# Feature Types

## Contents

# 10.1. Feature Types#

Before making an exploratory plot, or any plot for that matter, it’s a good idea to examine the feature (or features) and decide on its *feature type*. (Some times we refer to a feature as a variable and its type as *variable type*.) Although there are multiple ways of categorizing feature types, in this book we consider three basic ones.

*Nominal*A feature that represents “named” categories, where the categories do not have a natural ordering, is called nominal. Examples include: political party affiliation (Democrat, Republican, Green, Other); dog type (herding, hound, non-sporting, sporting, terrier, toy, working); and computer operating system (Windows, MacOS, Linux).

*Ordinal*Measurements that represent ordered categories are called ordinal. Examples of ordinal features are: T-shirt size (small, medium, large); Likert-scale response (disagree, neutral, agree); and level of education (high school, college, graduate school). It is important to note that with an ordinal feature, the difference between, say, small and medium, need not be the same as the difference between medium and large. Also, the differences between consecutive categories may not even be quantifiable. Think of the number of stars in a restaurant review and what one star means in comparison to two stars.

Ordinal and nominal data are subtypes of *categorical* data. Another name
for categorical data is *qualitative*. In contrast we also have
*quantitative* features.

*Quantitative*Data that represent numeric measurements or quantities are called quantitative. Examples include: height measured to the nearest cm, price reported in USD, and distance measured to the nearest kilometer. Quantitative features can be further divided into

*discrete*, meaning that only a few values of the feature are possible, and*continuous*, meaning that the quantity could in principal be measured to arbitrary precision. The number of siblings in a family takes on a discrete set of values (such as, 0, 1, 2,…, 8). In contrast, height can theoretically be reported to any number of decimal places so we consider it continuous. There is no hard and fast rule to determine whether a quantity is discrete or continuous. In some cases, it can be a judgment call and at other times we may want to purposefully consider a continuous feature to be discrete.

A feature type is not the same thing as a data storage type. Each column in a `pandas`

data frame has its own *storage type*. These types can be integer, floating point, boolean, date-time format, category, and object (strings of varying length are stored as objects in python with pointers to the strings).
We use the term *feature type* to refer to a
conceptual notion of the information, and the term *storage type* refers to the
representation of the information in the computer.

A feature stored as an integer can represent nominal data, strings can be quantitative (like “$100.00”), and, in practice, boolean values often represent nominal features that have only two possible values.

Note

Pandas calls the storage type `dtype`

, which is short for data type.
We refrain from using the term *data type* here because it can be confused with
both storage type and feature type.

In order to determine a feature type, we often need to consult a
dataset’s *data dictionary* or *codebook*. A data dictionary is a document
included with the data that describes what each column in the data table
represents. In the following example, we take a look at the storage and
feature types of the columns in a data frame about various breeds of dogs,
and we find that the storage type is often not a good indicator of the kind
of information contained in a field.

## 10.1.1. Example: Dog Breeds#

We use the American Kennel Club (AKC) data on registered dog breeds to introduce the various concepts related to EDA. The AKC, a non-profit that was founded in 1884, has the stated mission to “advance the study, breeding, exhibiting, running and maintenance of purebred dogs.” They organize events like the National Championship, Agility Invitational, and Obedience Classic, and mixed breed dogs are welcome to participate in most events. The Information is Beautiful website provides a dataset with information from the AKC on 172 breeds. Their visualization, Best in Show, incorporates many features of the breeds and is fun to look at.

The AKC dataset contains several different kinds of features, and we have extracted a handful of them that show a variety of types of information. These features include the name of the breed, its longevity, weight, and height, and other information such as its suitability for children and the number of repetitions needed to learn a new trick. Each record in the dataset is a breed of dog, and the information provided is meant to be typical of that breed.

