Fast link prediction for large networks using spectral embedding

Pachev, Benjamin; Webb, Benjamin

doi:10.1093/comnet/cnx021

Cited by 16 publications

(8 citation statements)

References 23 publications

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“…We observe that the proof given in [PW17] works equally well in the more general disconnected case as well, provided that we define everything as we have done.…”

Section: Resistance Embeddingsmentioning

confidence: 67%

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DynACPD Embedding Algorithm for Prediction Tasks in Dynamic Networks

Connell,

Wang

2021

Preprint

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Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper, we consider low dimensional embeddings of dynamic networks, that is a family of time varying networks where there exist both temporal and spatial link relationships between nodes. We present novel embedding methods for a dynamic network based on higher order tensor decompositions for tensorial representations of the dynamic network. In one sense, our embeddings are analogous to spectral embedding methods for static networks. We provide a rationale for our algorithms via a mathematical analysis of some potential reasons for their effectiveness. Finally, we demonstrate the power and efficiency of our approach by comparing our algorithms' performance on the link prediction task against an array of current baseline methods across three distinct real-world dynamic networks.

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“…We observe that the proof given in [PW17] works equally well in the more general disconnected case as well, provided that we define everything as we have done.…”

Section: Resistance Embeddingsmentioning

confidence: 67%

“…The following effective reformulation of Proposition 3.1 of [PW17] explains the relationship between these.…”

Section: Resistance Embeddingsmentioning

confidence: 99%

DynACPD Embedding Algorithm for Prediction Tasks in Dynamic Networks

Connell,

Wang

2021

Preprint

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“…Numerically estimating the group inverse. In [25] the authors use spectral embedding to create estimates for resistance distance. More specifically, given the spectral decomposition of the Laplacian matrix L = n−1 k=1 µ k z k z T k , the spectral decomposition of the Moore-Penrose pseudo inverse is given by L…”

Section: R(u V)mentioning

confidence: 99%

Algorithmic techniques for finding resistance distances on structured graphs

Evans¹,

Francis²

2021

Preprint

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In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in combinatorial matrix theory and spectral graph theory. Moreover resistance distance has applications ranging from quantifying biological structures, distributed control systems, network analysis, and power grid systems. In this paper we discuss both exact techniques and approximate techniques and for each method discussed we provide an illustrative example of the technique. We also present some open questions and conjectures.

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“…The authors view their method's output as predictions rather than candidates, and thus focus on high precision at small values of k relative to our setting. Another approach, Approximate Resistance Distance Link Predictor [21] generates spectral node embeddings by constructing a low-rank approximation of the graph's effective resistance matrix, and applies a k-closest pairs algorithm on the embeddings, predicting these as links. However, this approach does not scale to moderate embedding dimensions (e.g., the dimensionality of 128 often-used used in embedding methods), and is often outperformed by the simple common neighbors heuristic.…”

Section: Related Workmentioning

confidence: 99%

A Hidden Challenge of Link Prediction: Which Pairs to Check?

Belth,

Büyükçakır,

Koutra

2021

Preprint

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The traditional setup of link prediction in networks assumes that a test set of node pairs, which is usually balanced, is available over which to predict the presence of links. However, in practice, there is no test set: the ground-truth is not known, so the number of possible pairs to predict over is quadratic in the number of nodes in the graph. Moreover, because graphs are sparse, most of these possible pairs will not be links. Thus, link prediction methods, which often rely on proximity-preserving embeddings or heuristic notions of node similarity, face a vast search space, with many pairs that are in close proximity, but that should not be linked. To mitigate this issue, we introduce LINKWALDO, a framework for choosing from this quadratic, massively-skewed search space of node pairs, a concise set of candidate pairs that, in addition to being in close proximity, also structurally resemble the observed edges. This allows it to ignore some high-proximity but low-resemblance pairs, and also identify high-resemblance, lower-proximity pairs. Our framework is built on a model that theoretically combines Stochastic Block Models (SBMs) with node proximity models. The block structure of the SBM maps out where in the search space new links are expected to fall, and the proximity identifies the most plausible links within these blocks, using locality sensitive hashing to avoid expensive exhaustive search. LINKWALDO can use any node representation learning or heuristic definition of proximity, and can generate candidate pairs for any link prediction method, allowing the representation power of current and future methods to be realized for link prediction in practice. We evaluate LINKWALDO on 13 networks across multiple domains, and show that on average it returns candidate sets containing 7-33% more missing and future links than both embedding-based and heuristic baselines' sets.

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Fast link prediction for large networks using spectral embedding

Cited by 16 publications

References 23 publications

DynACPD Embedding Algorithm for Prediction Tasks in Dynamic Networks

DynACPD Embedding Algorithm for Prediction Tasks in Dynamic Networks

Algorithmic techniques for finding resistance distances on structured graphs

A Hidden Challenge of Link Prediction: Which Pairs to Check?

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