because the available information and data are incomplete. We develop a unified collaborative deep-learning framework consisting of three modules: network inference, state estimation, and dynamical learning. The complete network structure is first inferred and the states of the unobserved nodes are estimated, based on which the dynamical learning module is activated to determine the dynamical evolution rules. An alternating parameter updating strategy is deployed to improve the inference and prediction accuracy. Our framework outperforms baseline methods for synthetic and empirical networks hosting a variety of dynamical processes. A reciprocity emerges between network inference and dynamical prediction: better inference of network structure improves the accuracy of dynamical prediction, and vice versa. We demonstrate the superior performance of our framework on an influenza dataset consisting of 37 US States and a PM2.5 dataset covering 184 cities in China.

The maximum capability of a topological feature in link prediction

Networks offer a powerful approach to modeling complex systems by representing the underlying set of pairwise interactions. Link prediction is the task that predicts links of a network that are not directly visible, with profound applications in biological, social, and other complex systems. Despite intensive utilization of the topological feature in this task, it is unclear to what extent a feature can be leveraged to infer missing links. Here, we aim to unveil the capability of a topological feature in link prediction by identifying its prediction performance upper bound. We introduce a theoretical framework that is compatible with different indexes to gauge the feature, different prediction approaches to utilize the feature, and different metrics to quantify the prediction performance. The maximum capability of a topological feature follows a simple yet theoretically validated expression, which only depends on the extent to which the feature is held in missing and nonexistent links. Because a family of indexes based on the same feature shares the same upper bound, the potential of all others can be estimated from one single index. Furthermore, a feature's capability is lifted in the supervised prediction, which can be mathematically quantified, allowing us to estimate the benefit of applying machine learning algorithms. The universality of the pattern uncovered is empirically verified by 550 structurally diverse networks. The findings have applications in feature and method selection, and shed light on network characteristics that make a topological feature effective in link prediction.

Learning deep representation and discriminative features for clustering of multi-layer networks

The multi-layer network consists of the interactions between different layers, where each layer of the network is depicted as a graph, providing a comprehensive way to model the underlying complex systems. The layer-specific modules of multi-layer networks are critical to understanding the structure and function of the system. However, existing methods fail to characterize and balance the connectivity and specificity of layer-specific modules in networks because of the complicated inter- and intra-coupling of various layers. To address the above issues, a joint learning graph clustering algorithm (DRDF) for detecting layer-specific modules in multi-layer networks is proposed, which simultaneously learns the deep representation and discriminative features. Specifically, DRDF learns the deep representation with deep nonnegative matrix factorization, where the high-order topology of the multi-layer network is gradually and precisely characterized. Moreover, it addresses the specificity of modules with discriminative feature learning, where the intra-class compactness and inter-class separation of pseudo-labels of clusters are explored as self-supervised information, thereby providing a more accurate method to explicitly model the specificity of the multi-layer network. Finally, DRDF balances the connectivity and specificity of layer-specific modules with joint learning, where the overall objective of the graph clustering algorithm and optimization rules are derived. The experiments on ten multi-layer networks showed that DRDF not only outperforms eight baselines on graph clustering but also enhances the robustness of algorithms.

Land-use intensity influences European tetrapod food webs

Land use intensification favours particular trophic groups which can induce architectural changes in food webs. These changes can impact ecosystem functions, services, stability and resilience. However, the imprint of land management intensity on food-web architecture has rarely been characterized across large spatial extent and various land uses. We investigated the influence of land management intensity on six facets of food-web architecture, namely apex and basal species proportions, connectance, omnivory, trophic chain lengths and compartmentalization, for 67,051 European terrestrial vertebrate communities. We also assessed the dependency of this influence of intensification on land use and climate. In addition to more commonly considered climatic factors, the architecture of food webs was notably influenced by land use and management intensity. Intensification tended to strongly lower the proportion of apex predators consistently across contexts. In general, intensification also tended to lower proportions of basal species, favoured mesopredators, decreased food webs compartmentalization whereas it increased their connectance. However, the response of food webs to intensification was different for some contexts. Intensification sharply decreased connectance in Mediterranean and Alpine settlements, and it increased basal tetrapod proportions and compartmentalization in Mediterranean forest and Atlantic croplands. Besides, intensive urbanization especially favoured longer trophic chains and lower omnivory. By favouring mesopredators in most contexts, intensification could undermine basal tetrapods, the cascading effects of which need to be assessed. Our results support the importance of protecting top predators where possible and raise questions about the long-term stability of food webs in the face of human-induced pressures.

