standardnormer

Standardnormer is a term used in statistics and data preprocessing to describe the process of transforming data to a standard scale across features. The common objective is to center data around zero and scale it so that the resulting values have mean zero and standard deviation one. For a population with mean μ and standard deviation σ, a value x is transformed to z = (x − μ)/σ. When working with samples, μ and σ are estimated by the sample mean x̄ and the sample standard deviation s. The transformed values, or z-scores, facilitate comparability among different variables or datasets.

Standardnorming is primarily a preprocessing step in statistical modeling and machine learning. It improves numerical stability, often accelerates the convergence of optimization, and ensures that features contribute equally to distance-based methods. It is different from min-max normalization, which rescales data to a fixed range such as 0 to 1.

Robust variants replace μ and σ with robust estimators such as the median and the median absolute deviation (MAD) to lessen the influence of outliers. Per-feature standardization is common in multi-feature datasets, while global standardization may be applied to a single variable.

Limitations include sensitivity to outliers in non-robust forms and the assumption that a meaningful center and spread exist. If the data are highly skewed or contain many outliers, alternative transformations (e.g., log, Box-Cox) or robust standardization may be preferable.

Software implementations commonly expose standardization as a built-in option. In R, the scale function performs standardization; in Python's scikit-learn, StandardScaler provides a reusable transformer; NumPy can be used for manual calculations.

See also: z-score, standard normal distribution, normalization, feature scaling.