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# Aggregation and Grouping¶

An essential piece of analysis of large data is efficient summarization: computing aggregations like sum(), mean(), median(), min(), and max(), in which a single number gives insight into the nature of a potentially large dataset. In this section, we'll explore aggregations in Pandas, from simple operations akin to what we've seen on NumPy arrays, to more sophisticated operations based on the concept of a groupby.

For convenience, we'll use the same display magic function that we've seen in previous sections:

In :
import numpy as np
import pandas as pd

class display(object):
"""Display HTML representation of multiple objects"""
template = """<div style="float: left; padding: 10px;">
<p style='font-family:"Courier New", Courier, monospace'>{0}</p>{1}
</div>"""
def __init__(self, *args):
self.args = args

def _repr_html_(self):
return '\n'.join(self.template.format(a, eval(a)._repr_html_())
for a in self.args)

def __repr__(self):
return '\n\n'.join(a + '\n' + repr(eval(a))
for a in self.args)


## Planets Data¶

Here we will use the Planets dataset, available via the Seaborn package (see Visualization With Seaborn). It gives information on planets that astronomers have discovered around other stars (known as extrasolar planets or exoplanets for short). It can be downloaded with a simple Seaborn command:

In :
import seaborn as sns
planets.shape

Out:
(1035, 6)
In :
planets.head()

Out:
method number orbital_period mass distance year
0 Radial Velocity 1 269.300 7.10 77.40 2006
1 Radial Velocity 1 874.774 2.21 56.95 2008
2 Radial Velocity 1 763.000 2.60 19.84 2011
3 Radial Velocity 1 326.030 19.40 110.62 2007
4 Radial Velocity 1 516.220 10.50 119.47 2009

This has some details on the 1,000+ extrasolar planets discovered up to 2014.

## Simple Aggregation in Pandas¶

Earlier, we explored some of the data aggregations available for NumPy arrays ("Aggregations: Min, Max, and Everything In Between"). As with a one-dimensional NumPy array, for a Pandas Series the aggregates return a single value:

In :
rng = np.random.RandomState(42)
ser = pd.Series(rng.rand(5))
ser

Out:
0    0.374540
1    0.950714
2    0.731994
3    0.598658
4    0.156019
dtype: float64
In :
ser.sum()

Out:
2.8119254917081569
In :
ser.mean()

Out:
0.56238509834163142

For a DataFrame, by default the aggregates return results within each column:

In :
df = pd.DataFrame({'A': rng.rand(5),
'B': rng.rand(5)})
df

Out:
A B
0 0.155995 0.020584
1 0.058084 0.969910
2 0.866176 0.832443
3 0.601115 0.212339
4 0.708073 0.181825
In :
df.mean()

Out:
A    0.477888
B    0.443420
dtype: float64

By specifying the axis argument, you can instead aggregate within each row:

In :
df.mean(axis='columns')

Out:
0    0.088290
1    0.513997
2    0.849309
3    0.406727
4    0.444949
dtype: float64

Pandas Series and DataFrames include all of the common aggregates mentioned in Aggregations: Min, Max, and Everything In Between; in addition, there is a convenience method describe() that computes several common aggregates for each column and returns the result. Let's use this on the Planets data, for now dropping rows with missing values:

In :
planets.dropna().describe()

Out:
number orbital_period mass distance year
count 498.00000 498.000000 498.000000 498.000000 498.000000
mean 1.73494 835.778671 2.509320 52.068213 2007.377510
std 1.17572 1469.128259 3.636274 46.596041 4.167284
min 1.00000 1.328300 0.003600 1.350000 1989.000000
25% 1.00000 38.272250 0.212500 24.497500 2005.000000
50% 1.00000 357.000000 1.245000 39.940000 2009.000000
75% 2.00000 999.600000 2.867500 59.332500 2011.000000
max 6.00000 17337.500000 25.000000 354.000000 2014.000000

This can be a useful way to begin understanding the overall properties of a dataset. For example, we see in the year column that although exoplanets were discovered as far back as 1989, half of all known expolanets were not discovered until 2010 or after. This is largely thanks to the Kepler mission, which is a space-based telescope specifically designed for finding eclipsing planets around other stars.

The following table summarizes some other built-in Pandas aggregations:

Aggregation Description
count() Total number of items
first(), last() First and last item
mean(), median() Mean and median
min(), max() Minimum and maximum
std(), var() Standard deviation and variance
mad() Mean absolute deviation
prod() Product of all items
sum() Sum of all items

These are all methods of DataFrame and Series objects.

To go deeper into the data, however, simple aggregates are often not enough. The next level of data summarization is the groupby operation, which allows you to quickly and efficiently compute aggregates on subsets of data.

