Probabilistic reconstruction of spatio-temporal processes over multi-relational graphs

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Given nodal observations that can be limited due to sampling costs or privacy concerns, several network-science-related applications entail reconstruction of values on all network nodes by leveraging topology information. Such a semi-supervised learning (SSL) task has been tackled mainly for graphs capturing a single class of inter-dependencies (or relations) among nodal variables. Faced with multi-relational graphs (MRGs), which emerge in various real-world networks, the present work introduces a principled framework to extrapolate spatio-temporal nodal processes that could be stationary or nonstationary. Broadening the scope of graph kernel-based approaches to MRGs, stationary graph processes are modeled first using a Gaussian mixture (GM) prior, where the covariance matrix of each Gaussian component describes one of the relations in the MRG. To further cope with nonstationary nodal processes, a first-order topology-dependent Gaussian transition prior is considered per relation, what gives rise to a GM transition density that accounts for all relations. In both cases, adapting the expectation-maximization (EM) algorithm yields two novel graph-adaptive solvers that not only reconstructs nodal features over unobserved nodes, but also quantifies the contribution of each relation. To enrich expressiveness of these novel EM-based approaches, multiple kernels per relation are also explored. Experiments with real data showcase the merits of the proposed methods relative to the existing alternatives.

Original languageEnglish (US)
Article number9356235
Pages (from-to)166-176
Number of pages11
JournalIEEE Transactions on Signal and Information Processing over Networks
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2015 IEEE.


  • EM
  • Spatio-temporal process
  • multi-kernel learning
  • multi-relational graphs
  • semi-supervised learning


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