Network Alignment Methods Research Articles

On the Power of Gradual Network Alignment Using Dual-Perception Similarities.

Network alignment (NA) is the task of finding the correspondence of nodes between two networks based on the network structure and node attributes. Our study is motivated by the fact that, since most of existing NA methods have attempted to discover all node pairs at once, they do not harness information enriched through interim discovery of node correspondences to more accurately find the next correspondences during the node matching. To tackle this challenge, we propose Grad-Align, a new NA method that gradually discovers node pairs by making full use of node pairs exhibiting strong consistency, which are easy to be discovered in the early stage of gradual matching. Specifically, Grad-Align first generates node embeddings of the two networks based on graph neural networks along with our layer-wise reconstruction loss, a loss built upon capturing the first-order and higher-order neighborhood structures. Then, nodes are gradually aligned by computing dual-perception similarity measures including the multi-layer embedding similarity as well as the Tversky similarity, an asymmetric set similarity using the Tversky index applicable to networks with different scales. Additionally, we incorporate an edge augmentation module into Grad-Align to reinforce the structural consistency. Through comprehensive experiments using real-world and synthetic datasets, we empirically demonstrate that Grad-Align consistently outperforms state-of-the-art NA methods.

SAlign: A Graph Neural Attention Framework for Aligning Structurally Heterogeneous Networks

Network alignment techniques that map the same entities across multiple networks assume that the mapping nodes in two different networks have similar attributes and neighborhood proximity. However, real-world networks often violate such assumptions, having diverse attributes and structural properties. Node mapping across such structurally heterogeneous networks remains a challenge. Although capturing the nodes’ entire neighborhood (in low-dimensional embeddings) may help deal with these characteristic differences, the issue of over-smoothing in the representations that come from higherorder learning still remains a major problem. To address the above concerns, we propose SAlign: a supervised graph neural attention framework for aligning structurally heterogeneous networks that learns the correlation of structural properties of mapping nodes using a set of labeled (mapped) anchor nodes. SAlign incorporates nodes’ graphlet information with a novel structure-aware cross-network attention mechanism that transfers the required higher-order structure information across networks. The information exchanged across networks helps in enhancing the expressivity of the graph neural network, thereby handling any potential over-smoothing problem. Extensive experiments on three real datasets demonstrate that SAlign consistently outperforms the state-of-the-art network alignment methods by at least 1.3-8% in terms of accuracy score. The code is available at https://github.com/shruti400/SAlign for reproducibility.

HackGAN: Harmonious Cross-Network Mapping Using CycleGAN With Wasserstein–Procrustes Learning for Unsupervised Network Alignment

Network alignment (NA) that identifies equivalent nodes across networks is an effective tool for integrating knowledge from multiple networks. The state-of-the-art NA methods learn inter-network node similarities based on labeled anchor links, which are costly, time-consuming, and difficult to acquire. Therefore, a few unsupervised network alignment (UNA) methods propose solving NA problems without anchor links. However, most existing UNA methods rely on discriminative attributes to capture nodes’ similarities and are hard to obtain optimal one-to-one alignments. Toward these issues, this article proposes a novel method named HackGAN to solve the UNA problem solely based on the structural information. Specifically, HackGAN represents nodes with embeddings based on an unsupervised graph neural network (GNN) to capture their global and local structural features. After that, it initializes mapping functions to transform the embedding spaces of different networks into the same vector space by iteratively solving the Wasserstein–Procrustes problem. The mapping functions are then refined by an adversarial model with cycle-consistency and Sinkhorn distance losses to obtain optimized one-to-one mappings. Based on the distances between mapped embeddings, accurate and robust results are obtained with a collective alignment algorithm. Experimental comparisons on both synthetic and real-world datasets demonstrate the superiority of HackGAN.

Towards Improving Embedding Based Models of Social Network Alignment via Pseudo Anchors

Social network alignment aims at aligning person identities across social networks. Embedding based models have been shown effective for the alignment where the structural proximity preserving objective is typically adopted for the model training. With the observation that “overly-close” user embeddings are unavoidable for such models causing alignment inaccuracy, we propose a novel learning framework which tries to enforce the resulting embeddings to be more widely apart among the users via the introduction of carefully implanted pseudo anchors. We further proposed a meta-learning algorithm to guide the updating of the pseudo anchor embeddings during the learning process. The proposed intervention via the use of pseudo anchors and meta-learning allows the learning framework to be applicable to a wide spectrum of network alignment methods. We have incorporated the proposed learning framework into several state-of-the-art models. Our experimental results demonstrate its efficacy where the methods with the pseudo anchors implanted can outperform their counterparts without pseudo anchors by a fairly large margin, especially when there only exist very few labeled anchors.

