Rev. Bras. Ciênc. Solo.2025;49:e0240097.
Optimization algorithms for multivariate sampling reduction using spatial-temporal data
Tamara Cantú Maltauro 
, Luciana Pagliosa Carvalho Guedes , Miguel Angel Uribe-Opazo
31/Jul/2025
DOI: 10.36783/18069657rbcs20240097
Graphical Abstract
Highlights
Empirical orthogonal function.
K-means was the best clustering method, considering two application zones.
The optimization process made it possible to reduce the number of sampling points.
The best results were obtained with the optimized sample reduction with 70% of points.
ABSTRACT
Knowing and defining the spatial and temporal variability of soil chemical properties becomes important for soil management. The definition of application zones in agricultural areas consists of dividing the area into homogeneous subareas, thus allowing the development of localized management. These zones can be defined by cluster methods and one of their advantages is to direct the determination of a future soil sampling, with a possible sample reduction. This study aimed to propose a methodology that integrates multivariate and space-time analyses to obtain an optimized sample configuration, using spatio-temporal data and application zones. First, three spatial multivariate clustering methods were evaluated to obtain the application zone (fuzzy C-means, K-means and Ward). Clusters were obtained by considering the analysis of spatio-temporal dependence through the empirical orthogonal function. Afterward, 50, 60 and 70 % of the sampling points of the initial sampling configuration were selected in each application zone, generating an optimized sample configuration. This choice was made by an optimization process, whose efficiency was evaluated based on spatial prediction, using the sum of the Overall Accuracy Index, of all soil properties. The results indicated the division of the agricultural area into two application zones, considering the K-means method. For most soil properties, when comparing the original and reduced sampling configurations, a similarity was observed in descriptive statistics. Regarding the estimates of the accuracy indexes, considering all the optimized sample configurations, the best estimates were observed comparing the initial sample configurations and the optimized ones in 70 % for most soil chemical properties.
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