Finding the optimal number of groups in the context of a clustering algorithm is identified as a difficult problem. In this article, we automate this choice for the spectral clustering algorithm with a novel heuristic. Our method is deterministic, and remarkable by its low computational burden. We show its effectiveness with respect to the state of the art, and further investigate assumptions underlying previous work through an empirical study, with the support of synthetic and real data sets.
In precision agriculture, pesticides and other inputs shall be used precisely when (and where) they are needed. European Directive 2009/128/EC calls for respecting the principles of integrated pest management (IPM) in the member states. To clarify the question, when, for instance, fungicide use is needed, the well-established economic principle of IPM may be used. This principle says that pests shall be controlled when the costs of control correspond with the damage the pests will cause. Disease levels corresponding with the costs of control are referred to as control thresholds in IPM. Several models have been developed in plant pathology to predict when epidemics will occur, but hardly any of these models predicts a control threshold directly limiting their usefulness for answering the question when pest control is needed according to the principles of IPM. Previously, we quantified the temporal distance between critical rainfall periods and the breaking of the control threshold of Zymoseptoria tritici on winter wheat as being affected by temperature, based on data from 52 field experiments carried out in Luxembourg from 2005 to 2016. This knowledge was used to construct the ShIFT (SeptorIa ForecasT, https://shift.list.lu/) model, which has been validated using external data recorded between 2017 and 2019. Within the efficacy period of a systemic fungicide, the model allowed correct predictions in 84.6% of the cases, while 15.4% of the cases were predicted falsely. The average deviation between the observed and predicted dates of epidemic outbreaks was 0.62 ± 2.4 days with a maximum deviation of 19 days. The observed and predicted dates were closely correlated (r = 0.92, P < 0.0001). Apart from outliers, the forecast model tested here was reliable within the period of efficacy of current commercial fungicides.
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