Let’s read the data into a data frame:

```
dogs = pd.read_csv('data/akc.csv')
dogs
```

breed | group | score | longevity | ... | size | weight | height | repetition | |
---|---|---|---|---|---|---|---|---|---|

0 | Border Collie | herding | 3.64 | 12.52 | ... | medium | NaN | 51.0 | <5 |

1 | Border Terrier | terrier | 3.61 | 14.00 | ... | small | 6.0 | NaN | 15-25 |

2 | Brittany | sporting | 3.54 | 12.92 | ... | medium | 16.0 | 48.0 | 5-15 |

... | ... | ... | ... | ... | ... | ... | ... | ... | ... |

169 | Wire Fox Terrier | terrier | NaN | 13.17 | ... | small | 8.0 | 38.0 | 25-40 |

170 | Wirehaired Pointing Griffon | sporting | NaN | 8.80 | ... | medium | NaN | 56.0 | 25-40 |

171 | Xoloitzcuintli | non-sporting | NaN | NaN | ... | medium | NaN | 42.0 | NaN |

172 rows × 12 columns

A cursory glance at the table shows us that breed, group, and size appear to be
strings, and the other columns numbers. The summary of the data frame, shown
below, provides the index, name, count of non-null values, and `dtype`

for each column:

```
dogs.info()
```

```
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 172 entries, 0 to 171
Data columns (total 12 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 breed 172 non-null object
1 group 172 non-null object
2 score 87 non-null float64
3 longevity 135 non-null float64
4 ailments 148 non-null float64
5 purchase_price 146 non-null float64
6 grooming 112 non-null float64
7 children 112 non-null float64
8 size 172 non-null object
9 weight 86 non-null float64
10 height 159 non-null float64
11 repetition 132 non-null object
dtypes: float64(8), object(4)
memory usage: 16.2+ KB
```

Several columns of this data frame have a numeric computational type, as
signified by `float64`

, which means that the column can contain numbers other than integers.
We also confirm that `pandas`

encodes the string columns as the `object`

dtype, rather than a `string`

dtype.
Notice that we guessed incorrectly that `repetition`

is quantitative.
Looking a bit more carefully at the data table, we see that `repetition`

contains string values for ranges,
such as “< 5”, “15-25” and “25-40”, so this feature is ordinal.

Note

In computer architecture, a floating-point number, or “float” for short,
refers to a number that can have a decimal component. We won’t go in depth
into computer architecture in this book, but we will point it out when it
affects terminology, as in this case.
The `dtype`

`float64`

says that the column contains decimal numbers that each
take up 64 bits of space when stored in computer memory.

Additionally, `pandas`

uses optimized storage types for numeric data, like `float64`

or `int64`

.
However, it doesn’t have optimizations for Python objects like strings,
dictionaries, or sets, so these are all stored as the `object`

`dtype`

.
This means that the storage type is ambiguous, but in most settings
we know whether `object`

columns contain strings or some other Python type.

Looking at the column storage types, we might guess `ailments`

and `children`

are quantitative
features because they are stored as `float64`

`dtypes`

.
But, let’s tally their unique values:

```
display_df(dogs['ailments'].value_counts(), rows=8)
```

```
ailments
0.0 61
1.0 42
2.0 24
4.0 10
3.0 6
5.0 3
9.0 1
8.0 1
Name: count, dtype: int64
```

```
dogs['children'].value_counts()
```

```
children
1.0 67
2.0 35
3.0 10
Name: count, dtype: int64
```

Both `ailments`

and `children`

only take on a few integer values.
What does a value
of 3.0 for `children`

or 9.0 for `ailments`

mean? We need more information to
figure this out. The name of the column and how the information is stored in
the data frame is not enough.
Instead, we consult the data dictionary shown in Table 10.1.

Feature |
Description |
---|---|

breed |
dog breed, e.g., Border Collie, Dalmatian, Vizsla |

group |
American Kennel Club grouping (herding, hound, non-sporting, sporting, terrier, toy, working) |

score |
AKC score |

longevity |
typical lifetime (years) |

ailments |
number of serious genetic ailments |

purchase_price |
average purchase price from puppyfind.com |

grooming |
grooming required once every: 1 = day, 2 = week, 3 = few weeks |

children |
suitability for children: 1 = high, 2 = medium, 3 = low |

size |
size: small, medium, large |

weight |
typical weight (kg) |

height |
typical height from the shoulder (cm) |

repetition |
number of repetitions to understand a new command: <5, 5-15, 15-25, 25-40, 40-80, >80 |

Although the data dictionary does not explicitly specify the feature types, the
descriptions is enough for us to figure out that the feature, `children`

, represents the suitability of
the breed for children, and a value of 1.0 corresponds to “high” suitability.
We also find that the feature, `ailments`

, is a count of the number of serious genetic
ailments that dogs of this breed tend to have. Based on the codebook, we treat
`children`

as a categorical feature, even though it is stored as a floating
point number, and since low < medium < high, the feature is ordinal. Since
`ailments`

is a count, we treat it as a quantitative (numeric) type,
and for some analyses we further define it as discrete because there
are only a few possible values that `ailments`

can take on.

