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The growing success of graph signal processing (GSP) approaches relies heavily on prior identification of a graph over which network data admit certain regularity. However, adaptation to increasingly dynamic environments as well as demands for real-time processing of streaming data pose major challenges to this end. In this context, we develop novel algorithms for online network topology inference given streaming observations assumed to be smooth on the sought graph. Unlike existing batch algorithms, our goal is to track the (possibly) time-varying network topology while maintaining the memory and computational costs in check by processing graph signals sequentially-in-time. To recover the graph in an online fashion, we leverage proximal gradient (PG) methods to solve a judicious smoothness-regularized, time-varying optimization problem. Under mild technical conditions, we establish that the online graph learning algorithm converges to within a neighborhood of (i.e., it tracks) the optimal time-varying batch solution. Computer simulations using both synthetic and real financial market data illustrate the effectiveness of the proposed algorithm in adapting to streaming signals to track slowly-varying network connectivity.
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Variational Covariance Smoothing for Dynamic Functional Connectivity Analysis
Functional connectivity is among the widely used metrics to assess the network-level attributes of brain function. While most existing analysis frameworks assume static functional connectivity during the course of an experiment, to capture neural dynamics over short time scales, a time-varying notion of functional connectivity is required. By revealing how neural networks reconfigure in response to changing external stimuli, internal states, and task demands, time-varying functional connectivity can be leveraged to study flexible cognition, such as working memory, attention, and decision-making. A major challenge in estimating time-varying functional connectivity from high-dimensional neural is the associated computational complexity. Existing methods trade off accuracy for computational efficiency, especially in applications that require real-time or near real-time processing. Here, we build on existing work using covariance-domain state-space models and introduce a framework based on variational inference that allows low-complexity estimation of time-varying functional connectivity and construction of confidence intervals. We validate the performance of the proposed method using simulation studies. Our results reveal significant gains in computational complexity compared to existing methods, while maintaining high accuracy.
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- PAR ID:
- 10656775
- Publisher / Repository:
- IEEE
- Date Published:
- Page Range / eLocation ID:
- 245 to 249
- Format(s):
- Medium: X
- Location:
- 2024 58th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IEEECONF60004.2024.10942750
