When the categories in a classification problem possess a natural ordering—such as predicting sequential age groups like baby, toddler, adolescent, and adult—it is appropriate to represent the labels as integers $$y \in \{1, 2, 3, \dots\}$$. This setup can be cast as an ordinal regression problem, which preserves the inherent ranking among the classes rather than treating them as entirely independent categories.

Ordinal Regression

Because most classification problems lack a natural ordering among classes, categorical labels are typically represented using a one-hot encoding. A one-hot encoding is a vector with as many components as there are categories, where the element corresponding to the true category is set to $$ 1 $$ and all other elements are set to $$ 0 $$. For example, a label for three classes might be represented as the three-dimensional vector $$ (1, 0, 0) $$.

One-Hot Encoding

Supervised learning problems are divided into classification and regression. In classification problems, the predicted values are discrete categories. In regression problems, the predicted values are continuous numerical quantities.

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