The codebook also confirms that the features: `score`

, `longevity`

,
`purchase_price`

, `weight`

, and `height`

are quantitative.
The idea here is that numeric features have values that can be compared through differences.
It makes sense to say that chihuahuas typically live about four years longer than dachshunds (16.5 to 12.6 years). Another check is whether it makes sense to compare ratios of values:
a dachshund is usually about five times heavier than a chihuahua (11 kg to 2 kg).
All of these quantitative features are continuous; only `ailments`

is discrete.

The data dictionary descriptions for `breed`

, `group`

, `size`

and `repetition`

suggest that these features are qualitative. Each of these variables have
different, and yet commonly found, characteristics that are worth exploring a
bit more. We do this by examining the counts of each unique value for the various
features. We begin with `breed`

:

```
dogs['breed'].value_counts()
```

```
breed
Border Collie 1
Great Pyrenees 1
English Foxhound 1
..
Saluki 1
Giant Schnauzer 1
Xoloitzcuintli 1
Name: count, Length: 172, dtype: int64
```

The `breed`

feature has 172 unique values—that’s the same as the number of
records in the data frame—so we can think of `breed`

as the *primary key* for the data table.
By design, each dog breed has one record, and this `breed`

feature determines
the dataset’s granularity. Although `breed`

is also considered a nominal feature,
it doesn’t really make sense to analyze it. We do want to confirm that all
values are unique and clean, but otherwise we would only use it to, say, label
unusual values in a plot.

Next we examine the feature, `group`

:

```
dogs['group'].value_counts()
```

```
group
terrier 28
sporting 28
working 27
hound 26
herding 25
toy 19
non-sporting 19
Name: count, dtype: int64
```

This feature has seven unique values.
Since a dog breed labeled as “sporting” and another considered to be “toy”
differ from each other in several ways, the categories cannot be easily reduced to an ordering.
So, we consider `group`

a nominal feature.
Nominal features do not provide meaning in even the direction of the differences.

Next, we examine the unique values and their counts for `size`

:

```
dogs['size'].value_counts()
```

```
size
medium 60
small 58
large 54
Name: count, dtype: int64
```

The `size`

feature has a natural ordering: small < medium < large so it is
ordinal. We don’t know how the category “small” is determined, but we do know
that a small breed is in some sense smaller than a medium-size breed, which is
smaller than a large one. We have an ordering, but differences and ratios
don’t make sense conceptually for this feature.

The `repetition`

feature is an example of a quantitative variable that has been
collapsed into categories to become ordinal. The codebook tells us that
`repetition`

is the number of times a new command needs to be repeated before
the dog understands it:

```
dogs['repetition'].value_counts()
```

```
repetition
25-40 39
15-25 29
40-80 22
5-15 21
80-100 11
<5 10
Name: count, dtype: int64
```

The numeric values have been lumped together as: <5, 5-15, 15-25, 25-40, 40-80, >80, and notice that these categories have different widths. The first has 5 repetitions, while others are 10, 15, and 40 repetitions wide. The ordering is clear, but the gaps from one category to the next are not the same magnitude.

Now that we have double checked the values in the variables against the descriptions in the codebook, we can augment the data dictionary to include this additional information about the feature types. Our revised dictionary appears in Table 10.2.