Applications of information geometry to spiking neural network activity

The space of possible behaviors that complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is a prominent example of a biological system with complex behaviors. The number of possible patterns of spikes emitted by a local brain circuit is combinatorially large, although the brain may not make use of all of them. Understanding which of these possible patterns are actually used by the brain, and how those sets of patterns change as properties of neural circuitry change is a major goal in neuroscience. Recently, tools from information geometry have been used to study embeddings of probabilistic models onto a hierarchy of model manifolds that encode how model outputs change as a function of their parameters, giving a quantitative notion of "distances" between outputs. We apply this method to a network model of excitatory and inhibitory neural populations to understand how the competition between membrane and synaptic response timescales shapes the network's information geometry. The hyperbolic embedding allows us to identify the statistical parameters to which the model behavior is most sensitive, and demonstrate how the ranking of these coordinates changes with the balance of excitation and inhibition in the network.

Network-Based Methods and Their Applications in Drug Discovery

Drug discovery is time-consuming, expensive, and predominantly follows the "one drug → one target → one disease" paradigm. With the rapid development of systems biology and network pharmacology, a novel drug discovery paradigm, "multidrug → multitarget → multidisease", has emerged. This new holistic paradigm of drug discovery aligns well with the essence of networks, leading to the emergence of network-based methods in the field of drug discovery. In this Perspective, we initially introduce the concept and data sources of networks and highlight classical methodologies employed in network-based methods. Subsequently, we focus on the practical applications of network-based methods across various areas of drug discovery, such as target prediction, virtual screening, prediction of drug therapeutic effects or adverse drug events, and elucidation of molecular mechanisms. In addition, we provide representative web servers for researchers to use network-based methods in specific applications. Finally, we discuss several challenges of network-based methods and the directions for future development. In a word, network-based methods could serve as powerful tools to accelerate drug discovery.

Link prediction based on spectral analysis

Link prediction in complex network is an important issue in network science. Recently, various structure-based similarity methods have been proposed. Most of algorithms are used to analyze the topology of the network, and to judge whether there is any connection between nodes by calculating the similarity of two nodes. However, it is necessary to get the extra attribute information of the node in advance, which is very difficult. Compared to the difficulty in obtaining the attribute information of the node itself, the topology of the network is easy to obtain, and the structure of the network is an inherent attribute of the network and is more reliable. The proposed method measures kinds of similarity between nodes based on non-trivial eigenvectors of Laplacian Matrix of the network, such as Euclidean distance, Manhattan distance and Angular distance. Then the classical machine learning algorithm can be used for classification prediction (two classification in this case), so as to achieve the purpose of link prediction. Based on this process, a spectral analysis-based link prediction algorithm is proposed, and named it LPbSA (Link Prediction based on Spectral Analysis). The experimental results on seven real-world networks demonstrated that LPbSA has better performance on Accuracy, Precision, Receiver Operating Curve(ROC), area under the ROC curve(AUC), Precision and Recall curve(PR curve) and balanced F Score(F-score curve) evaluation metrics than other ten classic methods.

Applying network link prediction in drug discovery: an overview of the literature

INTRODUCTION

Network representation can give a holistic view of relationships for biomedical entities through network topology. Link prediction estimates the probability of link formation between the pair of unconnected nodes. In the drug discovery process, the link prediction method not only enables the detection of connectivity patterns but also predicts the effects of one biomedical entity to multiple entities simultaneously and vice versa, which is useful for many applications.

AREAS COVERED

The authors provide a comprehensive overview of network link prediction in drug discovery. Link prediction methodologies such as similarity-based approaches, embedding-based approaches, probabilistic model-based approaches, and preprocessing methods are summarized with examples. In addition to describing their properties and limitations, the authors discuss the applications of link prediction in drug discovery based on the relationship between biomedical concepts.

EXPERT OPINION

Link prediction is a powerful method to infer the existence of novel relationships in drug discovery. However, link prediction has been hampered by the sparsity of data and the lack of negative links in biomedical networks. With preprocessing to balance positive and negative samples and the collection of more data, the authors believe it is possible to develop more reliable link prediction methods that can become invaluable tools for successful drug discovery.

Greedy routing optimisation in hyperbolic networks

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods take advantage of the exponentially growing volume of the hyperbolic space as a function of the radius from the origin, allowing a (roughly) uniform spatial distribution of the nodes even for scale-free small-world networks, where the connection probability between pairs decays with hyperbolic distance. One of the motivations behind hyperbolic embedding is that optimal placement of the nodes in a hyperbolic space is widely thought to enable efficient navigation on top of the network. According to that, one of the measures that can be used to quantify the quality of different embeddings is given by the fraction of successful greedy paths following a simple navigation protocol based on the hyperbolic coordinates. In the present work, we develop an optimisation scheme for this score in the native disk representation of the hyperbolic space. This optimisation algorithm can be either used as an embedding method alone, or it can be applied to improve this score for embeddings obtained from other methods. According to our tests on synthetic and real networks, the proposed optimisation can considerably enhance the success rate of greedy paths in several cases, improving the given embedding from the point of view of navigability.

