Online Filtering over Expanding Graphs

Das, Bishwadeep; Isufi, Elvin

doi:10.1109/ieeeconf56349.2022.10052045

Cited by 4 publications

(2 citation statements)

References 26 publications

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“…We perform online forecasting on the expanding graph using the GEVAR filter bank. As an alternative to batch processing, we update the filter bank online using tools from online machine learning, which has already been used for graph signal processing tasks in time invariant setting [9,24,25]. Specifically, we use adaptive online gradient descent, with a provable sub-linear regret upper bound w.r.t the batch solution [26].…”

Section: Introductionmentioning

confidence: 99%

Online Vector Autoregressive Models Over Expanding Graphs

Das

Isufi

2023

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Current spatiotemporal learning methods for complex data exploit the graph structure as an inductive bias to restrict the function space and improve data and computation efficiency. However, these methods work principally on graphs with a fixed size, whereas in several applications there are expanding graphs where new nodes join the network; e.g., new sensors joining a sensor network or new users joining a recommender system. This paper focuses on the non-trivial extension of spatiotemporal methods to this setting, where now it is key to jointly capture both the topological and signal dynamics. Specifically, it considers a graph vector autoregressive (GVAR) model for multivariate time series. The GVAR is a multivariate linear model that leverages a bank of graph filters allowing scalability and data efficiency. To account for the dynamic nature of the graphs, the filters's parameters are learned on-the-fly via adaptive gradient descent with provable sub-linear regret. Numerical results on both synthetic and real data corroborate the proposed method.

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Section: Introductionmentioning

confidence: 99%

Online Vector Autoregressive Models Over Expanding Graphs

Das

Isufi

2023

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…To account for the underlying topological dynamics, we propose an online framework to perform edge flow prediction over an expanding simplicial complex. In detail, we first use the simplicial convolutional filter proposed in [10,21] as the flow predictor on the new edge; then we consider an online gradient descent algorithm to update the filter parameters [22,23], generalizing the methods developed for the node signal space [24,25,26]. Online gradient descent, as a simple update rule, has sub-linear regret bounds [22].…”

Section: Introductionmentioning

confidence: 99%

Online Edge Flow Prediction Over Expanding Simplicial Complexes

Yang

Das

Isufi

2023

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Simplicial convolutional filters can process signals defined over levels of a simplicial complex such as nodes, edges, triangles, and so on with applications in e.g., flow prediction in transportation or financial networks. However, the underlying topology expands over time in a way that new edges and triangles form. For example, in a transportation network, a new connection between two locations is newly built, or in a currency exchange market, two currencies can be exchanged without an intermediate currency that can be understood as a new edge between them. To handle the streaming nature of data, we propose an online prediction for edge flows which generalizes to other higher-order simplicial signals. This is achieved by updating the filter coefficients via an online gradient descent with a provable sub-linear regret relative to the simplicial filter optimized over the whole sequence of edge flows. The update of the filter coefficients associated with the lower and upper Hodge Laplacians can be uncoupled in general. We test the online edge flow prediction on an expanding synthetic simplicial complex and a coauthorship complex showing a close performance to the offline counterpart.

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Online Graph Filtering Over Expanding Graphs

Das,

Isufi

2024

IEEE Trans. Signal Process.

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Online Filtering over Expanding Graphs

Cited by 4 publications

References 26 publications

Online Vector Autoregressive Models Over Expanding Graphs

Online Vector Autoregressive Models Over Expanding Graphs

Online Edge Flow Prediction Over Expanding Simplicial Complexes

Online Graph Filtering Over Expanding Graphs

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