## GroupBy: Split, Apply, Combine¶

Simple aggregations can give you a flavor of your dataset, but often we would prefer to aggregate conditionally on some label or index: this is implemented in the so-called groupby operation. The name "group by" comes from a command in the SQL database language, but it is perhaps more illuminative to think of it in the terms first coined by Hadley Wickham of Rstats fame: split, apply, combine.

### Split, apply, combine¶

A canonical example of this split-apply-combine operation, where the "apply" is a summation aggregation, is illustrated in this figure: figure source in Appendix

This makes clear what the groupby accomplishes:

• The split step involves breaking up and grouping a DataFrame depending on the value of the specified key.
• The apply step involves computing some function, usually an aggregate, transformation, or filtering, within the individual groups.
• The combine step merges the results of these operations into an output array.

While this could certainly be done manually using some combination of the masking, aggregation, and merging commands covered earlier, an important realization is that the intermediate splits do not need to be explicitly instantiated. Rather, the GroupBy can (often) do this in a single pass over the data, updating the sum, mean, count, min, or other aggregate for each group along the way. The power of the GroupBy is that it abstracts away these steps: the user need not think about how the computation is done under the hood, but rather thinks about the operation as a whole.

As a concrete example, let's take a look at using Pandas for the computation shown in this diagram. We'll start by creating the input DataFrame:

In :
df = pd.DataFrame({'key': ['A', 'B', 'C', 'A', 'B', 'C'],
'data': range(6)}, columns=['key', 'data'])
df

Out:
key data
0 A 0
1 B 1
2 C 2
3 A 3
4 B 4
5 C 5

The most basic split-apply-combine operation can be computed with the groupby() method of DataFrames, passing the name of the desired key column:

In :
df.groupby('key')

Out:
<pandas.core.groupby.DataFrameGroupBy object at 0x117272160>

Notice that what is returned is not a set of DataFrames, but a DataFrameGroupBy object. This object is where the magic is: you can think of it as a special view of the DataFrame, which is poised to dig into the groups but does no actual computation until the aggregation is applied. This "lazy evaluation" approach means that common aggregates can be implemented very efficiently in a way that is almost transparent to the user.

To produce a result, we can apply an aggregate to this DataFrameGroupBy object, which will perform the appropriate apply/combine steps to produce the desired result:

In :
df.groupby('key').sum()

Out:
data
key
A 3
B 5
C 7

The sum() method is just one possibility here; you can apply virtually any common Pandas or NumPy aggregation function, as well as virtually any valid DataFrame operation, as we will see in the following discussion.

### The GroupBy object¶

The GroupBy object is a very flexible abstraction. In many ways, you can simply treat it as if it's a collection of DataFrames, and it does the difficult things under the hood. Let's see some examples using the Planets data.

Perhaps the most important operations made available by a GroupBy are aggregate, filter, transform, and apply. We'll discuss each of these more fully in "Aggregate, Filter, Transform, Apply", but before that let's introduce some of the other functionality that can be used with the basic GroupBy operation.

#### Column indexing¶

The GroupBy object supports column indexing in the same way as the DataFrame, and returns a modified GroupBy object. For example:

In :
planets.groupby('method')

Out:
<pandas.core.groupby.DataFrameGroupBy object at 0x1172727b8>
In :
planets.groupby('method')['orbital_period']

Out:
<pandas.core.groupby.SeriesGroupBy object at 0x117272da0>

Here we've selected a particular Series group from the original DataFrame group by reference to its column name. As with the GroupBy object, no computation is done until we call some aggregate on the object:

In :
planets.groupby('method')['orbital_period'].median()

Out:
method
Astrometry                         631.180000
Eclipse Timing Variations         4343.500000
Imaging                          27500.000000
Microlensing                      3300.000000
Orbital Brightness Modulation        0.342887
Pulsar Timing                       66.541900
Pulsation Timing Variations       1170.000000
Transit                              5.714932
Transit Timing Variations           57.011000
Name: orbital_period, dtype: float64

This gives an idea of the general scale of orbital periods (in days) that each method is sensitive to.

#### Iteration over groups¶

The GroupBy object supports direct iteration over the groups, returning each group as a Series or DataFrame:

In :
for (method, group) in planets.groupby('method'):
print("{0:30s} shape={1}".format(method, group.shape))

Astrometry                     shape=(2, 6)
Eclipse Timing Variations      shape=(9, 6)
Imaging                        shape=(38, 6)
Microlensing                   shape=(23, 6)
Orbital Brightness Modulation  shape=(3, 6)
Pulsar Timing                  shape=(5, 6)
Pulsation Timing Variations    shape=(1, 6)
Transit                        shape=(397, 6)
Transit Timing Variations      shape=(4, 6)


This can be useful for doing certain things manually, though it is often much faster to use the built-in apply functionality, which we will discuss momentarily.

