Assessing input-output relations in environemntal data by means of fuzzy clustering and Bayesian inference

When dealing with complex environmental datasets, it is also difficult to establish the strength of the input-output relation among variables. Correlation analysis may yield a preliminary indication, but is limited to the linear case. Mutual Information (MI) is a more powerful method which can establish input-output dependence regardless of the nature of their interaction. However, to avoid the heavy computational demand of MI, a simple method is presented based on fuzzy clustering and Bayes’ rule. After a preliminary conditioning phase, the data are grouped by fuzzy clustering and approximated with the value of the most relevant centroid. Then the prior and likelihood probabilities are computed by frequentist methods by counting the occurrences of each sample with respect to the precomputed clusters. In this way the MI can be quickly computed, to yield the relative importance of the informative content of each input.