Feature |
Description |
Feature Type |
Storage Type |
---|---|---|---|

breed |
dog breed, e.g., Border Collie, Dalmatian, Vizsla |
primary key |
string |

group |
AKC group (herding, hound, non-sporting, sporting, terrier, toy, working) |
qualitative - nominal |
string |

score |
AKC score |
quantitative |
floating point |

longevity |
typical lifetime (years) |
quantitative |
floating point |

ailments |
number of serious genetic ailments (0, 1, …, 9) |
quantitative - discrete |
floating point |

purchase_price |
average purchase price from puppyfind.com |
quantitative |
floating point |

grooming |
groom once every: 1 = day, 2 = week, 3 = few weeks |
qualitative - ordinal |
floating point |

children |
suitability for children: 1 = high, 2 = medium, 3 = low |
qualitative - ordinal |
floating point |

size |
size: small, medium, large |
qualitative - ordinal |
string |

weight |
typical weight (kg) |
quantitative |
floating point |

height |
typical height from the shoulder (cm) |
quantitative |
floating point |

repetition |
number of repetitions to understand a new command: <5, 5-15, 15-25, 25-40, 40-80, >80 |
qualitative - ordinal |
string |

This sharper understanding of the feature types of the Kennel Club data helps us make quality checks and transformations. We discussed transformations in Chapter 9, but there are a few additional transformations that were not covered. These pertain to categories of qualitative features, and we describe them next.

## 10.1.2. Transforming Qualitative Features#

Whether a feature is nominal or ordinal, we may find it useful to: relabel categories so they are more informative; collapse categories to simplify a visualization; and even convert a numeric feature to ordinal to focus on particular transition points. We explain when we may want to make each of these transformations and give examples.

### 10.1.2.1. Relabel Categories#

Summary statistics, like the mean and the median, make
sense for quantitative data, but typically not for qualitative data. For
example, the average price for toy breeds makes sense to calculate ($687), but
the “average” breed suitability for children doesn’t.
However, `pandas`

will happily compute the mean of the values in the `children`

column if we ask it to:

```
# Don't use this value in actual data analysis!
dogs["children"].mean()
```

```
1.4910714285714286
```

Instead, we want to consider the distribution of ones, twos, and threes of
the `children`

.

Note

The key difference between storage types and feature types: storage
types say what operations we can write code to *compute*, while
feature types say what operations *make sense for the data*.

We can transform `children`

by replacing the numbers with their string
descriptions. Changing 1, 2, 3 into high, medium, and low makes
it easier to recognize that `children`

is categorical. With strings, we would
not be tempted to compute a mean, the categories would be connected to their
meaning, and labels for plots would have reasonable values by default.
For example, let’s focus on just the toy breeds and make a bar plot of suitability for children. First, we create a new column with the categories of suitability as strings:

```
kids = {1:"High", 2:"Medium", 3:"Low"}
dogs = dogs.assign(kids=dogs['children'].replace(kids))
```

```
dogs
```

breed | group | score | longevity | ... | weight | height | repetition | kids | |
---|---|---|---|---|---|---|---|---|---|

0 | Border Collie | herding | 3.64 | 12.52 | ... | NaN | 51.0 | <5 | Low |

1 | Border Terrier | terrier | 3.61 | 14.00 | ... | 6.0 | NaN | 15-25 | High |

2 | Brittany | sporting | 3.54 | 12.92 | ... | 16.0 | 48.0 | 5-15 | Medium |

... | ... | ... | ... | ... | ... | ... | ... | ... | ... |

169 | Wire Fox Terrier | terrier | NaN | 13.17 | ... | 8.0 | 38.0 | 25-40 | NaN |

170 | Wirehaired Pointing Griffon | sporting | NaN | 8.80 | ... | NaN | 56.0 | 25-40 | NaN |

171 | Xoloitzcuintli | non-sporting | NaN | NaN | ... | NaN | 42.0 | NaN | NaN |

172 rows × 13 columns

Then we can make the bar plot of counts of each category of suitability among the toy breeds:

```
toy_dogs = dogs.query('group == "toy"').groupby('kids').count().reset_index()
px.bar(toy_dogs, x='kids', y='breed', width=350, height=250,
category_orders={"kids": ["Low", "Medium", "High"]},
labels={"kids": "Suitability for children", "breed": "Count"})
```

We do not always want to have categorical data represented by strings. Strings generally take up more space to store, which can greatly increase the size of a data set if it contains many categorical features.

At times a qualitative feature has many categories and we prefer a higher level view of the data so we collapse categories.

