2019 # Connecting the Dots: Identifying Network Structure via Graph Signal Processing

**Abstract:** 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 lackin…

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“…Several approaches address graph learning problem, and two overview papers about graph learning have been published recently [14], [15]. Among the techniques for learning timevarying graphs, the Kalofolias et al method, where constraints are introduced so that the edge weights change smoothly over time, is close to ours [33].…”

confidence: 99%

“…Several approaches address graph learning problem, and two overview papers about graph learning have been published recently [14], [15]. Among the techniques for learning timevarying graphs, the Kalofolias et al method, where constraints are introduced so that the edge weights change smoothly over time, is close to ours [33].…”

confidence: 99%

“…Note that graphs estimated with this approach often have negative edge weights. In contrast, our proposed method constrains to have non-negative edges in the estimated graph, because such graphs are often desired for many applications [14], [15]. Furthermore, our method has a lower computation complexity, as TVGL requires eigendecompositions of target matrices to calculate a proximal operator of a logarithm determinant term, whereas our approach is an eigendecomposition-free algorithm.…”

confidence: 99%

“…We treat the observations as filtered graph signals and learn the graph topology as a blind deconvolution problem. Several inference methods have been proposed, e.g., based on smoothness [14], spectral template [15], structures of topology [16] etc., see the overview in [17,18]. Meanwhile, for practitioners of graph learning, obtaining the graph topology is only the first step, and oftentimes the end goal is to deduce interpretable features from the graph topology such as node centrality, communities.…”

confidence: 99%

“…They can be used for online tasks, such as adaptive control and decision-making, and thus have attracted much interest in the control community. More attention has been paid, however, on batch algorithms for network estimation, e.g., [31], [35]. Quantized data are ubiquitous across domains, for example, active/inactive states of a gene [2], ordinal rating of an individual [16], and failure conditions of an infrastructure [5].…”

confidence: 99%

“…Quantized data are ubiquitous across domains, for example, active/inactive states of a gene [2], ordinal rating of an individual [16], and failure conditions of an infrastructure [5]. Network estimation problems based on quantized timeseries data need to be investigated in more depth with rigorous performance analysis [2], [31].…”

confidence: 99%