Online Network Topology Inference with Partial Connectivity Informatio

Shafipour, Rasoul; Mateos, Gonzalo

doi:10.1109/camsap45676.2019.9022677

Cited by 3 publications

(12 citation statements)

References 31 publications

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“…Unlike [13] but similar to link prediction problems ( [1], Ch. 7.2), [14], here we rely on a priori knowledge about the presence (or absence) of a few edges; conceivably leading to simpler algorithmic updates and better recovery performance. We may learn about edge status via limited questionnaires and experiments, or, we could perform edge screening prior to topology inference [15]; see also the discussion in Section 4.…”

Section: Technical Approach and Paper Outlinementioning

confidence: 99%

“…Few works have recently built on this rationale to identify a symmetric GSO given its eigenvectors, either assuming that the input is white [6,10]-equivalently implying y is graph stationary [7][8][9]; or, colored [30,31]. Unlike prior online algorithms developed based on the aforementioned graph spectral domain design [13,14], here we estimate the (possibly) time-varying GSO directly (without tracking its eigenvectors) and derive quantifiable recovery guarantees; see Remark 3. Recent algorithms for identifying topologies of time-varying graphs [32,33] operate in batch mode, they are non-recursive and hence their computational complexity grows linearly with time.…”

Section: Contributions In Context Of Prior Related Workmentioning

confidence: 99%

“…This so-termed infinite memory sample estimate is appropriate for time-invariant settings, i.e., when the graph topology remains fixed for all t. To track dynamic graphs, it is prudent to eventually forget about past observations (cf. (14) incorporates all signals {y τ } t τ=1 ). This can be accomplished via exponentially-weighted empirical covariance estimators or by using a (fixed-length) sliding window of data, both of which can be updated recursively via minor modifications to (14).…”

Section: Algorithm Constructionmentioning

confidence: 99%

“…(14) incorporates all signals {y τ } t τ=1 ). This can be accomplished via exponentially-weighted empirical covariance estimators or by using a (fixed-length) sliding window of data, both of which can be updated recursively via minor modifications to (14). Initialization of the covariance estimateĈ y,0 can be performed in practice via sample averaging of a few signals collected before the algorithm runs, or simply as a scaled identity matrix.…”

Section: Algorithm Constructionmentioning

confidence: 99%

“…Recall that the gradient ∇g t (S t ) is given by (9), and it is a function of the updated covariance matrixĈ y,t (cf. (14)). The proximal operator for the 1 −norm entails the pointwise nonlinearity in (12), with a threshold γ t that will in general be time varying.…”

Section: Algorithm Constructionmentioning

confidence: 99%

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Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Shafipour

Mateos

2020

Algorithms

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We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

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Section: Technical Approach and Paper Outlinementioning

confidence: 99%

Section: Contributions In Context Of Prior Related Workmentioning

confidence: 99%

Section: Algorithm Constructionmentioning

confidence: 99%

Section: Algorithm Constructionmentioning

confidence: 99%

Section: Algorithm Constructionmentioning

confidence: 99%

See 3 more Smart Citations

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Shafipour

Mateos

2020

Algorithms

Self Cite

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Community Inference From Partially Observed Graph Signals: Algorithms and Analysis

Wai

Eldar

Ozdaglar

et al. 2022

IEEE Trans. Signal Process.

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Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Shafipour¹,

Mateos²

2020

Preprint

Self Cite

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We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and effect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations' covariance matrix and the so-called graph shift operator (GSO -a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations' empirical covariance matrix. For streaming data said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

show abstract

Online Network Topology Inference with Partial Connectivity Informatio

Cited by 3 publications

References 31 publications

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Community Inference From Partially Observed Graph Signals: Algorithms and Analysis

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

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