Normalization of data for delineating management zones

Management zones (MZs) are a viable economic alternative to variable-rate application (VRA) based on prescription maps; however, unlike the latter, MZs can employ conventional machinery. The use of management zones (MZs) is considered an economically viable alternative because of its low initial cost and high return in economic and environmental benefits. Data clustering techniques and the Fuzzy C-Means algorithm are the most widely used processes for delineating MZs. The most common similarity measurement used is Euclidean distance; however, because the algorithm is sensitive to the range of the input variables, these variables are typically normalized dividing the value by the standard deviation, maximum value, average, or data set range. The objective of this study was to assess the influence of data normalization methods for delineating MZs. The experiment was conducted in three experimental fields with 9.9, 15.0, and 19.8 ha, located in Southern Brazil between 2010 and 2014. The variables used for delineating MZs were selected using spatial correlation statistics and data were normalized using methods of standard score, range, and average. The MZs were delineated using the Fuzzy C-Means algorithm, which created two, three, and four clusters. The normalization methods were evaluated by five indices (modified partition entropy [MPE], fuzziness performance index [FPI], variance reduction [VR], smoothness index [SI], and kappa), and ANOVA. It was found that when the MZs delineation uses more than one variable with different scales in the clustering process using Euclidean distance, normalization is required. The range method was considered the overall best normalization method.