## Advantages of Using Categorical Arrays

### Natural Representation of Categorical Data

`categorical` is a data type to store data with values from a finite set of discrete categories. One common alternative to using categorical arrays is to use character arrays or cell arrays of character vectors. To compare values in character arrays and cell arrays of character vectors, you must use `strcmp` which can be cumbersome. With categorical arrays, you can use the logical operator `eq` (`==`) to compare elements in the same way that you compare numeric arrays. The other common alternative to using categorical arrays is to store categorical data using integers in numeric arrays. Using numeric arrays loses all the useful descriptive information from the category names, and also tends to suggest that the integer values have their usual numeric meaning, which, for categorical data, they do not.

### Mathematical Ordering for Character Vectors

Categorical arrays are convenient and memory efficient containers for nonnumeric data with values from a finite set of discrete categories. They are especially useful when the categories have a meaningful mathematical ordering, such as an array with entries from the discrete set of categories `{'small','medium','large'}` where ```small < medium < large```.

An ordering other than alphabetical order is not possible with character arrays or cell arrays of character vectors. Thus, inequality comparisons, such as greater and less than, are not possible. With categorical arrays, you can use relational operations to test for equality and perform element-wise comparisons that have a meaningful mathematical ordering.

### Reduce Memory Requirements

This example shows how to compare the memory required to store data as a cell array of character vectors versus a categorical array. Categorical arrays have categories that are defined as character vectors, which can be costly to store and manipulate in a cell array of character vectors or `char` array. Categorical arrays store only one copy of each category name, often reducing the amount of memory required to store the array.

Create a sample cell array of character vectors.

```state = [repmat({'MA'},25,1);repmat({'NY'},25,1);... repmat({'CA'},50,1);... repmat({'MA'},25,1);repmat({'NY'},25,1)];```

Display information about the variable `state`.

`whos state`
``` Name Size Bytes Class Attributes state 150x1 16200 cell ```

The variable `state` is a cell array of character vectors requiring 17,400 bytes of memory.

Convert `state` to a categorical array.

`state = categorical(state);`

Display the discrete categories in the variable `state`.

`categories(state)`
```ans = 3x1 cell {'CA'} {'MA'} {'NY'} ```

`state` contains 150 elements, but only three distinct categories.

Display information about the variable `state`.

`whos state`
``` Name Size Bytes Class Attributes state 150x1 476 categorical ```

There is a significant reduction in the memory required to store the variable.