Network alignment aims at inferring a set of anchor links matching the shared entities between different information networks, which has become a prerequisite step for effective fusion of multiple information networks. In this paper, we will study the network alignment problem to fuse online social networks specifically. Social network alignment is extremely challenging to address due to several reasons, i.e., lack of training data, network heterogeneity and one-to-one constraint. Existing network alignment works usually require a large number of training data, but such a demand can hardly be met in applications, as manual anchor link labeling is extremely expensive. Significantly different from other homogeneous network alignment works, information in online social networks is usually of heterogeneous categories, the incorporation of which in model building is not an easy task. Furthermore, the one-to-one cardinality constraint on anchor links renders their inference process intertwistingly correlated. To resolve these three challenges, a novel network alignment model, namely ActiveIter, is introduced in this paper. ActiveIter defines a set of inter-network meta diagrams for anchor link feature extraction, adopts active learning for effective label query and uses greedy link selection for anchor link cardinality filtering. Extensive experiments are conducted on real-world aligned networks datasets, and the experimental results have demonstrated the effectiveness of ActiveIter compared with other state-of-the-art baseline methods.
Network alignment problem is an important research problem, which has been studied in various areas, e.g., protein-protein-interaction network alignment in bioinformatics @cite_20 @cite_4 @cite_27 , chemical compound matching in chemistry @cite_22 , data schemas matching data warehouse @cite_3 , ontology alignment web semantics @cite_24 , graph matching in combinatorial mathematics @cite_7 , and figure matching and merging in computer vision @cite_30 @cite_17 . Network alignment is an important problem for bioinformatics. By studying the cross-species variations of biological networks, network alignment problem can be applied to predict conserved functional modules @cite_32 and infer the functions of proteins @cite_1 . Graemlin @cite_28 conducts pairwise network alignment by maximizing an objective function based on a set of learned parameters. Some works have been done on aligning multiple network in bioinformatics. IsoRank proposed in @cite_5 can align multiple networks greedily based on the pairwise node similarity scores calculated with spectral graph theory. IsoRankN @cite_6 further extends IsoRank by exploiting a spectral clustering scheme.
@cite_30 @cite_4 @cite_22 @cite_7 @cite_28 @cite_1 @cite_32 @cite_3 @cite_6 @cite_24 @cite_27 @cite_5 @cite_20 @cite_17
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Network alignment refers to the problem of matching the vertex sets of two unlabeled graphs, which can be viewed as a generalization of the classic graph isomorphism problem. Network alignment has applications in several fields, including social network analysis, privacy, pattern recognition, computer vision, and computational biology. A number of heuristic algorithms have been proposed in these fields. Recent progress in the analysis of network alignment over stochastic models sheds light on the interplay between network parameters and matchability. In this paper, we consider the alignment problem when the two networks overlap only partially, i.e., there exist vertices in one network that have no counterpart in the other. We define a random bigraph model that generates two correlated graphs G1,2; it is parameterized by the expected node overlap t2 and by the expected edge overlap s2. We define a cost function for structural mismatch under a particular alignment, and we identify a threshold for perfect matchability: if the average node degrees of G1,2 grow as ω((s−2t−1 log(n)), then minimization of the proposed cost function results in an alignment which (i) is over exactly the set of shared nodes between G1 and G2, and (ii) agrees with the true matching between these shared nodes. Our result shows that network alignment is fundamentally robust to partial edge and node overlaps. Network alignment is the problem of matching the nodes of two graphs, maximizing the similarity of the matched nodes and the edges between them. This problem is encountered in a wide array of applications - from biological networks to social networks to ontologies - where multiple networked data sources need to be integrated. Due to the difficulty of the task, an accurate alignment can rarely be found without human assistance. Thus, it is of great practical importance to develop network alignment algorithms that can optimally leverage experts who are able to provide the correct alignment for a small number of nodes. Yet, only a handful of existing works address this active network alignment setting. The majority of the existing active methods focus on absolute queries ("are nodes @math and @math the same or not?"), whereas we argue that it is generally easier for a human expert to answer relative queries ("which node in the set @math is the most similar to node @math ?"). This paper introduces a novel relative-query strategy, TopMatchings, which can be applied on top of any network alignment method that constructs and solves a bipartite matching problem. Our method identifies the most informative nodes to query based on the top- @math matchings of a bipartite graph. We compare the proposed approach to several commonly-used query strategies and perform experiments on both synthetic and real-world datasets. Our matching-based strategy yields