Link prediction and feature relevance in knowledge networks: A machine learning approach

We propose a supervised machine learning approach to predict partnership formation between universities. We focus on successful joint R&D projects funded by the Horizon 2020 programme in three research domains: Social Sciences and Humanities, Physical and Engineering Sciences, and Life Sciences. We perform two related analyses: link formation prediction, and feature importance detection. In predicting link formation, we consider two settings: one including all features, both exogenous (pertaining to the node) and endogenous (pertaining to the network); and one including only exogenous features (thus removing the network attributes of the nodes). Using out-of-sample cross-validated accuracy, we obtain 91% prediction accuracy when both types of attributes are used, and around 67% when using only the exogenous ones. This proves that partnership predictive power is on average 24% larger for universities already incumbent in the programme than for newcomers (for which network attributes are clearly unknown). As for feature importance, by computing super-learner average partial effects and elasticities, we find that the endogenous attributes are the most relevant in affecting the probability to generate a link, and observe a largely negative elasticity of the link probability to feature changes, fairly uniform across attributes and domains.

Soil microbial diversity under different types of interference in birch secondary forest in the Greater Khingan Mountains in China

Introduction

Soil microorganisms are an important component of soil ecosystems with an indispensable role in forest ecosystems. We analyzed the soil microbial diversity in birch secondary forest formed by natural restoration or artificial reconstruction after interference by burning, clear cutting, and gradient cutting, and the Betula platyphylla Suk undisturbed forest in the Greater Khingan Mountains in China.

Methods

Illumina high-throughput sequencing technology was used to analyze the characteristics of the soil microbial community during the restoration process of birch secondary forest caused by the different types of interference. The relationships between bacteria and fungi were analyzed. The gene functions of the soil bacterial community and the ecological functions of soil fungi were predicted using PICRUSt and FunGuild, respectively.

Results

At the phylum level, the species and quantity of bacteria were more abundant than that of fungi. At the genus level, no obvious differences in the abundance of bacteria were observed; there were obvious differences in the abundance of fungi. Among the eight sample plots, the artificial larch forest belt had the highest bacterial and fungal alpha diversity, which was slightly higher than undisturbed forest, while the other sample plots were significantly lower. Gradual cutting pure birch forest bacteria and fungi had the highest beta diversity, and artificial larch forest belt bacteria and heavy burn sample plot fungi had the lowest beta diversity. Samples from the cutting and burning sample plots were significantly different from the undisturbed forest at the phylum level of Acidobacteriae, Acidimicrobiia, Mortierellomycetes and Sordariomycetes. We found statistical differences in biomarkers between bacterial and fungal communities in undisturbed forest and artificial larch forest belt and burn sample plots. PICRUSt prediction and FunGuild prediction showed that soil bacterial and fungal communities were rich in gene and ecological functions, respectively. In the microbial network, the stability or anti-interference performance of the fungal community was higher than that of bacteria.

Conclusion

Our data reveal the characteristics of the soil microbial community during the restoration process of Betula platyphylla Suk secondary forest under different types of disturbance, which is of great significance for understanding the role of soil microorganisms in the forest ecological cycle.

HEM: An Improved Parametric Link Prediction Algorithm Based on Hybrid Network Evolution Mechanism

Link prediction plays an important role in the research of complex networks. Its task is to predict missing links or possible new links in the future via existing information in the network. In recent years, many powerful link prediction algorithms have emerged, which have good results in prediction accuracy and interpretability. However, the existing research still cannot clearly point out the relationship between the characteristics of the network and the mechanism of link generation, and the predictability of complex networks with different features remains to be further analyzed. In view of this, this article proposes the corresponding link prediction indexes Reg, DFPA and LW on a regular network, scale-free network and small-world network, respectively, and studies their prediction properties on these three network models. At the same time, we propose a parametric hybrid index HEM and compare the prediction accuracies of HEM and many similarity-based indexes on real-world networks. The experimental results show that HEM performs better than other Birnbaum-Saunders. In addition, we study the factors that play a major role in the prediction of HEM and analyze their relationship with the characteristics of real-world networks. The results show that the predictive properties of factors are closely related to the features of networks.

MMiKG: a knowledge graph-based platform for path mining of microbiota-mental diseases interactions

The microbiota-gut-brain axis denotes a two-way system of interactions between the gut and the brain, comprising three key components: (1) gut microbiota, (2) intermediates and (3) mental ailments. These constituents communicate with one another to induce changes in the host's mood, cognition and demeanor. Knowledge concerning the regulation of the host central nervous system by gut microbiota is fragmented and mostly confined to disorganized or semi-structured unrestricted texts. Such a format hinders the exploration and comprehension of unknown territories or the further advancement of artificial intelligence systems. Hence, we collated crucial information by scrutinizing an extensive body of literature, amalgamated the extant knowledge of the microbiota-gut-brain axis and depicted it in the form of a knowledge graph named MMiKG, which can be visualized on the GraphXR platform and the Neo4j database, correspondingly. By merging various associated resources and deducing prospective connections between gut microbiota and the central nervous system through MMiKG, users can acquire a more comprehensive perception of the pathogenesis of mental disorders and generate novel insights for advancing therapeutic measures. As a free and open-source platform, MMiKG can be accessed at http://yangbiolab.cn:8501/ with no login requirement.

