Abstract
Abstract. This paper concerns the problem of optimal monitoring network layout using information-theoretical methods. Numerous different objectives based on information measures have been proposed in recent literature, often focusing simultaneously on maximum information and minimum dependence between the chosen locations for data collection stations. We discuss these objective functions and conclude that a single-objective optimization of joint entropy suffices to maximize the collection of information for a given number of stations. We argue that the widespread notion of minimizing redundancy, or dependence between monitored signals, as a secondary objective is not desirable and has no intrinsic justification. The negative effect of redundancy on total collected information is already accounted for in joint entropy, which measures total information net of any redundancies. In fact, for two networks of equal joint entropy, the one with a higher amount of redundant information should be preferred for reasons of robustness against failure. In attaining the maximum joint entropy objective, we investigate exhaustive optimization, a more computationally tractable greedy approach that adds one station at a time, and we introduce the “greedy drop” approach, where the full set of stations is reduced one at a time. We show that no greedy approach can exist that is guaranteed to reach the global optimum.
Highlights
Over the last decade, a large number of papers on information-theory-based design of monitoring networks have been published
We argue for the maximum joint entropy objective for maximizing the total information collected by a monitoring network
Before any interpretation of the placement, we must note that the choices made in quantization and the availability of data play an important role in the optimal networks identified
Summary
A large number of papers on information-theory-based design of monitoring networks have been published. These studies apply informationtheoretical measures on multiple time series from a set of sensors, to identify optimal subsets. Some have suggested that either a multi-objective approach or a single objective derived from multiple objectives is necessary to find an optimal monitoring network. These methods were often compared to other existing methods in case studies used to demonstrate that one objective should be preferred over the other based on the resulting networks. We argue that minimizing redundancy is a redundant objective
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