Learning time varying graphs

Kalofolias, Vassilis; Loukas, Andreas; Thanou, Dorina; Frossard, Pascal

doi:10.1109/icassp.2017.7952672

Cited by 77 publications

(85 citation statements)

References 14 publications

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“…For fixed Y, (23) reduces to a quadratic program (QP) subject to linear constraints, which can be solved via interior point methods. For large graphs, scalable alternatives include the alternating-direction method of multipliers (ADMM), or, primal-dual solvers of the reformulation described in the following section; see (26). For fixed L, the resulting problem is a matrix-valued counterpart of (22).…”

Section: A Laplacian-based Factor Analysis Model and Graph Kernel Rementioning

confidence: 99%

“…to diag(W) = 0, W ij = W ji ≥ 0, i = j, one can span a host of approaches to graph inference from smooth signals. Examples include the Laplacianbased factor analysis model [9] in (26), and common graph constructions using the Gaussian kernel to define edge weights W ij := exp −…”

Section: Comparative Summarymentioning

confidence: 99%

“…Joint identification of multiple graphshift operators can be useful even when interest is only in one of the networks, since joint formulations exploit additional sources of information and, hence, they are likely to result in more accurate topology estimates. Although noticeably less than its single-network counterpart, joint inference of multiple graphs has attracted attention, especially for the case of GMRFs and in the context of dynamic (time-varying) topologies [1], [15], [20], [26], [58]. All of the aforementioned works consider that the multiple graphs G t (V, E t , W t ), t = 1, .…”

Section: B Dynamic Network and Multi-layer Graphsmentioning

confidence: 99%

“…A general estimator for learning slowly time-varying graphs over which signals in X t exhibit smooth variations was put forth in [26]. Let S t = W t denote the adjacency matrix of G t and recall the Euclideandistance matrix Z t defined in Section V-B.…”

Section: B Dynamic Network and Multi-layer Graphsmentioning

confidence: 99%

“…Let S t = W t denote the adjacency matrix of G t and recall the Euclideandistance matrix Z t defined in Section V-B. The idea in [26]…”

Section: B Dynamic Network and Multi-layer Graphsmentioning

confidence: 99%

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Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This tutorial offers an overview of graph learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure, and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks, nonlinear models of pairwise interaction, as well as extensions to directed graphs and their relation to causal inference. All in all, this paper introduces readers to challenges and opportunities for signal processing research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time. †

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Section: A Laplacian-based Factor Analysis Model and Graph Kernel Rementioning

confidence: 99%

Section: Comparative Summarymentioning

confidence: 99%