the highest overall performance, outperforming all the baseline methods by more than 15 percentage points in some cases. Background: In addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes computationally more challenging, as most meaningful assumptions instantly lead to NPhard problems. Most previous algorithmic work on network alignments is heuristic in nature. Results: We introduce the graph-based maximum structural matching formulation for pairwise global network alignment. We relate the formulation to previous work and prove NP-hardness of the problem. Based on the new formulation we build upon recent results in computational structural biology and present a novel Lagrangian relaxation approach that, in combination with a branch-and-bound method, computes provably optimal network alignments. The Lagrangian algorithm alone is a powerful heuristic method, which produces solutions that are often near-optimal and – unlike those computed by pure heuristics – come with a quality guarantee. Conclusion: Computational experiments on the alignment of protein-protein interaction networks and on the classification of metabolic subnetworks demonstrate that the new method is reasonably fast and has advantages over pure heuristics. Our software tool is freely available as part of the LISA library. Local network alignment is an important component of the analysis of protein-protein interaction networks that may lead to the identification of evolutionary related complexes. We present AlignNemo, a new algorithm that, given the networks of two organisms, uncovers subnetworks of proteins that relate in biological function and topology of interactions. The discovered conserved subnetworks have a general topology and need not to correspond to specific interaction patterns, so that they more closely fit the models of functional complexes proposed in the literature. The algorithm is able to handle sparse interaction data with an expansion process that at each step explores the local topology of the networks beyond the proteins directly interacting with the current solution. To assess the performance of AlignNemo, we ran a series of benchmarks using statistical measures as well as biological knowledge. Based on reference datasets of protein complexes, AlignNemo shows better performance than other methods in terms of both precision and recall. We show our solutions to be biologically sound using the concept of semantic similarity applied to Gene Ontology vocabularies. The binaries of AlignNemo and supplementary details about the algorithms and the experiments are available at: sourceforge.net p alignnemo. Motivation: With the increasing availability of large protein–protein interaction networks, the question of protein network alignment is becoming central to systems biology. Network alignment is further delineated into two sub-problems: local alignment, to find small conserved motifs across networks, and global alignment, which attempts to find a best mapping between all nodes of the two networks. In this article, our aim is to improve upon existing global alignment results. Better network alignment will enable, among other things, more accurate identification of functional orthologs across species. Results: We introduce IsoRankN (IsoRank-Nibble) a global multiplenetwork alignment tool based on spectral clustering on the induced graph of pairwise alignment scores. IsoRankN outperforms existing algorithms for global network alignment in coverage and consistency on multiple alignments of the five available eukaryotic networks. Being based on spectral methods, IsoRankN is both error tolerant and computationally efficient. Availability: Our software is available freely for non-commercial purposes on request from: http: isorank.csail.mit.edu Motivation: Discovering and understanding patterns in networks of protein–protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. Results: We introduce a novel global network alignment tool, Lagrangian GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and Lagrangian relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. Availability and implementation: L-GRAAL is coded in C++. Software is available at: http: bio-nets.doc.ic.ac.uk L-GRAAL . Contact: ku.ca.lairepmi@ningod-dolam.n Supplementary information: Supplementary data are available at Bioinformatics online. Motivation: High-throughput methods for detecting molecular interactions have produced large sets of biological network data with much more yet to come. Analogous to sequence alignment, efficient and reliable network alignment methods are expected to improve our understanding of biological systems. Unlike sequence alignment, network alignment is computationally intractable. Hence, devising efficient network alignment heuristics is currently a foremost challenge in computational biology. Results: We introduce a novel network alignment algorithm, called Matching-based Integrative GRAph ALigner (MI-GRAAL), which can integrate any number and type of similarity measures between network nodes (e.g. proteins), including, but not limited to, any topological network similarity measure, sequence similarity, functional similarity and structural similarity. Hence, we resolve the ties in similarity measures and find a combination of similarity measures yielding the largest contiguous (i.e. connected) and biologically sound alignments. MI-GRAAL exposes the largest functional, connected regions of protein–protein interaction (PPI) network similarity to date: surprisingly, it reveals that 77.7 of proteins in the baker's yeast high-confidence PPI network participate in such a subnetwork that is fully contained in the human high-confidence PPI network. This is the first demonstration