8.2. Classifying by One Variable¶
Data scientists often need to classify individuals into groups according to shared features, and then identify some characteristics of the groups. For example, in the example using Galton’s data on heights, we saw that it was useful to classify families according to the parents’ midparent heights, and then find the average height of the children in each group.
This section is about classifying individuals into categories that are not numerical. We begin by recalling the basic use of
8.2.1. Counting the Number in Each Category¶
group method with a single argument counts the number of rows for each category in a column. The result contains one row per unique value in the grouped column.
Here is a small table of data on ice cream cones. The
group method can be used to list the distinct flavors and provide the counts of each flavor.
cones = Table().with_columns( 'Flavor', make_array('strawberry', 'chocolate', 'chocolate', 'strawberry', 'chocolate'), 'Price', make_array(3.55, 4.75, 6.55, 5.25, 5.25) ) cones
There are two distinct categories, chocolate and strawberry. The call to
group creates a table of counts in each category. The column is called
count by default, and contains the number of rows in each category.
Notice that this can all be worked out from just the
Flavor column. The
Price column has not been used.
But what if we wanted the total price of the cones of each different flavor? That’s where the second argument of
group comes in.
8.2.2. Finding a Characteristic of Each Category¶
The optional second argument of
group names the function that will be used to aggregate values in other columns for all of those rows. For instance,
sum will sum up the prices in all rows that match each category. This result also contains one row per unique value in the grouped column, but it has the same number of columns as the original table.
To find the total price of each flavor, we call
group again, with
Flavor as its first argument as before. But this time there is a second argument: the function name
To create this new table,
group has calculated the sum of the
Price entries in all the rows corresponding to each distinct flavor. The prices in the three
chocolate rows add up to \(\$16.55\) (you can assume that price is being measured in dollars). The prices in the two
strawberry rows have a total of \(\$8.80\).
The label of the newly created “sum” column is
Price sum, which is created by taking the label of the column being summed, and appending the word
group finds the
sum of all columns other than the one with the categories, there is no need to specify that it has to
sum the prices.
To see in more detail what
group is doing, notice that you could have figured out the total prices yourself, not only by mental arithmetic but also using code. For example, to find the total price of all the chocolate cones, you could start by creating a new table consisting of only the chocolate cones, and then accessing the column of prices:
array([4.75, 6.55, 5.25])
This is what
group is doing for each distinct value in
# For each distinct value in `Flavor, access all the rows # and create an array of `Price` cones_choc = cones.where('Flavor', are.equal_to('chocolate')).column('Price') cones_strawb = cones.where('Flavor', are.equal_to('strawberry')).column('Price') # Display the arrays in a table grouped_cones = Table().with_columns( 'Flavor', make_array('chocolate', 'strawberry'), 'Array of All the Prices', make_array(cones_choc, cones_strawb) ) # Append a column with the sum of the `Price` values in each array price_totals = grouped_cones.with_column( 'Sum of the Array', make_array(sum(cones_choc), sum(cones_strawb)) ) price_totals
|Flavor||Array of All the Prices||Sum of the Array|
|chocolate||[4.75 6.55 5.25]||16.55|
You can replace
sum by any other functions that work on arrays. For example, you could use
max to find the largest price in each category:
group creates arrays of the prices in each
Flavor category. But now it finds the
max of each array:
price_maxes = grouped_cones.with_column( 'Max of the Array', make_array(max(cones_choc), max(cones_strawb)) ) price_maxes
|Flavor||Array of All the Prices||Max of the Array|
|chocolate||[4.75 6.55 5.25]||6.55|
Indeed, the original call to
group with just one argument has the same effect as using
len as the function and then cleaning up the table.
lengths = grouped_cones.with_column( 'Length of the Array', make_array(len(cones_choc), len(cones_strawb)) ) lengths
|Flavor||Array of All the Prices||Length of the Array|
|chocolate||[4.75 6.55 5.25]||3|
8.2.3. Example: NBA Salaries¶
nba contains data on the 2015-2016 players in the National Basketball Association. We have examined these data earlier. Recall that salaries are measured in millions of dollars.
nba1 = Table.read_table(path_data + 'nba_salaries.csv') nba = nba1.relabeled("'15-'16 SALARY", 'SALARY') nba
|Paul Millsap||PF||Atlanta Hawks||18.6717|
|Al Horford||C||Atlanta Hawks||12|
|Tiago Splitter||C||Atlanta Hawks||9.75625|
|Jeff Teague||PG||Atlanta Hawks||8|
|Kyle Korver||SG||Atlanta Hawks||5.74648|
|Thabo Sefolosha||SF||Atlanta Hawks||4|
|Mike Scott||PF||Atlanta Hawks||3.33333|
|Kent Bazemore||SF||Atlanta Hawks||2|
|Dennis Schroder||PG||Atlanta Hawks||1.7634|
|Tim Hardaway Jr.||SG||Atlanta Hawks||1.30452|
... (407 rows omitted)
1. How much money did each team pay for its players’ salaries?
The only columns involved are
SALARY. We have to
group the rows by
TEAM and then
sum the salaries of the groups.
teams_and_money = nba.select('TEAM', 'SALARY') teams_and_money.group('TEAM', sum)
|Golden State Warriors||94.0851|
... (20 rows omitted)
2. How many NBA players were there in each of the five positions?
We have to classify by
POSITION, and count. This can be done with just one argument to group:
3. What was the average salary of the players at each of the five positions?
This time, we have to group by
POSITION and take the mean of the salaries. For clarity, we will work with a table of just the positions and the salaries.
positions_and_money = nba.select('POSITION', 'SALARY') positions_and_money.group('POSITION', np.mean)
Center was the most highly paid position, at an average of over 6 million dollars.
If we had not selected the two columns as our first step,
group would not attempt to “average” the categorical columns in
nba. (It is impossible to average two strings like “Atlanta Hawks” and “Boston Celtics”.) It performs arithmetic only on numerical columns and leaves the rest blank.
|POSITION||PLAYER mean||TEAM mean||SALARY mean|