Clustered Greedy Algorithm For Large-Scale Sensor Selection

In the problem of sensor selection, observations from L out of N sensors are chosen for data estimation, with the objective of minimizing an error metric. It is well known that a greedy selection (GS) method can achieve an error metric which is not worse than 1/e from that of the optimal algorithm, for a wide class of sensor selection problems. However, GS does not scale well with the problem size. The available accelerators to GS also fail to solve large scale problems in any reasonable time. In this paper, we propose a clustering-based solution called clustered greedy selection (CGS) which not only reduces the problem size, but also achieves a similar performance to GS. CGS first clusters the sensors based on a similarity metric and then applies GS on this lower dimensional problem. The method seems particularly suitable when the number of sensors to be selected is much less than the total number of sensors. We provide bounds for the worst-case performance of CGS and experimentally validate our results on some linear models.