A perturbation-based framework for link prediction via non-negative matrix factorization

Abstract

Many link prediction methods have been developed to infer unobserved links or predict latent links based on the observed network structure. However, due to network noises and irregular links in real network, the performances of existed methods are usually limited. Considering random noises and irregular links, we propose a perturbation-based framework based on Non-negative Matrix Factorization to predict missing links. We first automatically determine the suitable number of latent features, which is inner rank in NMF, by Colibri method. Then, we perturb training set of a network by perturbation sets many times and get a series of perturbed networks. Finally, the common basis matrix and coefficients matrix of these perturbed networks are obtained via NMF and form similarity matrix of the network for link prediction. Experimental results on fifteen real networks show that the proposed framework has competitive performances compared with state-of-the-art link prediction methods. Correlations between the performances of different methods and the statistics of networks show that those methods with good precisions have similar consistence.

Local-community network automata modelling based on length-three-paths for prediction of complex network structures in protein interactomes, food webs and more

“…The second objective of this study is to extend to paths of length n also the local community paradigm (LCP) theory and the associated network automata model for link prediction that at the moment are defined only on L2. The motivation to generalize LCP methods to L3 is that empirical evidences provided by several studies [3]- [9] in link prediction, and confirmed also by Kovács et al [1], show that Cannistraci resource allocation (CRA) -which is putatively the local community extension of RA-L2 -outperforms both RA-L2 and the large majority of other neighbourhood-based mechanistic and parameter-free L2-models. Hence, the question is whether also CRA-L3 would outperform RA-L3.…”

“…As a key intuition, Cannistraci et al [3] postulated also that the identification of this form of learning in neuronal networks was only a special case, hence the epitopological learning and the associated local-community-paradigm (LCP) were proposed as local rules of learning, organization and link-growth valid in general for topological link prediction in any complex network with LCP architecture [3]. On the basis of these ideas, they proposed a new class of link predictors that demonstrated -also in following studies of other authors -to outperform many state of the art local-based link predictors [3]- [9], [11] both in brain connectomes and in other types of complex networks (such as social, biological, economical, etc.). In addition, they proposed that the local-community-paradigm is a necessary paradigm of network organization to trigger epitopological learning in any type of complex network.…”

“…Hence, the current name is misleading. Since this model is a generalization and reinterpretation of a Hebbian learning local-rule to create new topology in networks, we decide to rename CRA as L2-based Cannistraci-Hebb network automaton model number one (CH1-L2), rather than Cannistraci-Resource-Allocation (CRA), as it was named in the previous articles [3]- [9], [11]- [13]. Yet, we have to admit that the formula of CH1-L2 is conceptually and mathematically awkward.…”

Leveraging the nonuniform PSO network model as a benchmark for performance evaluation in community detection and link prediction

“…We investigated if the nPSO networks could represent a realistic framework also for testing link prediction algorithms. We compared the performance of state-of-the-art approaches [30,31] (CRA [32][33][34], RA [35], SPM [36], SBM [37]) across both PSO and nPSO networks generated using diverse parameter combinations. Cannistraci-resource-allocation (CRA) is a mechanistic model which implements a local-topology-based parameter-free deterministic rule for topological link prediction motivated by the local-community-paradigm (LCP) [32][33][34]; the standard resource-allocation (RA) is instead motivated by the RA process; structural perturbation method (SPM) is a global and model-free approach that relies on a theory similar to the first-order perturbation in quantum mechanics [36]; SBM is a global approach based on general idea of a block model, where the nodes are partitioned into groups and the probability that two nodes are connected depends only on the groups to which they belong [37] (see Methods for details).…”

A Scalable Similarity-Popularity Link Prediction Method

“…Traditionally, the main performance measure used to evaluate the performance of link prediction methods has been the area under the receiver operating curve (AUROC) 5 , which can be computed as the probability that a false negative link (that is, a removed link) is assigned a score that is higher than that of a true negative link (a negative link in the original network). However, despite the fact that the AUROC metric is unbiased for imbalanced datasets, recent studies 18,20,27,28 have pointed out that it is unsuitable to use it for evaluating link prediction algorithms. Link prediction problems are characterized by a large skew within the class distribution, particularly in sparse networks.…”