#### Dispatch methods¶

Through some Python class magic, any method not explicitly implemented by the GroupBy object will be passed through and called on the groups, whether they are DataFrame or Series objects. For example, you can use the describe() method of DataFrames to perform a set of aggregations that describe each group in the data:

In :
planets.groupby('method')['year'].describe().unstack()

Out:
count mean std min 25% 50% 75% max
method
Astrometry 2.0 2011.500000 2.121320 2010.0 2010.75 2011.5 2012.25 2013.0
Eclipse Timing Variations 9.0 2010.000000 1.414214 2008.0 2009.00 2010.0 2011.00 2012.0
Imaging 38.0 2009.131579 2.781901 2004.0 2008.00 2009.0 2011.00 2013.0
Microlensing 23.0 2009.782609 2.859697 2004.0 2008.00 2010.0 2012.00 2013.0
Orbital Brightness Modulation 3.0 2011.666667 1.154701 2011.0 2011.00 2011.0 2012.00 2013.0
Pulsar Timing 5.0 1998.400000 8.384510 1992.0 1992.00 1994.0 2003.00 2011.0
Pulsation Timing Variations 1.0 2007.000000 NaN 2007.0 2007.00 2007.0 2007.00 2007.0
Radial Velocity 553.0 2007.518987 4.249052 1989.0 2005.00 2009.0 2011.00 2014.0
Transit 397.0 2011.236776 2.077867 2002.0 2010.00 2012.0 2013.00 2014.0
Transit Timing Variations 4.0 2012.500000 1.290994 2011.0 2011.75 2012.5 2013.25 2014.0

Looking at this table helps us to better understand the data: for example, the vast majority of planets have been discovered by the Radial Velocity and Transit methods, though the latter only became common (due to new, more accurate telescopes) in the last decade. The newest methods seem to be Transit Timing Variation and Orbital Brightness Modulation, which were not used to discover a new planet until 2011.

This is just one example of the utility of dispatch methods. Notice that they are applied to each individual group, and the results are then combined within GroupBy and returned. Again, any valid DataFrame/Series method can be used on the corresponding GroupBy object, which allows for some very flexible and powerful operations!

### Aggregate, filter, transform, apply¶

The preceding discussion focused on aggregation for the combine operation, but there are more options available. In particular, GroupBy objects have aggregate(), filter(), transform(), and apply() methods that efficiently implement a variety of useful operations before combining the grouped data.

For the purpose of the following subsections, we'll use this DataFrame:

In :
rng = np.random.RandomState(0)
df = pd.DataFrame({'key': ['A', 'B', 'C', 'A', 'B', 'C'],
'data1': range(6),
'data2': rng.randint(0, 10, 6)},
columns = ['key', 'data1', 'data2'])
df

Out:
key data1 data2
0 A 0 5
1 B 1 0
2 C 2 3
3 A 3 3
4 B 4 7
5 C 5 9

#### Aggregation¶

We're now familiar with GroupBy aggregations with sum(), median(), and the like, but the aggregate() method allows for even more flexibility. It can take a string, a function, or a list thereof, and compute all the aggregates at once. Here is a quick example combining all these:

In :
df.groupby('key').aggregate(['min', np.median, max])

Out:
data1 data2
min median max min median max
key
A 0 1.5 3 3 4.0 5
B 1 2.5 4 0 3.5 7
C 2 3.5 5 3 6.0 9

Another useful pattern is to pass a dictionary mapping column names to operations to be applied on that column:

In :
df.groupby('key').aggregate({'data1': 'min',
'data2': 'max'})

Out:
data1 data2
key
A 0 5
B 1 7
C 2 9

#### Filtering¶

A filtering operation allows you to drop data based on the group properties. For example, we might want to keep all groups in which the standard deviation is larger than some critical value:

In :
def filter_func(x):
return x['data2'].std() > 4

display('df', "df.groupby('key').std()", "df.groupby('key').filter(filter_func)")

Out:

df

key data1 data2
0 A 0 5
1 B 1 0
2 C 2 3
3 A 3 3
4 B 4 7
5 C 5 9

df.groupby('key').std()

data1 data2
key
A 2.12132 1.414214
B 2.12132 4.949747
C 2.12132 4.242641

df.groupby('key').filter(filter_func)

key data1 data2
1 B 1 0
2 C 2 3
4 B 4 7
5 C 5 9

The filter function should return a Boolean value specifying whether the group passes the filtering. Here because group A does not have a standard deviation greater than 4, it is dropped from the result.

