entropivektning

Entropivektning is a method used in data analysis and decision making to derive weights for a set of criteria or features from observed data. The approach uses entropy, an information-theoretic measure, to quantify the amount of information contained in the distribution of criterion values across alternatives. In essence, criteria with greater variability carry more information and receive higher weights, while criteria with little variation receive lower weights.

Methodology: Data matrix X with m alternatives and n criteria. Normalize nonnegative values to ensure comparability. Compute p_ij = x_ij / sum_i x_ij for each criterion j. Compute entropy e_j = - (1/ln m) sum_i p_ij ln p_ij. Compute diversification degree d_j = 1 - e_j. Compute weights w_j = d_j / sum_j d_j. Depending on context, different normalization schemes or base of the logarithm may be used, and small constants may be added to handle zeros. The resulting weights sum to one and can be used in downstream analyses such as scoring or ranking.

Applications: Used in multi-criteria decision analysis (MCDA) to determine objective weights for criteria; feature selection in machine learning; data fusion and sensor networks; image and signal processing where criteria represent different measurements.

Advantages and limitations: Provides an objective, data-driven weighting scheme free from subjective judgments; adapts to the information content of the data. Limitations include sensitivity to the normalization method, treatment of negative values, and potential overweighting of noisy, highly variable criteria. The method assumes that higher information content implies greater importance, which may not always align with domain knowledge.