An Unsupervised Rapid Network Alignment Framework via Network Coarsening

Network alignment aims to identify the correspondence of nodes between two or more networks. It is the cornerstone of many network mining tasks, such as cross-platform recommendation and cross-network data aggregation. Recently, with the development of network representation learning techniques, researchers have proposed many embedding-based network alignment methods. The effect is better than traditional methods. However, several issues and challenges remain for network alignment tasks, such as lack of labeled data, mapping across network embedding spaces, and computational efficiency. Based on the graph neural network (GNN), we propose the URNA (unsupervised rapid network alignment) framework to achieve an effective balance between accuracy and efficiency. There are two phases: model training and network alignment. We exploit coarse networks to accelerate the training of GNN after first compressing the original networks into small networks. We also use parameter sharing to guarantee the consistency of embedding spaces and an unsupervised loss function to update the parameters. In the network alignment phase, we first use a once-pass forward propagation to learn node embeddings of original networks, and then we use multi-order embeddings from the outputs of all convolutional layers to calculate the similarity of nodes between the two networks via vector inner product for alignment. Experimental results on real-world datasets show that the proposed method can significantly reduce running time and memory requirements while guaranteeing alignment performance.

Grad-Align: Gradual Network Alignment via Graph Neural Networks (Student Abstract)

Network alignment (NA) is the task of finding the correspondence of nodes between two networks. Since most existing NA methods have attempted to discover every node pair at once, they may fail to utilize node pairs that have strong consistency across different networks in the NA task. To tackle this challenge, we propose Grad-Align, a new NA method that gradually discovers node pairs by making full use of either node pairs exhibiting strong consistency or prior matching information. Specifically, the proposed method gradually aligns nodes based on both the similarity of embeddings generated using graph neural networks (GNNs) and the Tversky similarity, which is an asymmetric set similarity using the Tversky index applicable to networks with different scales. Experimental evaluation demonstrates that Grad-Align consistently outperforms state-of-the-art NA methods in terms of the alignment accuracy. Our source code is available at https://github.com/jindeok/Grad-Align.

Geometry interaction network alignment

Network alignment plays an important role in many fields. The main task of network alignment is to find the node correspondence between different networks, i.e. whether they represent the same natural entity. Most existing alignment methods obtain the relevant information of nodes in the network through network representation learning technology, and then calculate the relationship between different nodes based on the node representations. These methods mostly focus on Euclidean geometry to learn node representations, does Euclidean space fit well with the network alignment? Considering that real-world networks often exhibit hierarchical structure and hyperbolic geometry shows the advantage of expressing network hierarchical structure, some researchers use hyperbolic geometry to learn node representations. But the network is not all hierarchical structure, so we exploit Euclidean and hyperbolic geometries jointly for node representation learning through an interactive learning mechanism to exploit the reliable spatial features in networks. The proposed method can well adapt to the complex structure in the network, providing efficient node representations for network alignment. Extensive experiments on synthetic and real-world datasets show the superiority of our method for network alignment.

The protein-protein interaction network alignment using recurrent neural network.

The main challenge of biological network alignment is that the problem of finding the alignments in two graphs is NP-hard. The discovery of protein-protein interaction (PPI) networks is of great importance in bioinformatics due to their utilization in identifying the cellular pathways, finding new medicines, and disease recognition. In this regard, we describe the network alignment method in the form of a classification problem for the very first time and introduce a deep network that finds the alignment of nodes present in the two networks. We call this method RENA, which means Network Alignment using REcurrent neural network. The proposed solution consists of three steps; in the first phase, we obtain the sequence and topological similarities from the networks' structure. For the second phase, the dataset needed for the transformation of the problem into a classification problem is created from obtained features. In the third phase, we predict the nodes' alignment between two networks using deep learning. We used Biogrid dataset for RENA evaluation. The RENA method is compared with three classification approaches of support vector machine, K-nearest neighbors, and linear discriminant analysis. The experimental results demonstrate the efficiency of the RENA method and 100% accuracy in PPI network alignment prediction.

