Definition
Ordinal Data
Ordinal data is a categorical data type where the variables represent discrete categories with a well-defined intrinsic ordering. Formally, ordinal data equips the set of categories with a total preorder . For any two observations , one can determine equality () or a relative ranking ( or ). While the order is meaningful, the magnitude of the difference (distance) between categories remains mathematically undefined.
Encoding Strategies
To preserve the ranking information in numerical models, ordinal data is typically transformed using integer encoding (e.g., mapping {small, medium, large} to {0, 1, 2}). This allows algorithms to utilise the ordering, although it implicitly assumes equal distances between adjacent categories, which may not always reflect the true underlying semantics.