Kaushani Majumder | Searcharxiv

arXiv2024

Subsampling of Correlated Graph Signals

Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based generative model. The question then arises whether measurements can be obtained on a few nodes and whether the correlation structure between the signals can be used to reconstruct the graph signal on the remaining nodes. We show that node subsampling is always possible for graph signals obtained through a generative model. Further, a method to determine the number of nodes to select is proposed based on the tolerable error. A correlation-based fast greedy algorithm is developed for selecting the nodes. Finally, we verify the proposed method on different deterministic and random graphs, and show that near-perfect reconstruction is possible with node subsampling.

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arXiv2024

Greedy Selection for Heterogeneous Sensors

Simultaneous operation of all sensors in a large-scale sensor network is power-consuming and computationally expensive. Hence, it is desirable to select fewer sensors. A greedy algorithm is widely used for sensor selection in homogeneous networks with a theoretical worst-case performance of (1-1/e) ~ 63% of the optimal performance when optimizing submodular metrics. For heterogeneous sensor networks (HSNs) comprising multiple sets of sensors, most of the existing sensor selection methods optimize the performance constrained by a budget on the total value of the selected sensors. However, in many applications, the number of sensors to select from each set is known apriori, and solutions are not well-explored. For this problem, we propose a joint greedy heterogeneous sensor selection algorithm. Theoretically, we show that the worst-case performance of the proposed algorithm is bounded to 50% of the optimum for submodular cost metrics. In the special case of HSNs with two sensor networks, the performance guarantee can be improved to 63% when the number of sensors to select from one set is much smaller than the other. To validate our results experimentally, we propose a submodular metric based on the frame potential measure that considers both the correlation among the sensor measurements and their heterogeneity. We prove theoretical bounds for the mean squared error of the solution when this performance metric is used. We validate our results through simulation experiments considering both linear and non-linear measurement models corrupted by additive noise and quantization errors. Our experiments show that the proposed algorithm results in 4-10 dB lower error than existing methods.

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