Optimal Sampling for Dynamic Complex Networks with Graph-Bandlimited Initialization
Many engineering, social, and biological complex systems consist of dynamical elements connected via a large-scale network. Monitoring the network's dynamics is essential for a variety of maintenance and scientific purposes. Whilst we understand how to optimally sample a single dynamic element or a non-dynamic graph, we do not possess a theory on how to optimally sample networked dynamical elements. Here, we study nonlinear dynamic graph signals on a fixed complex network. We define the necessary conditions for optimal sampling in the combining time- and graph-domain to fully recover the networked dynamics. We firstly interpret the networked dynamics into a linearized matrix. Then, we prove that the dynamic signals can be sampled and fully recovered if the networked dynamics is stable and their initialization is bandlimited in the graph spectral domain. This new theory directly maps optimal sampling locations and rates to the graph properties and governing nonlinear dynamics. This can inform the optimal placement of experimental probes and sensors on dynamical networks as well as inform the design of each sensor's optimal sampling rate. We motivate the reader with two examples of recovering the networked dynamics for: social population growth and networked protein biochemical interactions with both bandlimited and arbitrary initialization.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Irregularity-Aware Bandlimited Approximation for Graph Signal Interpolation
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy the…
Random sampling of bandlimited signals on graphs
We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of t…
DecoderSampling Theory for Graph Signals on Product Graphs
In this paper, we extend the sampling theory on graphs by constructing a framework that exploits the structure in product graphs for efficient sampling and recovery of bandlimited graph signals that lie on them. Product …
Graph sampling with determinantal processes
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibi…
Graph SamplingPoint ProcessesSampling and Recovery of Graph Signals
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals…