Sensitivity of digital soil maps based on FCM to the fuzzy exponent and the number of clusters

Fuzzy c-means clustering (FCM) has been used frequently in digital soil mapping. One of the key issues in applying FCM is the determination of the appropriate classification parameters of the fuzzy exponent (m) and the number of clusters (c). To determine the optimal selection of appropriate m and c values, in this study, we first used two simulated datasets to demonstrate the sensitivity of three commonly used validity functions to m and c. These two simulated datasets contained overlapping clusters and hierarchical clusters, respectively. The three studied validity functions were fuzzy performance index (FPI), compactness and separation (S) and a derivative of the objective function with respect to the fuzzy exponent (-[(δJ _E/δm)c ^0.5]). Then, a case study mapping soil organic matter (SOM) based on memberships from FCM clustering terrain attributes was conducted to investigate the sensitivity of soil maps to m and c. The results of the study on the simulated datasets showed that the three validity functions were sensitive in differing degrees to the structures of the clustered datasets under a wide range of m, but the sensitivities and the range of m were different for different validity functions and depended on the clustered datasets. The results from the case study of the soil mapping showed that soil maps based on FCM clustering were sensitive to m and c, but only the spatial variations of SOM presented on the maps were significantly sensitive to c. Furthermore, mapping accuracy was slightly sensitive to m and c. It is concluded that there was a range of optimal m over which digital soil maps did not change very much, but this was not certain for c, given that the spatial variation presented on the maps changed significantly with c.