#### Transformation¶

While aggregation must return a reduced version of the data, transformation can return some transformed version of the full data to recombine. For such a transformation, the output is the same shape as the input. A common example is to center the data by subtracting the group-wise mean:

In :
df.groupby('key').transform(lambda x: x - x.mean())

Out:
data1 data2
0 -1.5 1.0
1 -1.5 -3.5
2 -1.5 -3.0
3 1.5 -1.0
4 1.5 3.5
5 1.5 3.0

#### The apply() method¶

The apply() method lets you apply an arbitrary function to the group results. The function should take a DataFrame, and return either a Pandas object (e.g., DataFrame, Series) or a scalar; the combine operation will be tailored to the type of output returned.

For example, here is an apply() that normalizes the first column by the sum of the second:

In :
def norm_by_data2(x):
# x is a DataFrame of group values
x['data1'] /= x['data2'].sum()
return x

display('df', "df.groupby('key').apply(norm_by_data2)")

Out:

df

key data1 data2
0 A 0 5
1 B 1 0
2 C 2 3
3 A 3 3
4 B 4 7
5 C 5 9

df.groupby('key').apply(norm_by_data2)

key data1 data2
0 A 0.000000 5
1 B 0.142857 0
2 C 0.166667 3
3 A 0.375000 3
4 B 0.571429 7
5 C 0.416667 9

apply() within a GroupBy is quite flexible: the only criterion is that the function takes a DataFrame and returns a Pandas object or scalar; what you do in the middle is up to you!

### Specifying the split key¶

In the simple examples presented before, we split the DataFrame on a single column name. This is just one of many options by which the groups can be defined, and we'll go through some other options for group specification here.

#### A list, array, series, or index providing the grouping keys¶

The key can be any series or list with a length matching that of the DataFrame. For example:

In :
L = [0, 1, 0, 1, 2, 0]
display('df', 'df.groupby(L).sum()')

Out:

df

key data1 data2
0 A 0 5
1 B 1 0
2 C 2 3
3 A 3 3
4 B 4 7
5 C 5 9

df.groupby(L).sum()

data1 data2
0 7 17
1 4 3
2 4 7

Of course, this means there's another, more verbose way of accomplishing the df.groupby('key') from before:

In :
display('df', "df.groupby(df['key']).sum()")

Out:

df

key data1 data2
0 A 0 5
1 B 1 0
2 C 2 3
3 A 3 3
4 B 4 7
5 C 5 9

df.groupby(df['key']).sum()

data1 data2
key
A 3 8
B 5 7
C 7 12

#### A dictionary or series mapping index to group¶

Another method is to provide a dictionary that maps index values to the group keys:

In :
df2 = df.set_index('key')
mapping = {'A': 'vowel', 'B': 'consonant', 'C': 'consonant'}
display('df2', 'df2.groupby(mapping).sum()')

Out:

df2

data1 data2
key
A 0 5
B 1 0
C 2 3
A 3 3
B 4 7
C 5 9

df2.groupby(mapping).sum()

data1 data2
consonant 12 19
vowel 3 8

#### Any Python function¶

Similar to mapping, you can pass any Python function that will input the index value and output the group:

In :
display('df2', 'df2.groupby(str.lower).mean()')

Out:

df2

data1 data2
key
A 0 5
B 1 0
C 2 3
A 3 3
B 4 7
C 5 9

df2.groupby(str.lower).mean()

data1 data2
a 1.5 4.0
b 2.5 3.5
c 3.5 6.0

#### A list of valid keys¶

Further, any of the preceding key choices can be combined to group on a multi-index:

In :
df2.groupby([str.lower, mapping]).mean()

Out:
data1 data2
a vowel 1.5 4.0
b consonant 2.5 3.5
c consonant 3.5 6.0

### Grouping example¶

As an example of this, in a couple lines of Python code we can put all these together and count discovered planets by method and by decade:

In :
decade = 10 * (planets['year'] // 10)

Out:
method
Astrometry 0.0 0.0 0.0 2.0
Eclipse Timing Variations 0.0 0.0 5.0 10.0
Imaging 0.0 0.0 29.0 21.0
Microlensing 0.0 0.0 12.0 15.0
Orbital Brightness Modulation 0.0 0.0 0.0 5.0
Pulsar Timing 0.0 9.0 1.0 1.0
Pulsation Timing Variations 0.0 0.0 1.0 0.0
Radial Velocity 1.0 52.0 475.0 424.0
Transit 0.0 0.0 64.0 712.0
Transit Timing Variations 0.0 0.0 0.0 9.0

This shows the power of combining many of the operations we've discussed up to this point when looking at realistic datasets. We immediately gain a coarse understanding of when and how planets have been discovered over the past several decades!

Here I would suggest digging into these few lines of code, and evaluating the individual steps to make sure you understand exactly what they are doing to the result. It's certainly a somewhat complicated example, but understanding these pieces will give you the means to similarly explore your own data.