Ordinal Coding

Our example with the Japanese car makes:

Make	Ordinal
Toyota	1
Honda	2
Subaru	3
Nissan	4
Mitsubishi	5

Ordinal encoding or sometimes known as label encoding is the simplest and perhaps most naive approach encoding for a categorical feature --- one simply assigns a number to each member of a category. This is often how data from surveys are encoded into spreadsheets for easy storage and calculation of basic statistics. An associated data dictionary is used to convert the values back and forth between a number and a category. Take for example the case of gender, male could be encoded as 1 and female as 2, with a data dictionary as follows: :code:{'male': 1, 'female': 2}

Suppose we have three categories of ethnic groups: White, Black, and Asian. Under ordinal encoding, suppose White is encoded as 1, Black is encoded as 2 and Asian is encoded as 3. If a machine learning classification is somehow confused between Asian and White and decides to split the difference and report the in-between value (2) which encodes Black. The issue is that arbitrary gradation between 1 and 3 introduces a natural interpolation (2) that may be nonsense. Thus, the natural ordering of the numbers imposes an ordered geometrical relationship between the categories that does not apply.

Nonetheless there are situations where ordinal encoding makes sense. For example, a `rate your satisfaction' survey typically encodes five levels (1) terrible, (2) acceptable (3) mediocre, (4) good, (5) excellent.

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