### 10.1.2.2. Collapse Categories#

Let’s create a new column, called `play`

, to represent
the groups of dogs whose “purpose” is to play (or not). (This is a fictitious
distinction used for demonstration purposes). This category consists of the toy
and non-sporting breeds. The new feature, `play`

, is a transformation of the feature
`group`

that collapses categories: toy and non-sporting are combined into one
category, and the remaining categories are placed in a second, non-play
category. The boolean (`bool`

) storage type is useful to indicate the
presence or absence of this characteristic:

```
with_play = dogs.assign(play=(dogs["group"] == "toy") |
(dogs["group"] == "non-sporting"))
```

Representing a two-category qualitative feature as a boolean has a few
advantages. For example, the mean of `play`

makes sense because it returns the
fraction of `True`

values. When booleans are used for numeric calcuations,
`True`

becomes 1 and `False`

becomes 0:

```
with_play['play'].mean()
```

```
0.22093023255813954
```

This storage type gives us a shortcut to compute counts and averages of boolean values. Later, in Chapter 15, we see that it’s also a handy encoding for modeling.

There are also times. like when a discrete quantitative feature has a long tail, that we want to truncate the higher values, which turns the quantitative feature into ordinal. We describe this next.

### 10.1.2.3. Convert Quantitative to Ordinal#

Finally, another transformation that we
sometimes find useful is to convert numeric values into categories. For
example, we might collapse the values in `ailments`

into categories: 0, 1, 2,
3, 4+. In other words, we turn `ailments`

from a quantitative feature into an
ordinal feature with the mapping 0→0, 1→1, 2→2, 3→3, and any value 4 or larger
→ 4+. We might want to make this transformation because few breeds have
more than three genetic ailments. This simplification can be clearer
and adequate for an investigation.

Note

As of this writing (late 2022), `pandas`

also
implements a `category`

dtype which is
designed to work with qualitative data.
However, this storage type is not yet widely
adopted by the visualization and modeling libraries, which limits its
usefulness. For that reason, we do not transform our qualitative variables into
the `category`

dtype.
We expect that future readers may want to use the `category`

dtype as more
libraries support it.

When we convert a quantitative feature to ordinal, we lose information. We can’t go back. That is, if we know the number of ailments for a breed is four or more, we can’t recreate the actual numeric value. The same thing happens when we collapse categories. For this reason, it’s good practice to keep the original feature. If we need to check our work or change categories we can document and recreate our steps.

In general, the feature type helps us figure out what kind of plot is most appropriate. We discuss the mapping between feature type and plots next.

## 10.1.3. The Importance of Feature Types#

Feature types guide us in our data analysis. They help specify the operations, visualizations, and models we can meaningfully apply to the data. Table 10.3 matches the feature type(s) to the various kinds of plots that are typically good options. Whether the variable(s) are quantitative or qualitative generally determines the set of viable plots to make, although there are exceptions. Other factors that enter into the decision are the number of observations and whether the feature takes on only a few distinct values. For example, we might make a bar chart, rather than a histogram, for a discrete quantitative variable.

Feature Type |
Dimension |
Plot |
---|---|---|

Quantitative |
One Feature |
Rug plot, histogram, density curve, box plot, violin plot |

Qualitative |
One Feature |
Bar plot, dot chart, line plot, pie chart |

Quantitative |
Two Features |
Scatter plot, smooth curve, contour plot, heat map, quantile-quantile plot |

Qualitative |
Two Features |
Side-by-side bar plots, mosaic plot, overlaid lines |

Mixed |
Two Features |
Overlaid density curves, side-by-side box plots, overlaid smooth curves, quantile-quantile plot |

The feature type also helps us decide the kind of summary statistics to calculate. With qualitative data, we usually don’t compute means or standard deviations, and instead compute the count, fraction, or percentage of records in each category. With a quantitative feature, we compute the mean or median as a measure of center, and, respectively, the standard deviation or inner quartile range (75th percentile - 25th percentile) as a measure of spread. In addition to the quartiles, we may find other percentiles informative.

Note

The *n*th percentile is that value *q* such that *n% of the data
values fall at or below it.* The value *q* might not be unique, and there are
several approaches to select a unique value from the possibilities. With enough
data, there should be little difference between these definitions.

To compute percentiles in Python, we prefer using:

```
np.percentile(data, method='lower')
```

When exploring data, we need to know how to interpret the shapes that our plots reveal. The next three sections give guidance with this interpretation. We also introduce many of the types of plots listed in Table 10.3 through the examples. Others are introduced here in Chapter 11.