Skip to content

Mastering Multi-Indexing and Hierarchical Data Structures in Pandas

Published: at 04:14 AM

Multi-indexing and hierarchical data structures are advanced techniques in Pandas that allow you to work with complex, multi-dimensional data in an organized and efficient way. A multi-index essentially enables multiple (two or more) index levels on an axis, usually the rows. This allows entries in a DataFrame to be accessed via multiple keys rather than a single key.

Hierarchical data structures take multi-indexing a step further by letting you create tree-like relationships between items using parent-child links. This is useful for representing data that has natural hierarchical relationships like geographical location or organizational structure.

In this comprehensive guide, we will learn how to:

We will illustrate the key concepts with easy-to-follow examples using Pandas, Python’s powerful data analysis library. Let’s get started!

Creating a Multi-Indexed DataFrame

A multi-index can be created by passing multiple columns or arrays during DataFrame construction:

import pandas as pd

data = {
  "Name": ["John", "Mary", "Steve", "Sarah"],
  "Subject": ["Math", "Science", "Math", "Science"],
  "Score": [90, 95, 80, 85]

df = pd.DataFrame(data)

# Create multi-index from columns
# Pass arrays as row indexes
df_mi = pd.DataFrame(data, index=[["Q1", "Q1", "Q2", "Q2"], ["A", "B", "C", "D"]])

   Name Subject  Score
Q1 A  John    Math     90
   B   Mary  Science     95
Q2 C  Steve    Math     80
   D  Sarah  Science     85

Here we passed two column arrays as row indexes to create a multi-indexed DataFrame with a 2-level index of [Quarter, Student ID]. The innermost array forms the outermost index level.

Alternatively, we can convert existing columns to MultiIndex:

# Convert columns to MultiIndex
df_mi = df.set_index(['Subject', 'Name'])
Subject Name
Math    John          90
       Steve          80
Science Mary          95
       Sarah          85

Multi-indexes allow efficient querying and slicing as we’ll see next.

Querying Multi-Indexed Data

We can query multi-indexed data using multiple indexers separated with commas. For example:

# Query specific row by multiple indexers
row = df_mi.loc[('Math', 'John')]
Score    90
Name: (Math, John), dtype: int64

The order of indexers must match the actual index order.

We can also select rows using Pandas .xs() method by level name or position. .xs() selects data at a particular level of the MultiIndex:

# Select by index name
row = df_mi.xs('John', level='Name')

# Select by index position
row = df_mi.xs(1, level=1)

For column selection, we slice with just the required columns separately after indexing rows:

# Select specific columns after row selection

We can query multiple rows and columns together:

# Multi-row & column selection
df_mi.loc[(['Math','Science'], ['John', 'Mary']), ['Score']]

The real power of multi-indexing comes from partially specifying the multi-indexers to slice the data at specific index levels.

For example, we can select all rows for ‘Math’ subject as:


Or extract all students with ‘Science’ as subject:

df_mi.loc[:, 'Science']

The : slices across all elements at that index level. We can mix and match partial and specific indices:

# Mix of partial and specific row selection
df_mi.loc[(['Math'], ['John', 'Steve']), ['Score']]

In essence, multi-indexing allows us to store and slice multi-dimensional data in a tabular structure efficiently.

Handling Missing Data in MultiIndexes

In real-world data, we often encounter missing (NaN) values in MultiIndex DataFrames. For example:

df_mi.loc[('Science', 'Sarah'), 'Score'] = np.nan

Subject Name
Math    John      90.0
       Steve      80.0
Science Mary      95.0
       Sarah      NaN

To filter out rows with NaN values:

df_mi = df_mi.dropna()

Alternatively, we can fillna() to replace NaNs with a value:

df_mi = df_mi.fillna(0)

Handling missing data properly is important before further analysis.

Reordering, Sorting and Renaming Index Levels

The index levels can be reordered using .reorder_levels():

# Reorder index levels
df_mi = df_mi.reorder_levels(['Name', 'Subject'], axis=0)

This changes the outermost index to Name. Reordering can help organize the data logically.

We can also sort the index lexicographically:

# Sort index lexicographically
df_mi = df_mi.sort_index()

Sorting arranges the index entries in a standard order for improved readability.

To reset the index or remove it entirely:

# Reset index - generates new integer index
df_mi = df_mi.reset_index()

# Remove index completely
df_mi = df_mi.reset_index(drop=True)

Resetting the index is useful when we need to convert back to a default integer index after manipulating the hierarchical index.

Finally, we can rename the index levels using .rename_axis():

# Rename index levels
df_mi = df_mi.rename_axis(index={'Subject': 'Course'})

Proper ordering, sorting and naming of index levels is crucial for readability and usability.

Converting Columns to Hierarchical Index

We can convert columns into hierarchical indexes to create nested categories.

For instance:

data = {
  'Year': [2019, 2020],
  'City': ['London','Toronto'],
  'Population': [8900000, 6000000],
  'GDP': [450000, 480000]

# Make sure 'Year' column is integer type
data['Year'] = data['Year'].astype(int)

df = pd.DataFrame(data)

# Convert columns to MultiIndex
df.columns = pd.MultiIndex.from_tuples([
  ('Stats', 'Population'),
  ('Stats', 'GDP')])

   Population    GDP
0   2019  8900000  450000
1   2020  6000000  480000

Here ‘Stats’ becomes the outer high-level category encompassing the two detailed metrics - Population and GDP.