Hierarchical core-periphery structure in networks

We study core-periphery structure in networks using inference methods based on a flexible network model that allows for traditional onionlike cores within cores, but also for hierarchical treelike structures and more general non-nested types of structures. We propose an efficient Monte Carlo scheme for fitting the model to observed networks and report results for a selection of real-world data sets. Among other things, we observe an empirical distinction between networks showing traditional core-periphery structure with a dense core weakly connected to a sparse periphery, and an alternative structure in which the core is strongly connected both within itself and to the periphery. Networks vary in whether they are better represented by one type of structure or the other. We also observe structures that are a hybrid between core-periphery structure and community structure, in which networks have a set of nonoverlapping cores that roughly correspond to communities, surrounded by a single undifferentiated periphery. Computer code implementing our methods is available.

Hierarchical community structure in networks

Modular and hierarchical community structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular have included identifying fundamental limits of detectability by formally defining community structure using probabilistic generative models. Detecting hierarchical community structure introduces additional challenges alongside those inherited from community detection. Here we present a theoretical study on hierarchical community structure in networks, which has thus far not received the same rigorous attention. We address the following questions. (1) How should we define a hierarchy of communities? (2) How do we determine if there is sufficient evidence of a hierarchical structure in a network? (3) How can we detect hierarchical structure efficiently? We approach these questions by introducing a definition of hierarchy based on the concept of stochastic externally equitable partitions and their relation to probabilistic models, such as the popular stochastic block model. We enumerate the challenges involved in detecting hierarchies and, by studying the spectral properties of hierarchical structure, present an efficient and principled method for detecting them.

Single-trajectory map equation

Community detection, the process of identifying module structures in complex systems represented on networks, is an effective tool in various fields of science. The map equation, which is an information-theoretic framework based on the random walk on a network, is a particularly popular community detection method. Despite its outstanding performance in many applications, the inner workings of the map equation have not been thoroughly studied. Herein, we revisit the original formulation of the map equation and address the existence of its "raw form," which we refer to as the single-trajectory map equation. This raw form sheds light on many details behind the principle of the map equation that are hidden in the steady-state limit of the random walk. Most importantly, the single-trajectory map equation provides a more balanced community structure, naturally reducing the tendency of the overfitting phenomenon in the map equation.

Assessment of community efforts to advance network-based prediction of protein-protein interactions

Comprehensive understanding of the human protein-protein interaction (PPI) network, aka the human interactome, can provide important insights into the molecular mechanisms of complex biological processes and diseases. Despite the remarkable experimental efforts undertaken to date to determine the structure of the human interactome, many PPIs remain unmapped. Computational approaches, especially network-based methods, can facilitate the identification of previously uncharacterized PPIs. Many such methods have been proposed. Yet, a systematic evaluation of existing network-based methods in predicting PPIs is still lacking. Here, we report community efforts initiated by the International Network Medicine Consortium to benchmark the ability of 26 representative network-based methods to predict PPIs across six different interactomes of four different organisms: A. thaliana, C. elegans, S. cerevisiae, and H. sapiens. Through extensive computational and experimental validations, we found that advanced similarity-based methods, which leverage the underlying network characteristics of PPIs, show superior performance over other general link prediction methods in the interactomes we considered.

The Absence of a Weak-Tie Effect When Predicting Large-Weight Links in Complex Networks

Link prediction is a hot issue in information filtering. Link prediction algorithms, based on local similarity indices, are widely used in many fields due to their high efficiency and high prediction accuracy. However, most existing link prediction algorithms are available for unweighted networks, and there are relatively few studies for weighted networks. In the previous studies on weighted networks, some scholars pointed out that links with small weights play a more important role in link prediction and emphasized that weak-ties theory has a significant impact on prediction accuracy. On this basis, we studied the edges with different weights, and we discovered that, for edges with large weights, this weak-ties theory actually does not work; Instead, the weak-ties theory works in the prediction of edges with small weights. Our discovery has instructive implications for link predictions in weighted networks.