A generation probability based percolation network alignment method

A generation probability based percolation network alignment method

Cross-Temporal Snapshot Alignment for Dynamic Networks

In this paper, we study the task of cross-temporal snapshot alignment for dynamic networks. The goal of this task is to match equivalent nodes across temporal snapshots of a given dynamic network. Previous static network alignment methods ignore the non-stationary nature of networks, while existing dynamic counterparts focusing on two separate evolving networks lose sight of the problem of aligning two snapshots of the same dynamic network. To alleviate these issues, we propose a Cross-Temporal Snapshot Alignment model (CTSA), which maps nodes from different snapshots into the same semantic space and makes the equivalent nodes in the source and target snapshots to be aligned locate as closely as possible. Our CTSA model utilizes graph neural networks to embed nodes for each snapshot by aggregating the local structural information, and integrates the self-attention based encoders to model the dependencies in different snapshots over time. Additionally, to improve the alignment performance of the model, we contrive a novel positional embedding learning method, which takes into account both the ordering information of input representation sequences at each time step and the graph information of each network snapshot. Experimental results on real-world dynamic networks demonstrate that our model outperforms the state-of-the-art baselines.

HUNA: A Method of Hierarchical Unsupervised Network Alignment for IoT

With the advent of the era of the Internet of Things (IoT), a large number of interconnected smart devices form a huge network. The network can be abstracted as a graph, and we propose to identify similar IoT devices in different networks by graph alignment. However, most methods rely on prelabeled cross-network node pairs such as anchor links, which are difficult to obtain due to personal privacy and security restrictions, especially in IoT. In addition, existing network entity alignment methods focus on individual pairs of nodes but ignore the tightly connected group structure in the network, which is a significant feature of IoT devices. In this article, we propose a method of hierarchical unsupervised network alignment (HUNA) to identify similar IoT devices in different networks by a deep learning approach. First, we propose an unsupervised network alignment method based on cycle adversarial networks (UNA), which utilizes the adversarial characteristics of cycle adversarial networks to achieve entity alignment under unsupervised conditions. Second, we further expand the model by carefully designing the group structure aggregation optimization module to aggregate the nodes with closely related attributes and structures into a coarse-grained node and align the coarse-grained nodes. Finally, we evaluate HUNA with real and synthetic data sets. Experimental results show that this method can improve the accuracy of node alignment by 10% and perform well in terms of parameter sensitivity.

Incomplete Network Alignment

Networks are prevalent in many areas and are often collected from multiple sources. However, due to the veracity characteristics, more often than not, networks are incomplete. Network alignment and network completion have become two fundamental cornerstones behind a wealth of high-impact graph mining applications. The state-of-the-art have been addressing these two tasks in parallel . That is, most of the existing network alignment methods have implicitly assumed that the topology of the input networks for alignment are perfectly known a priori, whereas the existing network completion methods admit either a single network (i.e., matrix completion) or multiple aligned networks (e.g., tensor completion). In this article, we argue that network alignment and completion are inherently complementary with each other, and hence propose to jointly address them so that the two tasks can mutually benefit from each other. We formulate the problem from the optimization perspective, and propose an effective algorithm ( iNeAt ) to solve it. The proposed method offers two distinctive advantages. First ( Alignment accuracy ), our method benefits from the higher-quality input networks while mitigates the effect of the incorrectly inferred links introduced by the completion task itself. Second ( Alignment efficiency ), thanks to the low-rank structure of the complete networks and the alignment matrix, the alignment process can be significantly accelerated. We perform extensive experiments which show that (1) the network completion can significantly improve the alignment accuracy, i.e., up to 30% over the baseline methods; (2) the network alignment can in turn help recover more missing edges than the baseline methods; and (3) our method achieves a good balance between the running time and the accuracy, and scales with a provable linear complexity in both time and space.

Attributed Network Alignment: Problem Definitions and Fast Solutions

Networks are prevalent and often collected from multiple sources in many high-impact domains, which facilitate many emerging applications that require the connections across multiple networks. Network alignment (i.e., to find the node correspondence between different networks) has become the very first step in many applications and thus has been studied in decades. Although some existing works can use the attribute information as part of the alignment process, they still have certain limitations. For example, some existing network alignment methods can use node attribute similarities as part of the prior alignment information, whereas most of them solely explore the topology consistency without the consistency among attributes of the underlying networks. On the other hand, traditional graph matching methods encode both the node and edge attributes (and possibly the topology) into an affinity matrix and formulate it as a constrained nonconvex quadratic maximization problem. However, these methods cannot scale well to the large-scale networks. In this paper, we propose a family of network alignment algorithms (FINAL) to efficiently align the attributed networks. The key idea is to leverage the node/edge attribute information to guide the (topology-based) alignment process. We formulate this problem as a convex quadratic optimization problem, and develop effective and efficient algorithms to solve it. Moreover, we derive FINAL On-Query, an online variant of FINAL that can find similar nodes for the query nodes across networks. We perform extensive evaluations on real networks to substantiate the superiority of our proposed approaches.