that species as diverse as yeast and human contain so large, continuous regions of global network similarity. We apply MI-GRAAL's alignments to predict functions of un-annotated proteins in yeast, human and bacteria validating our predictions in the literature. Furthermore, using network alignment scores for PPI networks of different herpes viruses, we reconstruct their phylogenetic relationship. This is the first time that phylogeny is exactly reconstructed from purely topological alignments of PPI networks. Availability: Supplementary files and MI-GRAAL executables: http: bio-nets.doc.ic.ac.uk MI-GRAAL . Contact: natasha@imperial.ac.uk Supplementary information:Supplementary data are available at Bioinformatics online. Important biological information is encoded in the topology of biological networks. Comparative analyses of biological networks are proving to be valuable, as they can lead to transfer of knowledge between species and give deeper insights into biological function, disease, and evolution. We introduce a new method that uses the Hungarian algorithm to produce optimal global alignment between two networks using any cost function. We design a cost function based solely on network topology and use it in our network alignment. Our method can be applied to any two networks, not just biological ones, since it is based only on network topology. We use our new method to align protein-protein interaction networks of two eukaryotic species and demonstrate that our alignment exposes large and topologically complex regions of network similarity. At the same time, our alignment is biologically valid, since many of the aligned protein pairs perform the same biological function. From the alignment, we predict function of yet unannotated proteins, many of which we validate in the literature. Also, we apply our method to find topological similarities between metabolic networks of different species and build phylogenetic trees based on our network alignment score. The phylogenetic trees obtained in this way bear a striking resemblance to the ones obtained by sequence alignments. Our method detects topologically similar regions in large networks that are statistically significant. It does this independent of protein sequence or any other information external to network topology. Biological network alignment aims to find regions of topological and functional (dis)similarities between molecular networks of different species. Then, network alignment can guide the transfer of biological knowledge from well-studied model species to less well-studied species between conserved (aligned) network regions, thus complementing valuable insights that have already been provided by genomic sequence alignment. Here, we review computational challenges behind the network alignment problem, existing approaches for solving the problem, ways of evaluating their alignment quality, and the approaches’ biomedical applications. We discuss recent innovative efforts of improving the existing view of network alignment. We conclude with open research questions in comparative biological network research that could further our understanding of principles of life, evolution, disease, and therapeutics. Motivation: Protein interaction networks provide an important system-level view of biological processes. One of the fundamental problems in biological network analysis is the global alignment of a pair of networks, which puts the proteins of one network into correspondence with the proteins of another network in a manner that conserves their interactions while respecting other evidence of their homology. By providing a mapping between the networks of different species, alignments can be used to inform hypotheses about the functions of unannotated proteins, the existence of unobserved interactions, the evolutionary divergence between the two species and the evolution of complexes and pathways. Results: We introduce GHOST, a global pairwise network aligner that uses a novel spectral signature to measure topological similarity between subnetworks. It combines a seed-and-extend global alignment phase with a local search procedure and exceeds state-of-the-art performance on several network alignment tasks. We show that the spectral signature used by GHOST is highly discriminative, whereas the alignments it produces are also robust to experimental noise. When compared with other recent approaches, we find that GHOST is able to recover larger and more biologically significant, shared subnetworks between species. Availability: An efficient and parallelized implementation of GHOST, released under the Apache 2.0 license, is available at http: cbcb.umd.edu kingsford_group ghost Contact: rob@cs.umd.edu In this paper, we survey algorithms that perform global alignment of networks or graphs. Global network alignment aligns two or more given networks to find the best mapping from nodes in one network to nodes in other networks. Since graphs are a common method of data representation, graph alignment has become important with many significant applications. Protein-protein interactions can be modeled as networks and aligning these networks of protein interactions has many applications in biological research. In this survey, we review algorithms for global pairwise alignment highlighting various proposed approaches, and classify them based on their methodology. Evaluation metrics that are used to measure the quality of the resulting alignments are also surveyed. We discuss and present a comparison between selected aligners on the same datasets and evaluate using the same evaluation metrics. Finally, a quick overview of the most popular databases of protein interaction networks is presented focusing on