Coarse-to-Fine: Progressive Knowledge Transfer-Based Multitask Convolutional Neural Network for Intelligent Large-Scale Fault Diagnosis

In modern industry, large-scale fault diagnosis of complex systems is emerging and becoming increasingly important. Most deep learning-based methods perform well on small number of fault diagnosis, but cannot converge to satisfactory results when handling large-scale fault diagnosis because the huge number of fault types will lead to the problems of intra/inter-class distance unbalance and poor local minima in neural networks. To address the above problems, a progressive knowledge transfer-based multitask convolutional neural network (PKT-MCNN) is proposed. First, to construct the coarse-to-fine knowledge structure intelligently, a structure learning algorithm is proposed via clustering fault types in different coarse-grained nodes. Thus, the intra/inter-class distance unbalance problem can be mitigated by spreading similar tasks into different nodes. Then, an MCNN architecture is designed to learn the coarse and fine-grained task simultaneously and extract more general fault information, thereby pushing the algorithm away from poor local minima. Last but not least, a PKT algorithm is proposed, which can not only transfer the coarse-grained knowledge to the fine-grained task and further alleviate the intra/inter-class distance unbalance in feature space, but also regulate different learning stages by adjusting the attention weight to each task progressively. To verify the effectiveness of the proposed method, a dataset of a nuclear power system with 66 fault types was collected and analyzed. The results demonstrate that the proposed method can be a promising tool for large-scale fault diagnosis.

Computational Methods and Deep Learning for Elucidating Protein Interaction Networks

Protein interactions play a critical role in all biological processes, but experimental identification of protein interactions is a time- and resource-intensive process. The advances in next-generation sequencing and multi-omics technologies have greatly benefited large-scale predictions of protein interactions using machine learning methods. A wide range of tools have been developed to predict protein-protein, protein-nucleic acid, and protein-drug interactions. Here, we discuss the applications, methods, and challenges faced when employing the various prediction methods. We also briefly describe ways to overcome the challenges and prospective future developments in the field of protein interaction biology.

Machine learning prediction of academic collaboration networks

We investigate the different roles played by nodes' network and non-network attributes in explaining the formation of European university collaborations from 2011 to 2016, in three European Research Council (ERC) domains: Social Sciences and Humanities (SSH), Physical and Engineering Sciences (PE), Life Sciences (LS), as well as multidisciplinary collaborations. On link formation in collaboration networks, existing research has not yet compared and simultaneously examined both network and non-network attributes. Using four machine learning predictive algorithms (LASSO, Neural Network, Gradient Boosting, and Random Forest) our results show that, over various model specifications: (i) best model link formation accuracy is larger than 80%, (ii) among the non-network attributes, public funding plays an important role in PE and LS, (iii) network attributes count more than non-network attributes for the formation, sensibly increasing accuracy, (iv) feature-importance scores show a different ordering in the four domains, thus signalling different modes of knowledge production and transmission taking place within these different scientific communities.

Detecting hierarchical organization of pervasive communities by modular decomposition of Markov chain

Connecting nodes that contingently co-appear, which is a common process of networking in social and biological systems, normally leads to modular structure characterized by the absence of definite boundaries. This study seeks to find and evaluate methods to detect such modules, which will be called 'pervasive' communities. We propose a mathematical formulation to decompose a random walk spreading over the entire network into localized random walks as a proxy for pervasive communities. We applied this formulation to biological and social as well as synthetic networks to demonstrate that it can properly detect communities as pervasively structured objects. We further addressed a question that is fundamental but has been little discussed so far: What is the hierarchical organization of pervasive communities and how can it be extracted? Here we show that hierarchical organization of pervasive communities is unveiled from finer to coarser layers through discrete phase transitions that intermittently occur as the value for a resolution-controlling parameter is quasi-statically increased. To our knowledge, this is the first elucidation of how the pervasiveness and hierarchy, both hallmarks of community structure of real-world networks, are unified.

Statistical inference links data and theory in network science

The number of network science applications across many different fields has been rapidly increasing. Surprisingly, the development of theory and domain-specific applications often occur in isolation, risking an effective disconnect between theoretical and methodological advances and the way network science is employed in practice. Here we address this risk constructively, discussing good practices to guarantee more successful applications and reproducible results. We endorse designing statistically grounded methodologies to address challenges in network science. This approach allows one to explain observational data in terms of generative models, naturally deal with intrinsic uncertainties, and strengthen the link between theory and applications.

Theoretical models and structures recovered from measured data serve for analysis of complex networks. The authors discuss here existing gaps between theoretical methods and real-world applied networks, and potential ways to improve the interplay between theory and applications.

De novo prediction of RNA-protein interactions with graph neural networks

RNA-binding proteins (RBPs) are key co- and post-transcriptional regulators of gene expression, playing a crucial role in many biological processes. Experimental methods like CLIP-seq have enabled the identification of transcriptome-wide RNA-protein interactions for select proteins; however, the time- and resource-intensive nature of these technologies call for the development of computational methods to complement their predictions. Here, we leverage recent, large-scale CLIP-seq experiments to construct a de novo predictor of RNA-protein interactions based on graph neural networks (GNN). We show that the GNN method allows us not only to predict missing links in an RNA-protein network, but to predict the entire complement of targets of previously unassayed proteins, and even to reconstruct the entire network of RNA-protein interactions in different conditions based on minimal information. Our results demonstrate the potential of modern machine learning methods to extract useful information on post-transcriptional regulation from large data sets.

