Distribution Plots

Let’s discuss some plots that allow us to visualize the distribution of a data set. These plots are:

  • distplot
  • jointplot
  • pairplot
  • rugplot
  • kdeplot

Imports

import seaborn as sns
%matplotlib inline

Data

Seaborn comes with built-in data sets!

tips = sns.load_dataset('tips')
tips.head()

total_billtipsexsmokerdaytimesize
016.991.01FemaleNoSunDinner2
110.341.66MaleNoSunDinner3
221.013.50MaleNoSunDinner3
323.683.31MaleNoSunDinner2
424.593.61FemaleNoSunDinner4

distplot

The distplot shows the distribution of a univariate set of observations.

sns.distplot(tips['total_bill'])
# Safe to ignore warnings
<matplotlib.axes._subplots.AxesSubplot at 0x7f094c6b3a90>

png

To remove the kde layer and just have the histogram use:

sns.distplot(tips['total_bill'],kde=False,bins=30)
<matplotlib.axes._subplots.AxesSubplot at 0x7f094a543e10>

png

jointplot

jointplot() allows you to basically match up two distplots for bivariate data. With your choice of what kind parameter to compare with:

  • “scatter”
  • “reg”
  • “resid”
  • “kde”
  • “hex”
sns.jointplot(x='total_bill',y='tip',data=tips,kind='scatter')
<seaborn.axisgrid.JointGrid at 0x7f0949ed63c8>

png

sns.jointplot(x='total_bill',y='tip',data=tips,kind='hex')
<seaborn.axisgrid.JointGrid at 0x7f094cf28cc0>

png

sns.jointplot(x='total_bill',y='tip',data=tips,kind='reg')
<seaborn.axisgrid.JointGrid at 0x7f0949ce0eb8>

png

pairplot

pairplot will plot pairwise relationships across an entire dataframe (for the numerical columns) and supports a color hue argument (for categorical columns).

sns.pairplot(tips)
<seaborn.axisgrid.PairGrid at 0x7f0949a907f0>

png

sns.pairplot(tips,hue='sex',palette='coolwarm')
<seaborn.axisgrid.PairGrid at 0x7f094968dda0>

png

rugplot

rugplots are actually a very simple concept, they just draw a dash mark for every point on a univariate distribution. They are the building block of a KDE plot:

sns.rugplot(tips['total_bill'])
<matplotlib.axes._subplots.AxesSubplot at 0x7f094913c898>

png

kdeplot

kdeplots are Kernel Density Estimation plots. These KDE plots replace every single observation with a Gaussian (Normal) distribution centered around that value. For example:

# Don't worry about understanding this code!
# It's just for the diagram below
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

#Create dataset
dataset = np.random.randn(25)

# Create another rugplot
sns.rugplot(dataset);

# Set up the x-axis for the plot
x_min = dataset.min() - 2
x_max = dataset.max() + 2

# 100 equally spaced points from x_min to x_max
x_axis = np.linspace(x_min,x_max,100)

# Set up the bandwidth, for info on this:
url = 'http://en.wikipedia.org/wiki/Kernel_density_estimation#Practical_estimation_of_the_bandwidth'

bandwidth = ((4*dataset.std()**5)/(3*len(dataset)))**.2


# Create an empty kernel list
kernel_list = []

# Plot each basis function
for data_point in dataset:
    
    # Create a kernel for each point and append to list
    kernel = stats.norm(data_point,bandwidth).pdf(x_axis)
    kernel_list.append(kernel)
    
    #Scale for plotting
    kernel = kernel / kernel.max()
    kernel = kernel * .4
    plt.plot(x_axis,kernel,color = 'grey',alpha=0.5)

plt.ylim(0,1)
(0, 1)

png

# To get the kde plot we can sum these basis functions.

# Plot the sum of the basis function
sum_of_kde = np.sum(kernel_list,axis=0)

# Plot figure
fig = plt.plot(x_axis,sum_of_kde,color='indianred')

# Add the initial rugplot
sns.rugplot(dataset,c = 'indianred')

# Get rid of y-tick marks
plt.yticks([])

# Set title
plt.suptitle("Sum of the Basis Functions")
Text(0.5, 0.98, 'Sum of the Basis Functions')

png

So with our tips dataset:

sns.kdeplot(tips['total_bill'])
sns.rugplot(tips['total_bill'])
<matplotlib.axes._subplots.AxesSubplot at 0x7f09491856a0>

png

sns.kdeplot(tips['tip'])
sns.rugplot(tips['tip'])
<matplotlib.axes._subplots.AxesSubplot at 0x7f0948023e80>

png

Greydon Gilmore
Greydon Gilmore
Ph.D. Candidate in Biomedical Engineering

My research interests include deep brain stimulation, machine learning and signal processing.

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