# 5.0 Introduction

It is often useful to measure objects not in terms of their quantity but in terms of some quality. We frequently represent this qualitative information as an observation’s membership in a discrete category such as gender, colors, or brand of car. However, not all categorical data is the same. Sets of categories with no intrinsic ordering is called nominal. Examples of nominal categories include:

• Blue, Red, Green

• Man, Woman

• Banana, Strawberry, Apple

In contrast, when a set of categories has some natural ordering we refer to it as ordinal. For example:

• Low, Medium, High

• Young, Old

• Agree, Neutral, Disagree

Furthermore, categorical information is often represented in data as a vector or column of strings (e.g., `"Maine"`, `"Texas"`, `"Delaware"`). The problem is that most machine learning algorithms require inputs be numerical values.

The k-nearest neighbor algorithm provides a simple example. One step in the algorithm is calculating the distances between observations—often using Euclidean distance:

$\sqrt{{\sum }_{i=1}^{n}{\left({x}_{i}-{y}_{i}\right)}^{2}}$

where x and y are two observations and subscript i denotes the value for the observations’ ith feature. However, the distance calculation obviously is impossible if the value of xi is a string (e.g., `"Texas"`). Instead, we need to convert the string into some numerical format so that it can be inputted into the Euclidean distance equation. Our goal is to make a transformation that properly conveys ...

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