datasets that have been used recently. Comparative analysis of protein networks has proven to be a powerful approach for elucidating network structure and predicting protein function and interaction. A fundamental challenge for the successful application of this approach is to devise an efficient multiple network alignment algorithm. Here we present a novel framework for the problem. At the heart of the framework is a novel representation of multiple networks that is only linear in their size as opposed to current exponential representations. Our alignment algorithm is very efficient, being capable of aligning 10 networks with tens of thousands of proteins each in minutes. We show that our algorithm outperforms a previous strategy for the problem that is based on progressive alignment, and produces results that are more in line with current biological knowledge. Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. In this paper we present a method for global network alignment that is fast and robust, and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. It is based on an integer linear programming formulation, generalizing the well-studied quadratic assignment problem. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the software tool natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative state-of-the-art methods with respect to quality and running time. The recent proliferation of protein interaction networks has motivated research into network alignment: the cross-species comparison of conserved functional modules. Previous studies have laid the foundations for such comparisons and demonstrated their power on a select set of sparse interaction networks. Recently, however, new computational techniques have produced hundreds of predicted interaction networks with interconnection densities that push existing alignment algorithms to their limits. To find conserved functional modules in these new networks, we have developed Graemlin, the first algorithm capable of scalable multiple network alignment. Graemlin's explicit model of functional evolution allows both the generalization of existing alignment scoring schemes and the location of conserved network topologies other than protein complexes and metabolic pathways. To assess Graemlin's performance, we have developed the first quantitative benchmarks for network alignment, which allow comparisons of algorithms in terms of their ability to recapitulate the KEGG database of conserved functional modules. We find that Graemlin achieves substantial scalability gains over previous methods while improving sensitivity. Motivation: Given protein–protein interaction (PPI) networks of a pair of species, a pairwise global alignment corresponds to a one-to-one mapping between their proteins. Based on the presupposition that such a mapping provides pairs of functionally orthologous proteins accurately, the results of the alignment may then be used in comparative systems biology problems such as function prediction verification or construction of evolutionary relationships. Results: We show that the problem is NP-hard even for the case where the pair of networks are simply paths. We next provide a polynomial time heuristic algorithm, SPINAL, which consists of two main phases. In the first coarse-grained alignment phase, we construct all pairwise initial similarity scores based on pairwise local neighborhood matchings. Using the produced similarity scores, the fine-grained alignment phase produces the final one-to-one mapping by iteratively growing a locally improved solution subset. Both phases make use of the construction of neighborhood bipartite graphs and the contributors as a common primitive. We assess the performance of our algorithm on the PPI networks of yeast, fly, human and worm. We show that based on the accuracy measures used in relevant work, our method outperforms the state-of-the-art algorithms. Furthermore, our algorithm does not suffer from scalability issues, as such accurate results are achieved in reasonable running times as compared with the benchmark algorithms. Availability: Supplementary Document, open source codes, useful scripts, all the experimental data and the results are freely available at http: code.google.com p spinal . Contact: cesim@khas.edu.tr Supplementary information: Supplementary data are available at Bioinformatics online. Multiple networks naturally appear in numerous high-impact applications. Network alignment (i.e., finding the node correspondence across different networks) is often the very first step for many data mining tasks. Most, if not all, of the existing alignment methods are solely based on the topology of the underlying networks. Nonetheless, many real networks often have rich attribute information on nodes and or edges. In this paper, we propose a family of algorithms FINAL to align attributed networks. The key idea is to leverage the node edge attribute information to guide (topology-based) alignment process. We formulate this problem from an optimization perspective based on the alignment consistency principle, and develop effective and scalable algorithms to solve it. Our experiments on real networks show that (1) by leveraging the attribute information, our algorithms can significantly improve the alignment accuracy (i.e., up to a 30 improvement over the existing methods); (2) compared with the exact solution, our proposed fast alignment algorithm leads to a more than 10 times speed-up, while preserving a 95 accuracy; and (3) our on-query alignment method scales linearly, with an around 90 ranking accuracy compared with our exact full alignment method and a near real-time response time. Evolutionary analysis and comparison of biological networks