normalizeScoresscores

normalizeScoresscores is a family of techniques for transforming a set of numerical scores into a common scale, enabling fair comparison and combination across disparate sources. It is commonly used when multiple indicators must be integrated, when inputs to a model come from different units, or when ranking items on a unified basis.

Common methods include min-max normalization, which rescales values to a fixed range such as [0, 1] using the formula x' = (x - min(X)) / (max(X) - min(X)); z-score standardization, which centers and scales data to have mean 0 and standard deviation 1 with x' = (x - μ) / σ; robust scaling, which uses the median and interquartile range to reduce the influence of outliers; and softmax transformation, which converts a vector of scores into a probability distribution with p_i = exp(x_i) / sum_j exp(x_j).

Selection depends on the intended goal. Min-max preserves the order and the relative distance within the original range, but is sensitive to outliers. Z-score standardization preserves order and contextual distances, which is useful for many machine learning models. Robust scaling provides resilience to outliers, while softmax is appropriate when probabilistic interpretation is needed.

Practical considerations include ensuring consistent normalization parameters across data splits to avoid leakage, handling missing values appropriately, and being aware that normalization changes the meaning of scores. Recalibration may be necessary if the underlying data distribution shifts, and the chosen method should align with downstream analysis or modeling requirements.