A comparative study on network alignment techniques

Network alignment is a method to align nodes that belong to the same entity from different networks. A well-known application of network alignment is to map user accounts from different social networks that belong to the same person. As network alignment has a wide range of applications from recommendation to link prediction, there are several proposed approaches to aligning nodes from different networks. These techniques, however, have been rarely compared and analyzed under the same setting, rendering a right choice for a particular set of networks very difficult. Addressing this problem, this paper presents a benchmark that offers a comprehensive empirical study on the performance comparison of network alignment methods. Specifically, we integrate several state-of-the-art network alignment techniques in a comparable manner, and measure distinct characteristics of these techniques with various settings. We then provide in-depth analysis of the benchmark results, obtained by using both real data and synthetic data. We believe that the findings from the benchmark will serve as a practical guideline for potential applications.

Functional protein representations from biological networks enable diverse cross-species inference.

Transferring knowledge between species is key for many biological applications, but is complicated by divergent and convergent evolution. Many current approaches for this problem leverage sequence and interaction network data to transfer knowledge across species, exemplified by network alignment methods. While these techniques do well, they are limited in scope, creating metrics to address one specific problem or task. We take a different approach by creating an environment where multiple knowledge transfer tasks can be performed using the same protein representations. Specifically, our kernel-based method, MUNK, integrates sequence and network structure to create functional protein representations, embedding proteins from different species in the same vector space. First we show proteins in different species that are close in MUNK-space are functionally similar. Next, we use these representations to share knowledge of synthetic lethal interactions between species. Importantly, we find that the results using MUNK-representations are at least as accurate as existing algorithms for these tasks. Finally, we generalize the notion of a phenolog (‘orthologous phenotype’) to use functionally similar proteins (i.e. those with similar representations). We demonstrate the utility of this broadened notion by using it to identify known phenologs and novel non-obvious ones supported by current research.

A genome-scale metabolic network alignment method within a hypergraph-based framework using a rotational tensor-vector product

Biological network alignment aims to discover important similarities and differences and thus find a mapping between topological and/or functional components of different biological molecular networks. Then, the mapped components can be considered to correspond to both their places in the network topology and their biological attributes. Development and evolution of biological network alignment methods has been accelerated by the rapidly increasing availability of such biological networks, yielding a repertoire of tens of methods based upon graph theory. However, most biological processes, especially the metabolic reactions, are more sophisticated than simple pairwise interactions and contain three or more participating components. Such multi-lateral relations are not captured by graphs, and computational methods to overcome this limitation are currently lacking. This paper introduces hypergraphs and association hypergraphs to describe metabolic networks and their potential alignments, respectively. Within this framework, metabolic networks are aligned by identifying the maximal Z-eigenvalue of a symmetric tensor. A shifted higher-order power method was utilized to identify a solution. A rotational strategy has been introduced to accelerate the tensor-vector product by 250-fold on average and reduce the storage cost by up to 1,000-fold. The algorithm was implemented on a spark-based distributed computation cluster to significantly increase the convergence rate further by 50- to 80-fold. The parameters have been explored to understand their impact on alignment accuracy and speed. In particular, the influence of initial value selection on the stationary point has been simulated to ensure an accurate approximation of the global optimum. This framework was demonstrated by alignments among the genome-wide metabolic networks of Escherichia coli MG-1655 and Halophilic archaeon DL31. To our knowledge, this is the first genome-wide metabolic network alignment at both the metabolite level and the enzyme level. These results demonstrate that it can supply quite a few valuable insights into metabolic networks. First, this method can access the driving force of organic reactions through the chemical evolution of metabolic network. Second, this method can incorporate the chemical information of enzymes and structural changes of compounds to offer new way defining reaction class and module, such as those in KEGG. Third, as a vertex-focused treatment, this method can supply novel structural and functional annotation for ill-defined molecules. The related source code is available on request.

