Citation: Kalini´c, H.;
´
Catipovi´c L.;
Mati´c, F. Optimal Sensor Placement
Using Learning Models—A
Mediterranean Case Study. Remote
Sens. 2022, 14, 2989. https://doi.org/
10.3390/rs14132989
Academic Editors: M. Jamal Deen,
Subhas Mukhopadhyay, Yangquan
Chen, Simone Morais, Nunzio
Cennamo and Junseop Lee
Received: 27 April 2022
Accepted: 17 June 2022
Published: 22 June 2022
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Technical Note
Optimal Sensor Placement Using Learning
Models—A Mediterranean Case Study
Hrvoje Kalini´c
1,
* , Leon
´
Catipovi´c
2
and Frano Mati´c
3,4
1
Department of Informatics, Faculty of Science, University of Split, 21000 Split, Croatia
2
Department of Physics, Faculty of Science, University of Split, 21000 Split, Croatia; leon.catipovic@pmfst.hr
3
Physical Oceanography Laboratory, Institute of Oceanography and Fisheries, 21000 Split, Croatia;
fmatic@izor.hr
4
University Department of Marine Studies, University of Split, 21000 Split, Croatia
* Correspondence: hrvoje.kalinic@pmfst.hr
Abstract:
In this paper, we discuss different approaches to optimal sensor placement and propose
that an optimal sensor location can be selected using unsupervised learning methods such as self-
organising maps, neural gas or the K-means algorithm. We show how each of the algorithms can be
used for this purpose and that additional constraints such as distance from shore, which is presumed
to be related to deployment and maintenance costs, can be considered. The study uses wind data
over the Mediterranean Sea and uses the reconstruction error to evaluate sensor location selection.
The reconstruction error shows that results deteriorate when additional constraints are added to the
equation. However, it is also shown that a small fraction of the data is sufficient to reconstruct wind
data over a larger geographic area with an error comparable to that of a meteorological model. The
results are confirmed by several experiments and are consistent with the results of previous studies.
Keywords:
optimal sensor placement; feature selection; unsupervised learning; clustering; self-
organizing maps; neural gas; k-means
1. Introduction
When faced with the problem of selecting a site for sensor placement, one usually
asks how this can be done in an “optimal” way. Phrasing the question this way, one might
tacitly assume that it is an optimisation problem. This assumption could direct our search
for a solution to the definition of a criterion that defines “optimal” and enables a search for
an optimal solution. In most cases, the optimisation criterion is related to the budget in one
way or another. For example, one might try to optimise sensor cost by finding the smallest
number of sensors with the greatest coverage. Or one could optimise the total cost of a
measuring endeavour by including deployment and maintenance costs. Alternatively, the
problem can be formulated as an optimization problem with constraints, where a budget
or a certain number of sensors is an additional constraint. In such scenarios, the constraint
might be some other scarce resource (e.g., energy) rather than budget, but coverage or
even accuracy of measurements is the primary concern. Much previous work falls into this
category, and one could say that this describes a traditional approach in which optimal
sensor placement is treated as an optimisation problem [
1
–
3
]. However, we will not only
treat the optimal sensor location problem as an optimisation problem, but also discuss an
alternative in which we treat the optimal sensor location problem as a feature selection
problem. Next, we will propose that classical clustering approaches can be used for sensor
location selection.
The optimal sensor placement problem could also be approached differently, asking
whether there are certain locations that are better suited for data collection. This problem
could be called a selection problem rather than an optimisation problem. In this case, the
question is whether a particular site (out of a set of available sites) is more suitable than
Remote Sens. 2022, 14, 2989. https://doi.org/10.3390/rs14132989 https://www.mdpi.com/journal/remotesensing
