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Register a new userSPECTRE: Seedless Network Alignment via Spectral Centralities
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Added by
Mikhail Hayhoe
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Network alignment consists of finding a structure-preserving correspondence between the nodes of two correlated, but not necessarily identical, networks. This problem finds applications in a wide variety of fields, from the alignment of proteins in computational biology, to the de-anonymization of social networks, as well as recognition tasks in computer vision. In this work we introduce SPECTRE, a scalable algorithm that uses spectral centrality measures and percolation techniques. Unlike most network alignment algorithms, SPECTRE requires no seeds (i.e., pairs of nodes identified beforehand), which in many cases are expensive, or impossible, to obtain. Instead, SPECTRE generates an initial noisy seed set via spectral centrality measures which is then used to robustly grow a network alignment via bootstrap percolation techniques. We show that, while this seed set may contain a majority of incorrect pairs, SPECTRE is still able to obtain a high-quality alignment. Through extensive numerical simulations, we show that SPECTRE allows for fast run times and high accuracy on large synthetic and real-world networks, even those which do not exhibit a high correlation.
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Social network alignment, aligning different social networks on their common users, is receiving dramatic attention from both academic and industry. All existing studies consider the social network to be static and neglect its inherent dynamics. In fact, the dynamics of social networks contain the discriminative pattern of an individual, which can be leveraged to facilitate social network alignment. Hence, we for the first time propose to study the problem of aligning dynamic social networks. Towards this end, we propose a novel Dynamic social Network Alignment (DNA) framework, a unified optimization approach over deep neural architectures, to unfold the fruitful dynamics to perform alignment. However, it faces tremendous challenges in both modeling and optimization: (1) To model the intra-network dynamics, we explore the local dynamics of the latent pattern in friending evolvement and the global consistency of the representation similarity with neighbors. We design a novel deep neural architecture to obtain the dual embedding capturing local dynamics and global consistency for each user. (2) To model the inter-network alignment, we exploit the underlying identity of an individual from the dual embedding in each dynamic social network. We design a unified optimization approach interplaying proposed deep neural architectures to construct a common subspace of identity embeddings. (3) To address this optimization problem, we design an effective alternating algorithm with solid theoretical guarantees.We conduct extensive experiments on real-world datasets and show that the proposed DNA framework substantially outperforms the state-of-the-art methods.
Networks model a variety of complex phenomena across different domains. In many applications, one of the most essential tasks is to align two or more networks to infer the similarities between cross-network vertices and discover potential node-level correspondence. In this paper, we propose ELRUNA (Elimination rule-based network alignment), a novel network alignment algorithm that relies exclusively on the underlying graph structure. Under the guidance of the elimination rules that we defined, ELRUNA computes the similarity between a pair of cross-network vertices iteratively by accumulating the similarities between their selected neighbors. The resulting cross-network similarity matrix is then used to infer a permutation matrix that encodes the final alignment of cross-network vertices. In addition to the novel alignment algorithm, we also improve the performance of local search, a commonly used post-processing step for solving the network alignment problem, by introducing a novel selection method RAWSEM (Randomwalk based selection method) based on the propagation of the levels of mismatching (defined in the paper) of vertices across the networks. The key idea is to pass on the initial levels of mismatching of vertices throughout the entire network in a random-walk fashion. Through extensive numerical experiments on real networks, we demonstrate that ELRUNA significantly outperforms the state-of-the-art alignment methods in terms of alignment accuracy under lower or comparable running time. Moreover, ELRUNA is robust to network perturbations such that it can maintain a close to optimal objective value under a high level of noise added to the original networks. Finally, the proposed RAWSEM can further improve the alignment quality with a less number of iterations compared with the naive local search method.
Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes eigenvector-based centralities, including PageRank and hub/authority scores, to provide a common framework for two popular classes of multilayer networks: multiplex networks (which have layers that encode different types of relationships) and temporal networks (in which the relationships change over time). Our approach involves the study of joint, marginal, and conditional supracentralities that one can calculate from the dominant eigenvector of a supracentrality matrix [Taylor et al., 2017], which couples centrality matrices that are associated with individual network layers. We extend this prior work (which was restricted to temporal networks with layers that are coupled by adjacent-in-time coupling) by allowing the layers to be coupled through a (possibly asymmetric) interlayer-adjacency matrix $tilde{{bf A}}$, where the entry $tilde{A}_{tt} geq 0$ encodes the coupling between layers $t$ and $t$. Our framework provides a unifying foundation for centrality analysis of multiplex and temporal networks; it also illustrates a complicated dependency of the supracentralities on the topology and weights of interlayer coupling. By scaling $tilde{{bf A}}$ by an interlayer-coupling strength $omegage0$ and developing a singular perturbation theory for the limits of weak ($omegato0^+$) and strong coupling ($omegatoinfty$), we also reveal an interesting dependence of supracentralities on the dominant left and right eigenvectors of $tilde{{bf A}}$.
We study the problem of embedding edgeless nodes such as users who newly enter the underlying network, while using graph neural networks (GNNs) widely studied for effective representation learning of graphs thanks to its highly expressive capability via message passing. Our study is motivated by the fact that existing GNNs cannot be adopted for our problem since message passing to such edgeless nodes having no connections is impossible. To tackle this challenge, we propose Edgeless-GNN, a new framework that enables GNNs to generate node embeddings even for edgeless nodes through unsupervised inductive learning. Specifically, we start by constructing a $k$-nearest neighbor graph ($k$NNG) based on the similarity of node attributes to replace the GNNs computation graph defined by the neighborhood-based aggregation of each node. As our main contributions, the known network structure is used to train model parameters, while a new loss function is established using energy-based learning in such a way that our model learns the network structure. For the edgeless nodes, we inductively infer embeddings for the edgeless nodes by using edges via $k$NNG construction as a computation graph. By evaluating the performance of various downstream machine learning (ML) tasks, we empirically demonstrate that Edgeless-GNN consistently outperforms state-of-the-art methods of inductive network embedding. Moreover, our findings corroborate the effectiveness of Edgeless-GNN in judiciously combining the replaced computation graph with our newly designed loss. Our framework is GNN-model-agnostic; thus, GNN models can be appropriately chosen according to ones needs and ML tasks.
Network alignment is a problem of finding the node mapping between similar networks. It links the data from separate sources and is widely studied in bioinformation and social network fields. The critical difference between network alignment and exact graph matching is that the network alignment considers node mapping in non-isomorphic graphs with error tolerance. Researchers usually utilize AC (accuracy) to measure the performance of network alignments which comparing each output element with the benchmark directly. However, this metric neglects that some nodes are naturally indistinguishable even in single graphs (e.g., nodes have the same neighbors) and no need to distinguish across graphs. Such neglect leads to the underestimation of models. We propose an unbiased metric for network alignment that takes indistinguishable nodes into consideration to address this problem. Our detailed experiments with different scales on both synthetic and real-world datasets demonstrate that the proposed metric correctly reflects the deviation of result mapping from benchmark mapping as standard metric AC does. Comparing with the AC, the proposed metric effectively blocks the effect of indistinguishable nodes and retains stability under increasing indistinguishable nodes.
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