Prediction of Partially Observed Dynamical Processes Over Networks via Dictionary Learning

Forero, Pedro A.; Rajawat, Ketan; Giannakis, Georgios B.

doi:10.1109/tsp.2014.2325798

Cited by 31 publications

(17 citation statements)

References 37 publications

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“…Other works target time-invariant functions, but can afford tracking sufficiently slow variations. This is the case of the dictionary learning approach in [20] and the distributed algorithms in [21] and [22]. Unfortunately, the flexibility of these algorithms to capture spatial information is also limited since [20] focuses on Laplacian regularization, whereas [21] and [22] require the signal to be bandlimited.…”

Section: Introductionmentioning

confidence: 99%

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Romero

Ioannidis

Giannakis

2017

IEEE J. Sel. Top. Signal Process.

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Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the cost of sampling. Alleviating the limited flexibility of existing approaches, the present paper broadens the existing kernel-based graph function reconstruction framework to accommodate time-evolving functions over possibly time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-time kernels with complementary strengths. The first facilitates judicious control of regularization on a space-time frequency plane, whereas the second can afford time-varying topologies. Batch and online estimators are also put forth, and a novel kernel Kalman filter is developed to obtain these estimates at affordable computational cost. Numerical tests with real data sets corroborate the merits of the proposed methods relative to competing alternatives.

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Section: Introductionmentioning

confidence: 99%

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Romero

Ioannidis

Giannakis

2017

IEEE J. Sel. Top. Signal Process.

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“…Other works target time-invariant functions, but can only afford tracking sufficiently slow variations. This is the case with the dictionary learning approach in [51] and the distributed algorithms in [52] and [53]. Unfortunately, the flexibility of these algorithms to capture spatial information is also limited since [51] focuses on Laplacian regularization, whereas [52] and [53] require the signal to be bandlimited.…”

Section: Inference Of Dynamic Functions Over Dynamic Graphsmentioning

confidence: 99%

Kernel-Based Inference of Functions Over Graphs

Ioannidis

Νικολακόπουλος

et al. 2018

Adaptive Learning Methods for Nonlinear System Modeling

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The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -and prevalent in several fields of study -problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.

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“…Instead of using existing dictionaries, a data-driven one is proposed to learn from historical data and the network topology information. Such dictionary learning techniques have been successfully applied to image processing [16], network load prediction [6], and cognitive radio spectrum sensing [13].…”

Section: Spat Io-temporal Wind Power Prediction Using Dictionarymentioning

confidence: 99%

“…The norm of each atom d m is bounded in(6) to prevent the degeneracy of obtaining arbitrarily large D by replacing (D, St) with (�D,cst) for c« 1.Since the wind power outputs {pd[= l are inherently nonnegative, naturally (D, S) are constrained to be nonnegative as well. Problem (4) is nonconvex, and hence difficult to solve in general.…”

mentioning

confidence: 99%

Short-term wind power forecasting using nonnegative sparse coding

Kim

Giannakis

2015

2015 49th Annual Conference on Information Sciences and Systems (CISS)

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State-of-the-art statistical learning techniques are adapted in this contribution for real-time wind power forecasting. Spatio-temporal wind power outputs are modeled as a linear combination of "few" atoms in a dictionary. By exploiting geographical information of wind farms, a graph Laplacian based regularizer encourages positive correlation of wind power levels of adjacent farms. Real-time forecasting is achieved by online nonnegative sparse coding with elastic net regularization.The resultant convex optimization problems are efficiently solved using a block coordinate descent solver. Numerical tests on real data corroborate the merits of the proposed approach, which outperforms competitive alternatives in forecasting accuracy.

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Prediction of Partially Observed Dynamical Processes Over Networks via Dictionary Learning

Cited by 31 publications

References 37 publications

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Kernel-Based Inference of Functions Over Graphs

Short-term wind power forecasting using nonnegative sparse coding

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