Zscorestandardoiminen

Zscorestandardoiminen is a term that refers to the standardization of data by converting variables into z-scores. The idea is to transform each observation so that the feature has a mean of zero and a standard deviation of one, making different features comparable and stabilizing numerical calculations.

The standard formula is z_i = (x_i − μ)/σ, where μ and σ are the population mean and standard deviation, or using the sample mean x̄ and sample standard deviation s for empirical data. The transformation is usually applied per feature across all observations. If a feature has zero variance, it cannot be standardized and may be removed or set to a constant value.

Z-score standardization is widely used in data preprocessing for machine learning and statistics. It helps algorithms that rely on distance or gradient calculations, such as k-nearest neighbors, support vector machines, and regularized regression, and it facilitates comparisons among features with different scales. It is also a common preparatory step before dimensionality reduction methods like principal component analysis.

Practical considerations include fitting the transformation on training data and applying the same parameters to the test data to avoid data leakage. Handle missing values before standardization, and be mindful that standardized features lose original units and interpretation. Outliers can influence the mean and standard deviation, affecting the transformation; in such cases robust alternatives (e.g., using median and MAD) may be considered.

Terminology-wise, the more conventional terms are z-score standardization or standardization by z-scores. zscorestandardoiminen may be encountered as a coined or hybrid term, but standard practice uses the established phrases.