Review of the Self-Organizing Map (SOM) approach in water resources: Commentary

We provide some additional input and perspectives on Kalteh et al's review of the Self-Organizing Map (SOM) approach (Environ. Model. Softw. (2008), 23, 835-845). Map size selection is a key issue in SOM applications. Although there is no theoretical principle to determine the optimum map size, quantitative indicators such as quantization error, topographic error and eigenvalues have proven to be relevant tools to determine the optimal number of map units. Second, one of the most innovative applications of the SOM is the possibility of introducing a set of variables (e.g., biological) into a SOM previously trained with other variables (e.g. environmental). This can be achieved by calculating the mean value of each environmental variable in each output neuron of a SOM trained with biological variables, or by using a mask function to give a null weight to the biological variables, whereas environmental variables are given a weight of 1 so that the values for biological variables are visualized on a SOM previously trained with environmental variables only. We conclude that our different levels of expertise represent an opportunity for stimulating cross-fertilisation in the vast field of water research rather than simply yielding a collection of case studies to be re-examined.