A Simplified Quantum Walk Model for Predicting Missing Links of Complex Networks

Prediction of missing links is an important part of many applications, such as friends' recommendations on social media, reduction of economic cost of protein functional modular mining, and implementation of accurate recommendations in the shopping platform. However, the existing algorithms for predicting missing links fall short in the accuracy and the efficiency. To ameliorate these, we propose a simplified quantum walk model whose Hilbert space dimension is only twice the number of nodes in a complex network. This property facilitates simultaneous consideration of the self-loop of each node and the common neighbour information between arbitrary pair of nodes. These effects decrease the negative effect generated by the interference effect in quantum walks while also recording the similarity between nodes and its neighbours. Consequently, the observed probability after the two-step walk is utilised to represent the score of each link as a missing link, by which extensive computations are omitted. Using the AUC index as a performance metric, the proposed model records the highest average accuracy in the prediction of missing links compared to 14 competing algorithms in nine real complex networks. Furthermore, experiments using the precision index show that our proposed model ranks in the first echelon in predicting missing links. These performances indicate the potential of our simplified quantum walk model for applications in network alignment and functional modular mining of protein-protein networks.

A Supervised Link Prediction Method Using Optimized Vertex Collocation Profile

Classical link prediction methods mainly utilize vertex information and topological structure to predict missing links in networks. However, accessing vertex information in real-world networks, such as social networks, is still challenging. Moreover, link prediction methods based on topological structure are usually heuristic, and mainly consider common neighbors, vertex degrees and paths, which cannot fully represent the topology context. In recent years, network embedding models have shown efficiency for link prediction, but they lack interpretability. To address these issues, this paper proposes a novel link prediction method based on an optimized vertex collocation profile (OVCP). First, the 7-subgraph topology was proposed to represent the topology context of vertexes. Second, any 7-subgraph can be converted into a unique address by OVCP, and then we obtained the interpretable feature vectors of vertexes. Third, the classification model with OVCP features was used to predict links, and the overlapping community detection algorithm was employed to divide a network into multiple small communities, which can greatly reduce the complexity of our method. Experimental results demonstrate that the proposed method can achieve a promising performance compared with traditional link prediction methods, and has better interpretability than network-embedding-based methods.

Experimental guidance for discovering genetic networks through hypothesis reduction on time series

Large programs of dynamic gene expression, like cell cyles and circadian rhythms, are controlled by a relatively small "core" network of transcription factors and post-translational modifiers, working in concerted mutual regulation. Recent work suggests that system-independent, quantitative features of the dynamics of gene expression can be used to identify core regulators. We introduce an approach of iterative network hypothesis reduction from time-series data in which increasingly complex features of the dynamic expression of individual, pairs, and entire collections of genes are used to infer functional network models that can produce the observed transcriptional program. The culmination of our work is a computational pipeline, Iterative Network Hypothesis Reduction from Temporal Dynamics (Inherent dynamics pipeline), that provides a priority listing of targets for genetic perturbation to experimentally infer network structure. We demonstrate the capability of this integrated computational pipeline on synthetic and yeast cell-cycle data.

Toward Detecting Previously Undiscovered Interaction Types in Networked Systems

Studying networked systems in a variety of domains, including biology, social science, and Internet of Things, has recently received a surge of attention. For a networked system, there are usually multiple types of interactions between its components, and such interaction-type information is crucial since it always associated with important features. However, some interaction types that actually exist in the network may not be observed in the metadata collected in practice. This article proposes an approach aiming to detect previously undiscovered interaction types (PUITs) in networked systems. The first step in our proposed PUIT detection approach is to answer the following fundamental question: is it possible to effectively detect PUITs without utilizing metadata other than the existing incomplete interaction-type information and the connection information of the system? Here, we first propose a temporal network model which can be used to mimic any real network and then discover that some special networks which fit the model shall a common topological property. Supported by this discovery, we finally develop a PUIT detection method for networks which fit the proposed model. Both analytical and numerical results show this detection method is more effective than the baseline method, demonstrating that effectively detecting PUITs in networks is achievable. More studies on PUIT detection are of significance and in great need since this approach should be as essential as the previously undiscovered node-type detection which has gained great success in the field of biology.

ProteinPrompt: a webserver for predicting protein-protein interactions

Motivation

Protein-protein interactions (PPIs) play an essential role in a great variety of cellular processes and are therefore of significant interest for the design of new therapeutic compounds as well as the identification of side effects due to unexpected binding. Here, we present ProteinPrompt, a webserver that uses machine learning algorithms to calculate specific, currently unknown PPIs. Our tool is designed to quickly and reliably predict contact propensities based on an input sequence in order to scan large sequence libraries for potential binding partners, with the goal to accelerate and assure the quality of the laborious process of drug target identification.

