Categories Without an Invented Ranking

A roof can be glass, plastic, or mesh. Assigning those names arbitrary numbers can accidentally suggest a ranking. We need a representation that preserves category membership without inventing a numerical relationship.

10 sections · 3 questions · 2 coding challenges

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Giving Each Category Its Own Question

BOTIE

Statistical models need representations for properties that are names rather than quantities. Indicator variables answer separate membership questions, allowing categories to contribute without forcing their arbitrary codes onto a numerical scale.

Modern preprocessing libraries document one-hot encoding as one way to create those indicators. Our roof materials are an invented example. The practical contribution we need is the representation: one fixed column per known category, with a clear policy for unfamiliar categories.

Sources for this history

Scikit-learn: Encoding categorical features

Is Glass Really Twice as Much Roof as Plastic?

Botie wants to include greenhouse roof material in a temperature model. The materials are glass, plastic, and mesh. A model needs usable inputs, so assigning each name an ID seems like a reasonable start.

But an ID is an address, not a measurement. If a numerical model multiplies those IDs by a shared coefficient, it treats the gaps between IDs as meaningful. We need a way to indicate the material without claiming that one material is twice another.

Start with names

The roof materials identify categories. Their order here is simply our chosen vocabulary order.

Vocabulary

glass
plastic
mesh

An invented example for this lesson.

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What we can now calculate

Each comparison builds a separate category column. Collecting and transposing those columns puts one material's answers together in each row.

Explore the full example

Choose an example, then change a value. Follow the calculation below to see which result changes and why. These are small teaching examples; the construction later asks you to choose the operations yourself.

BOTIE

Botie needs a stable numerical description of roof material without treating an arbitrary ID as a quantity. We will build the three indicator columns separately, then arrange them into rows.

Choose an example

Roof materials

Three training categories in fixed order

Result from these values

1	0	0
0	0	1
0	0	0

Follow the operations

1. Roof materials
1. 0glass
2. 1mesh
3. 2foil
2. Three training categories in fixed order
1. 0glass
2. 1plastic
3. 2mesh
3. Set a constant
```
0
```
4. Choose an entry
```
glass
```
5. Match one category
1. 01
2. 10
3. 20
6. Set a constant
```
1
```
7. Choose an entry
```
plastic
```
8. Match one category
1. 00
2. 10
3. 20
9. Collect two results
1 0 0
0 0 0
10. Set a constant
```
2
```
11. Choose an entry
```
mesh
```
12. Match one category
1. 00
2. 11
3. 20
13. Append one item
1 0 0
0 0 0
0 1 0
14. Swap rows and columns
1 0 0
0 0 1
0 0 0
15. Result
1 0 0
0 0 1
0 0 0

This construction uses exactly three vocabulary categories so the comparisons remain visible. It does not fit a model or remove redundant columns. Editing this example does not change the workshop tests.

1. Distinguish an ID From a Quantity

A temperature difference has units and a physical interpretation. A material ID does not. Renaming glass from ID one to ID seven should not change the properties of the roof.

Some model families handle categorical IDs specially. A plain numerical coefficient does not: it will multiply the number it receives. We therefore need to consider how the model interprets the representation.

Do not conclude that every integer-coded feature is invalid. An ordered category or a categorical-aware algorithm has different assumptions. Our problem concerns unordered names passed to ordinary numerical operations.

2. Make a Column for Each Membership Question

Choose a vocabulary, then compare each material with every entry. A matching column receives one and the other columns receive zero. This is called one-hot encoding when exactly one column is active.

Column order: glass, plastic, mesh
glass → [1, 0, 0]
mesh  → [0, 0, 1]

The zeros do not say that a roof has no properties. They say that it is not a member of those particular categories.

3. Keep the Vocabulary Fixed After Fitting

The model's coefficients attach to column positions. If we fit with glass first and later move mesh into the first position, the arithmetic still runs while the meaning changes. Fit the vocabulary on training data and preserve its order.

An unfamiliar material needs an explicit policy. We can reserve an unknown category, reject the record for review, or use an all-zero representation with care. This workshop uses all zeros and makes that policy visible.

Vocabulary: [glass, plastic, mesh]
Unknown foil roof → [0, 0, 0]

All zeros cannot identify which unfamiliar material appeared. If one known category is also represented by all zeros after dropping a reference column, unknowns become ambiguous unless handled separately.

4. Decide What the Representation Leaves Out

Separate indicators let a model learn separate contributions. They do not teach it that two materials have similar insulation or cost. If those measured properties matter, we may want additional features that describe them directly.

With an intercept in a linear model, all category columns together create a redundant description. Dropping a reference column is one way to remove that redundancy. We keep all columns here so the membership mechanism is easy to inspect.

Botie's workshop constructs the indicator table. Later modelling lessons decide how to fit coefficients to it.