ConnectedAlign: a PPI network alignment method for identifying conserved protein complexes across multiple species

BackgroundIn bioinformatics, network alignment algorithms have been applied to protein-protein interaction (PPI) networks to discover evolutionary conserved substructures at the system level. However, most previous methods aim to maximize the similarity of aligned proteins in pairwise networks, while concerning little about the feature of connectivity in these substructures, such as the protein complexes.ResultsIn this paper, we identify the problem of finding conserved protein complexes, which requires the aligned proteins in a PPI network to form a connected subnetwork. By taking the feature of connectivity into consideration, we propose ConnectedAlign, an efficient method to find conserved protein complexes from multiple PPI networks. The proposed method improves the coverage significantly without compromising of the consistency in the aligned results. In this way, the knowledge of protein complexes in well-studied species can be extended to that of poor-studied species.ConclusionsWe conducted extensive experiments on real PPI networks of four species, including human, yeast, fruit fly and worm. The experimental results demonstrate dominant benefits of the proposed method in finding protein complexes across multiple species.

DEEPAligner: Deep encoding of pathways to align epigenetic signatures

Background and objectiveRecently, differential DNA Methylation is known to affect the regulatory mechanism of biological pathways. A pathway encompasses a set of interacting genes or gene products that altogether perform a given biological function. Pathways often encode strong methylation signatures that are capable of distinguishing biologically distinct subtypes. Even though Next Generation Sequencing techniques such as MeDIP-seq and MBD-isolated genome sequencing (MiGS) allow for genome-wide identification of clinical and biological subtypes, there is a pressing need for computational methods to compare epigenetic signatures across pathways. MethodsA novel alignment method, called DEEPAligner (Deep Encoded Epigenetic Pathway Aligner), is proposed in this paper that finds functionally consistent and topologically sound alignments of epigenetic signatures from pathway networks. A deep embedding framework is used to obtain epigenetic signatures from pathways which are then aligned for functional consistency and local topological similarity. ResultsExperiments on four benchmark cancer datasets reveal epigenetic signatures that are conserved in cancer-specific and across-cancer subtypes. ConclusionThe proposed deep embedding framework obtains highly coherent signatures that are aligned for biological as well as structural orthology. Comparison with state-of-the-art network alignment methods clearly suggest that the proposed method obtains topologically and functionally more consistent alignments. Availabilityhttp://bdbl.nitc.ac.in/DEEPAligner

A Novel Computational Approach for Global Alignment for Multiple Biological Networks.

Due to the rapid progress of biological networks for modeling biological systems, a lot of biomolecular networks have been producing more and more protein-protein interaction (PPI) data. Analyzing protein-protein interaction networks aims to find regions of topological and functional (dis)similarities between molecular networks of different species. The study of PPI networks has the potential to teach us as much about life process and diseases at the molecular level. Although few methods have been developed for multiple PPI network alignment and thus, new network alignment methods are of a compelling need. In this paper, we propose a novel algorithm for a global alignment of multiple protein-protein interaction networks called MAPPIN. The latter relies on information available for the proteins in the networks, such as sequence, function, and network topology. Our algorithm is perfectly designed to exploit current multi-core CPU architectures, and has been extensively tested on a real data (eight species). Our experimental results show that MAPPIN significantly outperforms NetCoffee in terms of coverage. Nevertheless, MAPPIN is handicapped by the time required to load the gene annotation file. An extensive comparison versus the pioneering PPI methods also show that MAPPIN is often efficient in terms of coverage, mean entropy, or mean normalized.

Unified Alignment of Protein-Protein Interaction Networks

Paralleling the increasing availability of protein-protein interaction (PPI) network data, several network alignment methods have been proposed. Network alignments have been used to uncover functionally conserved network parts and to transfer annotations. However, due to the computational intractability of the network alignment problem, aligners are heuristics providing divergent solutions and no consensus exists on a gold standard, or which scoring scheme should be used to evaluate them. We comprehensively evaluate the alignment scoring schemes and global network aligners on large scale PPI data and observe that three methods, HUBALIGN, L-GRAAL and NATALIE, regularly produce the most topologically and biologically coherent alignments. We study the collective behaviour of network aligners and observe that PPI networks are almost entirely aligned with a handful of aligners that we unify into a new tool, Ulign. Ulign enables complete alignment of two networks, which traditional global and local aligners fail to do. Also, multiple mappings of Ulign define biologically relevant soft clusterings of proteins in PPI networks, which may be used for refining the transfer of annotations across networks. Hence, PPI networks are already well investigated by current aligners, so to gain additional biological insights, a paradigm shift is needed. We propose such a shift come from aligning all available data types collectively rather than any particular data type in isolation from others.