We can query hierarchical indexes by category (Stats) or leaf node (Population) directly:

df['Stats'] # or

Later we’ll see how hierarchical indexes assist in grouped operations.

Joining/Merging Multi-Indexed Datasets

Multi-indexes allow straightforward merging or joining of datasets having one or more matching indexes.

For example:

df1 = pd.DataFrame({
  'A': [1, 2],
  'B': [3, 4]

df2 = pd.DataFrame({
  'A': [1, 2],
  'C': [5, 6]

df = df1.merge(df2, left_index=True, right_index=True)
   B  C
1  3  5
2  4  6

Here df1 and df2 were merged on index A producing a multi-indexed result set.

We can also join by multiple common indexes:

df3 = pd.DataFrame({
  'A': [1, 2],
  'B': [7, 8]
}).set_index(['A', 'B'])

df = df1.merge(df3, left_index=True, right_index=True)

Any shared indexes when set as the left_index and right_index will merge two DataFrames like a database join.

Aggregating Hierarchical Data

A common operation on hierarchical data is aggregation across a specific index level. The groupby() method in Pandas groups data by one or more indexes allowing fast data aggregation.

For example, let’s analyze sales data by product categories:

data = {
  'Category': ['Electronics', 'Electronics', 'Clothing', 'Home & Kitchen', 'Clothing'],
  'Product': ['TV', 'Smart Phone', 'T-Shirt', 'Furniture', 'Trousers'],
  'Revenue': [5000, 4000, 1000, 8000, 600]

df = pd.DataFrame(data)

# Set category as index
df = df.set_index('Category')

# Groupby index and aggregate
df.groupby(level=0).aggregate({'Revenue': 'sum'})
Clothing        1600
Electronics     9000
Home & Kitchen  8000

Here we were able to quickly sum revenue by product category using the set index.

We can also apply multiple aggregation functions together:

df.groupby(level=0).agg({'Revenue': ['sum', 'mean', 'max']})

This shows the flexibility of aggregations on hierarchical data.

Real World Use Cases

Let’s take a look at some real-world use cases where multi-indexing and hierarchical data structures unlock Pandas’ true potential for data analysis.

Modeling Geographical Data

Geo-spatial data can be modeled using a multi-index with location hierarchies like country, region, state, city acting as index levels:

locations = [
  ('Asia', 'Southern', 'India', 'Hyderabad'),
  ('Asia', 'Southern', 'India', 'Bangalore'),
  ('Asia', 'Eastern', 'China', 'Shanghai'),
  ('North America', 'Northern', 'USA', 'New York')

populations = [
  12500000, 11500000, 26000000, 8500000

city_df = pd.DataFrame(populations, index=pd.MultiIndex.from_tuples(locations),

Asia      Southern India   Hyderabad     12500000
                        Bangalore     11500000
           Eastern  China Shanghai     26000000
North America Northern USA   New York    8500000

Here, multi-indexing allows us to model the geographical hierarchy in a tidy structure suitable for slicing:

city_df.loc[(['Asia', 'Southern', 'India'], :), 'Population']
# or
city_df.loc[('Asia', 'Southern'):, 'Population']

Time Series Analysis

Time series data with a DateTimeIndex can be converted into a multi-index with date parts as levels for handy analysis and visualization:

dates = pd.date_range('2019-01-01', '2019-12-31')
data = np.random.rand(len(dates))
df = pd.DataFrame(data, index=dates, columns=['Value'])

df.index = df.index.to_period('M')

# Convert to multi-index
df.index = [df.index.year, df.index.month]

2019 1    0.126918
     2    0.526506
     3    0.029268
2019 10   0.554134
     11   0.710316
     12   0.073417

Now the data is structured by year and month for intuitive querying:

df.loc[2019] # All months in 2019
df.loc[(2019, 12), :] # Dec 2019 data

Multiple time series can also be merged easily with date indexes.

Analysis Using Categorical Data

Data science datasets often contain categorical features like gender, country, education level etc.

We can model them using a category index:

data = {
  'Name': ['Alice', 'Bob', 'Claire', 'Dylan'],
  'Gender': ['F', 'M', 'F', 'M'],
  'Age': [25, 32, 28, 40],
  'Salary': [50000, 60000, 55000, 75000]

df = pd.DataFrame(data).set_index('Gender')

   Age  Name  Salary
F   25  Alice   50000
M   32    Bob   60000
F   28  Claire  55000
M   40  Dylan   75000

Now rows can be selected by category value:

df.loc['F'] # All females

We can even have multiple categories as a multi-index:

df = df.set_index(['Gender', 'Age'], drop=True)

Hierarchical indexing provides the foundation for pivot tables, cross tabs and analytical cubes frequently used in data science.


In summary, multi-indexing and hierarchical data structures in Pandas empower efficient data access and analysis. They allow handling higher dimensional data packed within a 2D DataFrame intuitively.

The key benefits are:

With this comprehensive guide, you should now feel comfortable applying these techniques to handle real-world data modeling and analysis challenges in Python.