Results

We collected and thoroughly filtered a comprehensive database of known binders from several sources, which is available as download. ProteinPrompt provides two complementary search methods of similar accuracy for comparison and consensus building. The default method is a random forest (RF) algorithm that uses the auto-correlations of seven amino acid scales. Alternatively, a graph neural network (GNN) implementation can be selected. Additionally, a consensus prediction is available. For each query sequence, potential binding partners are identified from a protein sequence database. The proteom of several organisms are available and can be searched for binders. To evaluate the predictive power of the algorithms, we prepared a test dataset that was rigorously filtered for redundancy. No sequence pairs similar to the ones used for training were included in this dataset. With this challenging dataset, the RF method achieved an accuracy rate of 0.88 and an area under the curve of 0.95. The GNN achieved an accuracy rate of 0.86 using the same dataset. Since the underlying learning approaches are unrelated, comparing the results of RF and GNNs reduces the likelihood of errors. The consensus reached an accuracy of 0.89.

Availability and implementation

ProteinPrompt is available online at: http://proteinformatics.org/ProteinPrompt, where training and test data used to optimize the methods are also available. The server makes it possible to scan the human proteome for potential binding partners of an input sequence within minutes. For local offline usage, we furthermore created a ProteinPrompt Docker image which allows for batch submission: https://gitlab.hzdr.de/proteinprompt/ProteinPrompt. In conclusion, we offer a fast, accurate, easy-to-use online service for predicting binding partners from an input sequence.

Emergence of dynamic properties in network hypermotifs

Networks are fundamental for our understanding of complex systems. The study of networks has uncovered common principles that underlie the behavior of vastly different fields of study, including physics, biology, sociology, and engineering. One of these common principles is the existence of network motifs-small recurrent patterns that can provide certain features that are important for the specific network. However, it remains unclear how network motifs are joined in real networks to make larger circuits and what properties emerge from interactions between network motifs. Here, we develop a framework to explore the mesoscale-level behavior of complex networks. Considering network motifs as hypernodes, we define the rules for their interaction at the network's next level of organization. We develop a method to infer the favorable arrangements of interactions between network motifs into hypermotifs from real evolved and designed network data. We mathematically explore the emergent properties of these higher-order circuits and their relations to the properties of the individual minimal circuit components they combine. We apply this framework to biological, neuronal, social, linguistic, and electronic networks and find that network motifs are not randomly distributed in real networks but are combined in a way that both maintains autonomy and generates emergent properties. This framework provides a basis for exploring the mesoscale structure and behavior of complex systems where it can be used to reveal intermediate patterns in complex networks and to identify specific nodes and links in the network that are the key drivers of the network's emergent properties.

Heterogeneous Hypergraph Variational Autoencoder for Link Prediction

Link prediction aims at inferring missing links or predicting future ones based on the currently observed network. This topic is important for many applications such as social media, bioinformatics and recommendation systems. Most existing methods focus on homogeneous settings and consider only low-order pairwise relations while ignoring either the heterogeneity or high-order complex relations among different types of nodes, which tends to lead to a sub-optimal embedding result. This paper presents a method named Heterogeneous Hypergraph Variational Autoencoder (HeteHG-VAE) for link prediction in heterogeneous information networks (HINs). It first maps a conventional HIN to a heterogeneous hypergraph with a certain kind of semantics to capture both the high-order semantics and complex relations among nodes, while preserving the low-order pairwise topology information of the original HIN. Then, deep latent representations of nodes and hyperedges are learned by a Bayesian deep generative framework from the heterogeneous hypergraph in an unsupervised manner. Moreover, a hyperedge attention module is designed to learn the importance of different types of nodes in each hyperedge. The major merit of HeteHG-VAE lies in its ability of modeling multi-level relations in heterogeneous settings. Extensive experiments on real-world datasets demonstrate the effectiveness and efficiency of the proposed method.

Maximizing synchronizability of networks with community structure based on node similarity

In reality, numerous networks have a community structure characterized by dense intra-community connections and sparse inter-community connections. In this article, strategies are proposed to enhance synchronizability of such networks by rewiring a certain number of inter-community links, where the research scope is complete synchronization on undirected and diffusively coupled dynamic networks. First, we explore the effect of adding links between unconnected nodes with different similarity levels on network synchronizability and find that preferentially adding links between nodes with lower similarity can improve network synchronizability more than that with higher similarity, where node similarity is measured by our improved Asymmetric Katz (AKatz) and Asymmetric Leicht-Holme-Newman (ALHNII) methods from the perspective of link prediction. Additional simulations demonstrate that the node similarity-based link-addition strategy is more effective in enhancing network synchronizability than the node centrality-based methods. Furthermore, we apply the node similarity-based link-addition or deletion strategy as the valid criteria to the rewiring process of inter-community links and then propose a Node Similarity-Based Rewiring Optimization (NSBRO) algorithm, where the optimization process is realized by a modified simulated annealing technique. Simulations show that our proposed method performs better in optimizing synchronization of such networks compared with other centrality-based heuristic methods. Finally, simulations on the Rössler system indicate that the network structure optimized by the NSBRO algorithm also leads to better synchronizability of coupled oscillators.

