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. (Sometimes 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 km. 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 principle 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 in others, 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 dataframe 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 to refer 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 dataframe about various dog breeds, 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 nonprofit that was founded in 1884, has the stated mission to “advance the study, breeding, exhibiting, running and maintenance of purebred dogs.” The AKC organizes 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. Its 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 dataframe:

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 dataframe, shown here, 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 dataframe 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 dataframe is not enough. Instead, we consult the data dictionary shown in Table 10.1.

Table 10.1 AKC dog breed codebook

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 description 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 versus 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 versus 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 variable has 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 dataframe—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-sized 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, 80-100, 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 of 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.

Table 10.2 Revised AKC dog breed codebook

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, 80–100	Qualitative - ordinal	string

This sharper understanding of the feature types of the AKC 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 that 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 is that 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, and 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 dataset 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 calculations, 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. In Chapter 15, we’ll 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 an 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 that 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 re-create the actual numeric value. The same thing happens when we collapse categories. For this reason, it’s a good practice to keep the original feature. If we need to check our work or change categories, we can document and re-create 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.

Table 10.3 Mapping feature types to plots

Feature type	Dimension	Plot
Quantitative	One feature	Rug plot, histogram, density curve, box plot, violin plot
Qualitative	One feature	Bar plot, dot plot, 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 to 25th percentile) as a measure of spread. In addition to the quartiles, we may find other percentiles informative.

Note

The nth 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 in Chapter 11.