may result in the identification of conserved mechanism between species as well as conserved modules, such as protein complexes and pathways. Following an holistic philosophy several algorithms, known as network alignment algorithms, have been proposed recently as counterpart of sequence and structure alignment algorithms, to unravel relations between different species at the interactome level. In this work we present AlignMCL, a local alignment algorithm for the identification of conserved subnetworks in different species. As many other existing tools, AlignMCL is based on the idea of merging many protein interaction networks in a single alignment graph and subsequently mining it to identify potentially conserved subnetworks. In order to asses AlignMCL we compared it to the state of the art local alignment algorithms over a rather extensive and updated dataset. Finally, to improve the usability of our tool we developed a Cytoscape plugin, AlignMCL, that offers a graphical user interface to an MCL engine. We describe an algorithm, IsoRank, for global alignment of two protein-protein interaction (PPI) networks. IsoRank aims to maximize the overall match between the two networks; in contrast, much of previous work has focused on the local alignment problem-- identifying many possible alignments, each corresponding to a local region of similarity. IsoRank is guided by the intuition that a protein should be matched with a protein in the other network if and only if the neighbors of the two proteins can also be well matched. We encode this intuition as an eigenvalue problem, in a manner analogous to Google's PageRank method. We use IsoRank to compute the first known global alignment between the S. cerevisiae and D. melanogaster PPI networks. The common subgraph has 1420 edges and describes conserved functional components between the two species. Comparisons of our results with those of a well-known algorithm for local network alignment indicate that the globally optimized alignment resolves ambiguity introduced by multiple local alignments. Finally, we interpret the results of global alignment to identify functional orthologs between yeast and fly; our functional ortholog prediction method is much simpler than a recently proposed approach and yet provides results that are more comprehensive. Motivation: Given the growth of large scale protein-protein interaction (PPI) networks obtained across multiple species and conditions, network alignment is now important research problem. Network alignment performs comparative analysis across multiple PPI networks to understand their connections and relationships. However, PPI data in high-throughput experiments still suffer from significant false positive and false negatives rates. Consequently, high confidence network alignment across entire PPI networks is not possible. At best, local network alignment attempts to alleviate this problem by completely ignoring low confidence mappings; global network alignment, on the other hand, pairs all proteins regardless. To this end, we propose an alternative strategy: instead of full alignment across the entire network or completely ignoring low confidence regions, we aim to perform highly specific protein-to-protein alignments where data confidence is high, and fall back on broader functional region-to-region alignment where detailed protein-protein alignment cannot be ascertained. The basic idea is to provide an alignment of multiple granularities to allow biological predictions at varying specificity. Results: DualAligner performs dual network alignment, in which both region-to-region alignment, where whole subgraph of one network is aligned to subgraph of another, and protein-to-protein alignment, where individual proteins in networks are aligned to one another, are performed to achieve higher accuracy network alignments. Dual network alignment is achieved in DualAligner via background information provided by a combination of GO annotation information and protein interaction network data. We tested DualAligner on the global networks from IntAct and demonstrated the superiority of our approach compared to state-of-the-art network alignment methods. We studied the effects of parameters in DualAligner in controlling the quality of the alignment. We also performed a case study that illustrates the utility of our approach. Availability: http: www.cais.ntu.edu.sg assourav DualAligner Motivation: The global alignment of protein interaction networks is a widely studied problem. It is an important first step in understanding the relationship between the proteins in different species and identifying functional orthologs. Furthermore, it can provide useful insights into the species’ evolution. Results: We propose a novel algorithm, PISwap, for optimizing global pairwise alignments of protein interaction networks, based on a local optimization heuristic that has previously demonstrated its effectiveness for a variety of other intractable problems. PISwap can begin with different types of network alignment approaches and then iteratively adjust the initial alignments by incorporating network topology information, trading it off for sequence information. In practice, our algorithm efficiently refines other well-studied alignment techniques with almost no additional time cost. We also show the robustness of the algorithm to noise in protein interaction data. In addition, the flexible nature of this algorithm makes it suitable for different applications of network alignment. This algorithm can yield interesting insights into the evolutionary dynamics of related species. Availability: Our software is freely available for non-commercial purposes from our Web site, http: piswap.csail.mit.edu .