Skip to main content
HomeAbout RLearn R

Bivariate Distribution Heatmaps in R

Learn how to visually show the relationship between two features, how they interact with each other, and where data points are concentrated.
Jul 2018  · 6 min read

As a data scientist, you will have to analyze the distribution of the features in your dataset. Usually, this is done by using histograms, this is really useful to show the variable range of values, their deviation and where values are concentrated.

This tutorial uses R. If you're not yet familiar with R, I suggest you take our free Introduction to R course on DataCamp.

Bike Sharing Dataset

For this tutorial, you are going to use the Bike Sharing Demand Dataset from a kaggle competition.

Follow the link and go to the data tab, then download the train.csv file.

bike sharing data

Load the dataset into R.

bike<- read.csv("train.csv",
                na.strings = FALSE,
                strip.white = TRUE)

Dataset Features

Feature Description
datetime hourly date + timestamp
season 1 = spring
2 = summer
3 = fall
4 = winter
holiday whether the day is considered a holiday
workingday whether the day is neither a weekend nor holiday
weather 1: Clear, Few clouds, Partly cloudy, Partly cloudy
2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist
3: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds
4: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog
temp temperature in Celsius
atemp "feels like" temperature in Celsius
humidity relative humidity
windspeed wind speed
casual number of non-registered user rentals initiated
registered number of registered user rentals initiated
count number of total rentals

Feature Selection

You are going to analyze the relationship between atemp and humidity by season, so select them from the dataset. Remember to load dplyr package.

  bike %>%  
  dplyr::select(season, atemp, humidity)


Ok now you are ready to start analyzing the data, start by creating a histogram for each of the features by season. You are going to do this using ggplot2 library so don´t forget to load it.

Humidity Histogram

bike_data %>%
  ggplot( aes(x=humidity) ) +
  geom_histogram(bins=30) +
  facet_wrap(~season,ncol = 2)


With the histogram, you can see that there is a higher humidity during winter (which is obvious) but you can have a sense of how it is distributed during each season.

Now add the density, a density rug and change the names of the facets, just to have a better-looking visualization.

bike_data %>%
  mutate(season_label = case_when(
    season == 1 ~ "Spring",
    season == 2 ~ "Summer",
    season == 3 ~ "fall",
    season == 4 ~ "winter")) %>%
  ggplot( aes(x=humidity) ) +
  geom_histogram(bins=30,aes(y = ..density..)) +
  facet_wrap(~season_label,ncol = 2)+
  ggtitle("Histogram of humidity by season")

histogram of humidity by season

Now, this gives you a better feel of how humidity behaves, do the same with atemp.

atemp Histogram

Reuse the above code and change the variable to atemp,

bike_data %>%
  mutate(season_label = case_when(
    season == 1 ~ "Spring",
    season == 2 ~ "Summer",
    season == 3 ~ "fall",
    season == 4 ~ "winter")) %>%
  ggplot( aes(x=atemp) ) +
  geom_histogram(bins=30,aes(y = ..density..)) +
  facet_wrap(~season_label,ncol = 2)+
  ggtitle("Histogram of atemp by season")
Histogram of atemp by seasonhistogram of atemp by season

Ok, so far so good, everything is going according to what you would expect for each season. In each graph, you have an approximation of the probability distribution function.

But it is difficult based on this graphs to visualize how the features interact with each other. The first difficulty you encounter is that your histogram needs to be in 3D because you're trying to find the distribution function for the two features.

Fitting a Bivariate Distribution to your Data

The goal is to visualize the bivariate distribution, to be able to do this you first need to fit a bivariate distribution to the data. This will be done using the MASS library and the kde2d function. The kde2d function will estimate the bivariate distribution, assuming normality for the random variables. The inputs to this function are as follows,

input description
x x coordinate data
y y coordinate data
n number of grid point for each axis
lims limits for x and y

Now apply it to the dataset filtering for summer,

bike_data_summer <- bike_data %>% filter(season==1)
bike_density <- kde2d(bike_data_summer$atemp,bike_data_summer$humidity, n=1000)

Note: When loading the MASS library it comes with a select function, this will have an issue with dplyr select function so to fix this when using the dplyr select you need to add dplyr:: to it like this dplyr::select() for it to work correctly.

Now look at the class and the structure of bike_density


It is a list that has 3 values x, y, and z. The first two have the features values and the third one is a matrix with the value of the pdf. Take a look at the density using the contour function,



Looking at this you can identify some accumulation points, that could be understood as the most frequent values for the combination of the two features. The values for each point are resumed on the following table,

point atemp (°C) hummidity (%)
1 12.2 89
2 10.4 43
3 21 43
4 21.6 78


To create your heatmap you first need to define the color scale you want to use, you can do this using the function colorRampPalette


hm_col_scale is a vector going from black to red using RGB code in 1000 steps.

Now plot your heat map using the image function, this function is used to plot matrixes.

      col = hm_col_scale,
      zlim=c(min(bike_density$z), max(bike_density$z)))
text(0.31,0.46,"Most Frequent",col="blue",cex=0.8)


Now, as you can see this has more information than the contour plot because now the colors tell us how high the accumulation point goes. You can see that the most frequent values for humidity and atemp during spring is around the point $(10.4,43)$


Now you know how to create a heat map, it's your turn to create your own. Start by looking at the other season and the relation with the other variables.

Think about how could you use this to gain insight on how many bikes you have to supply for the different values of the variables based on the fact that most frequent points have a higher probability.

If you would like to learn more about generating data visualizations with ggplot, be sure to take a look at our Data Visualization with ggplot2 course.


Learn more about R

Certification available


Introduction to R

4 hr
Master the basics of data analysis in R, including vectors, lists, and data frames, and practice R with real data sets.
See DetailsRight Arrow
Start Course
See MoreRight Arrow

Data Science in Finance: Unlocking New Potentials in Financial Markets

Discover the role of data science in finance, shaping tomorrow's financial strategies. Gain insights into advanced analytics and investment trends.
 Shawn Plummer's photo

Shawn Plummer

9 min

5 Common Data Science Challenges and Effective Solutions

Emerging technologies are changing the data science world, bringing new data science challenges to businesses. Here are 5 data science challenges and solutions.
DataCamp Team's photo

DataCamp Team

8 min

Navigating R Certifications in 2024: A Comprehensive Guide

Explore DataCamp's R programming certifications with our guide. Learn about Data Scientist and Data Analyst paths, preparation tips, and career advancement.
Matt Crabtree's photo

Matt Crabtree

8 min

A Data Science Roadmap for 2024

Do you want to start or grow in the field of data science? This data science roadmap helps you understand and get started in the data science landscape.
Mark Graus's photo

Mark Graus

10 min

Data Storytelling and Visualization with Lea Pica from Present Beyond Measure

Richie and Lea cover the full picture of data presentation, how to understand your audience, leverage hollywood storytelling and much more.
Richie Cotton's photo

Richie Cotton

71 min

Introduction to DynamoDB: Mastering NoSQL Database with Node.js | A Beginner's Tutorial

Learn to master DynamoDB with Node.js in this beginner's guide. Explore table creation, CRUD operations, and scalability in AWS's NoSQL database.
Gary Alway's photo

Gary Alway

11 min

See MoreSee More