In Precision Agriculture, the utilization of management zones (MZs) that take
into account within-field variability facilitates effective fertilizer
management. This approach enables the optimization of nitrogen (N) rates to
maximize crop yield production and enhance agronomic use efficiency. However,
existing works often neglect the consideration of responsivity to fertilizer as
a factor influencing MZ determination. In response to this gap, we present a MZ
clustering method based on fertilizer responsivity. We build upon the statement
that the responsivity of a given site to the fertilizer rate is described by
the shape of its corresponding N fertilizer-yield response (N-response) curve.
Thus, we generate N-response curves for all sites within the field using a
convolutional neural network (CNN). The shape of the approximated N-response
curves is then characterized using functional principal component analysis.
Subsequently, a counterfactual explanation (CFE) method is applied to discern
the impact of various variables on MZ membership. The genetic algorithm-based
CFE solves a multi-objective optimization problem and aims to identify the
minimum combination of features needed to alter a site's cluster assignment.
Results from two yield prediction datasets indicate that the features with the
greatest influence on MZ membership are associated with terrain characteristics
that either facilitate or impede fertilizer runoff, such as terrain slope or
topographic aspect.

本研究提出了一种基于化肥响应的管理区（MZ）聚类方法，通过使用卷积神经网络（CNN）生成所有田地内的 N 响应曲线，并利用函数主成分分析对其进行特征化。结果显示，对于 MZ 成员资格影响最大的特征与地形特性相关，例如地势坡度或地势方位等，这些特性可能促进或阻碍化肥径流。

神经网络用于创建化肥管理区域的反事实分析

Counterfactual Analysis of Neural Networks Used to Create Fertilizer  Management Zones

Response curves exhibit the magnitude of the response of a sensitive system
to a varying stimulus. However, response of such systems may be sensitive to
multiple stimuli (i.e., input features) that are not necessarily independent.
As a consequence, the shape of response curves generated for a selected input
feature (referred to as "active feature") might depend on the values of the
other input features (referred to as "passive features"). In this work, we
consider the case of systems whose response is approximated using regression
neural networks. We propose to use counterfactual explanations (CFEs) for the
identification of the features with the highest relevance on the shape of
response curves generated by neural network black boxes. CFEs are generated by
a genetic algorithm-based approach that solves a multi-objective optimization
problem. In particular, given a response curve generated for an active feature,
a CFE finds the minimum combination of passive features that need to be
modified to alter the shape of the response curve. We tested our method on a
synthetic dataset with 1-D inputs and two crop yield prediction datasets with
2-D inputs. The relevance ranking of features and feature combinations obtained
on the synthetic dataset coincided with the analysis of the equation that was
used to generate the problem. Results obtained on the yield prediction datasets
revealed that the impact on fertilizer responsivity of passive features depends
on the terrain characteristics of each field.

使用反事实解释（CFE）标识神经网络的输入特征对响应曲线的影响，并在两个 2-D 输入的作物产量预测数据集上测试通过改变被动特征的最小组合来改变响应曲线的形状，发现被动特征对于肥料反应性的影响取决于每个地块的地形特征。