Nominal Data

data-analysis statistics machine-learning

Definition

Nominal Data

Nominal data is a categorical data type where variables represent discrete categories without any intrinsic ordering or quantitative value. Formally, nominal data defines a partition on the set of observations such that for any two observations $x_i,x_j$, the only permissible relation is equality ($x_i=x_j$) or inequality ($x_i\ne x_j$). Operations such as addition, subtraction, or comparison are mathematically undefined.

Numerical Representation

In machine learning, nominal variables must be transformed into numerical vectors to be processed by most algorithms. The standard approach is One-Hot Encoding, which maps each category to a unique binary basis vector, thereby ensuring that no erroneous ordinal relationships are introduced.