Exploiting node metadata to predict interactions in bipartite networks using graph embedding and neural networks

Networks are increasingly used in various fields to represent systems with the aim of understanding the underlying rules governing observed interactions, and hence predict how the system is likely to behave in the future. Recent developments in network science highlight that accounting for node metadata improves both our understanding of how nodes interact with one another, and the accuracy of link prediction. However, to predict interactions in a network within existing statistical and machine learning frameworks, we need to learn objects that rapidly grow in dimension with the number of nodes. Thus, the task becomes computationally and conceptually challenging for networks. Here, we present a new predictive procedure combining a statistical, low-rank graph embedding method with machine learning techniques which reduces substantially the complexity of the learning task and allows us to efficiently predict interactions from node metadata in bipartite networks. To illustrate its application on real-world data, we apply it to a large dataset of tourist visits across a country. We found that our procedure accurately reconstructs existing interactions and predicts new interactions in the network. Overall, both from a network science and data science perspective, our work offers a flexible and generalizable procedure for link prediction.

A Hierarchical Random Graph Efficient Sampling Algorithm Based on Improved MCMC Algorithm

A hierarchical random graph (HRG) model combined with a maximum likelihood approach and a Markov Chain Monte Carlo algorithm can not only be used to quantitatively describe the hierarchical organization of many real networks, but also can predict missing connections in partly known networks with high accuracy. However, the computational cost is very large when hierarchical random graphs are sampled by the Markov Chain Monte Carlo algorithm (MCMC), so that the hierarchical random graphs, which can describe the characteristics of network structure, cannot be found in a reasonable time range. This seriously limits the practicability of the model. In order to overcome this defect, an improved MCMC algorithm called two-state transitions MCMC (TST-MCMC) for efficiently sampling hierarchical random graphs is proposed in this paper. On the Markov chain composed of all possible hierarchical random graphs, TST-MCMC can generate two candidate state variables during state transition and introduce a competition mechanism to filter out the worse of the two candidate state variables. In addition, the detailed balance of Markov chain can be ensured by using Metropolis–Hastings rule. By using this method, not only can the convergence speed of Markov chain be improved, but the convergence interval of Markov chain can be narrowed as well. Three example networks are employed to verify the performance of the proposed algorithm. Experimental results show that our algorithm is more feasible and more effective than the compared schemes.

MSGWO-MKL-SVM: A Missing Link Prediction Method for UAV Swarm Network Based on Time Series

Missing link prediction technology (MLP) is always a hot research area in the field of complex networks, and it has been extensively utilized in UAV swarm network reconstruction recently. UAV swarm is an artificial network with strong randomness, in the face of which prediction methods based on network similarity often perform poorly. To solve those problems, this paper proposes a Multi Kernel Learning algorithm with a multi-strategy grey wolf optimizer based on time series (MSGWO-MKL-SVM). The Multiple Kernel Learning (MKL) method is adopted in this algorithm to extract the advanced features of time series, and the Support Vector Machine (SVM) algorithm is used to determine the hyperplane of threshold value in nonlinear high dimensional space. Besides that, we propose a new measurable indicator of Multiple Kernel Learning based on cluster, transforming a Multiple Kernel Learning problem into a multi-objective optimization problem. Some adaptive neighborhood strategies are used to enhance the global searching ability of grey wolf optimizer algorithm (GWO). Comparison experiments were conducted on the standard UCI datasets and the professional UAV swarm datasets. The classification accuracy of MSGWO-MKL-SVM on UCI datasets is improved by 6.2% on average, and the link prediction accuracy of MSGWO-MKL-SVM on professional UAV swarm datasets is improved by 25.9% on average.

Hyperbolic disc embedding of functional human brain connectomes using resting-state fMRI

The brain presents a real complex network of modular, small-world, and hierarchical nature, which are features of non-Euclidean geometry. Using resting-state functional magnetic resonance imaging, we constructed a scale-free binary graph for each subject, using internodal time series correlation of regions of interest as a proximity measure. The resulting network could be embedded onto manifolds of various curvatures and dimensions. While maintaining the fidelity of embedding (low distortion, high mean average precision), functional brain networks were found to be best represented in the hyperbolic disc. Using the 𝕊¹/ℍ² model, we reduced the dimension of the network into two-dimensional hyperbolic space and were able to efficiently visualize the internodal connections of the brain, preserving proximity as distances and angles on the hyperbolic discs. Each individual disc revealed relevance with its anatomic counterpart and absence of center-spaced node. Using the hyperbolic distance on the 𝕊¹/ℍ² model, we could detect the anomaly of network in autism spectrum disorder subjects. This procedure of embedding grants us a reliable new framework for studying functional brain networks and the possibility of detecting anomalies of the network in the hyperbolic disc on an individual scale.