EntropieGewichtung

EntropieGewichtung (entropy weighting) is a statistical method used to determine the relative importance of variables in multivariate data sets based on the information entropy of each variable. The concept originates from information theory, where entropy measures the uncertainty or disorder associated with a probability distribution. By interpreting each variable’s distribution as a source of information, the method assigns higher weights to variables that exhibit greater variability and thus convey more information about the data structure.

The standard procedure begins with normalising the raw data to a common scale, often by min‑max or z‑score transformation. For each variable the probability distribution is estimated, typically by dividing each normalised value by the sum of all values for that variable. The entropy H_i of variable i is then calculated as the negative sum of p_{ij} log(p_{ij}) over all observations j. A dispersion coefficient d_i = 1 – H_i is derived, reflecting the degree of contrast in the variable. Finally, the weight w_i is obtained by normalising the dispersion coefficients: w_i = d_i / Σ d_k. Variables with low entropy (high contrast) receive larger weights, while those with near‑uniform distributions obtain smaller weights.

EntropieGewichtung is applied in fields such as environmental assessment, economic index construction, decision‑making, and machine‑learning feature selection. It offers an objective, data‑driven alternative to subjective weighting schemes, though it assumes that variability directly correlates with relevance, which may not hold in all contexts. Variants of the method incorporate fuzzy logic, entropy‑based distance measures, or combine entropy weights with other techniques like principal component analysis to improve robustness.