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Kernel Density Estimate Plot using matplotlib python

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by aryaman@openweaver.com dot icon Updated: Jul 26, 2023

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A kernel density plot, also known as a kernel density estimation (KDE) plot. It is a graphical representation of the probability density function random variable. It is a non-parametric way of estimating the underlying probability data set. Kernel density plots are useful for visualizing the shape of a dataset. They can provide insights into the presence of many peaks, skewness, or gaps in the data. The result is a continuous curve that represents the probability distribution of data.  

 

The main idea behind a kernel density plot is to distribute data points as a smooth curve. This kernel density estimate curve was created by placing a kernel at each data point.  

Tips for Improving the Accuracy of Kernel Density Plot:  

  1. Adjust the Smoothing Parameter: The parameter referred to bandwidth control fine details. By adjusting the smoothing parameter, you can find the level of smoothness in the plot.  
  2. Experiment with Kernel Size: The kernel's size affects the kernel's width in density. A larger kernel size leads to a smoother plot with less detail. If your kernel density plot appears fails to reduce the kernel size can increase the level of detail.  
  3. Consider Data Preprocessing: Preprocessing your data can also increase the accuracy of the kernel density. For example, removing outliers or handling missing values can reduce the influence.  
  4. Evaluate Multiple Plots: Generating kernel density with parameters can be beneficial. By examining the plots, you can assess the accuracy and quality of representation.  

 

The kernel density plot holds significant importance as a powerful data analysis. Its ability to provide a smooth and informative representation of the underlying distribution. Its ability to present data in an appealing makes it an essential tool in the data analyst's toolkit. Its aids in problem-solving and driving data-driven strategies across various industries and domains. 

Code

In this solution, we use the kerneldensity function of the scikit-learn library

how does 2d kernel density estimation in python (sklearn) work?

PythondotLines of Code : 32dotLicense : Strong Copyleft (CC BY-SA 4.0)

Dependent Libraries : 
from sklearn.neighbors import KernelDensity

def kde2D(x, y, bandwidth, xbins=100j, ybins=100j, **kwargs): 
    """Build 2D kernel density estimate (KDE)."""

    # create grid of sample locations (default: 100x100)
    xx, yy = np.mgrid[x.min():x.max():xbins, 
                      y.min():y.max():ybins]

    xy_sample = np.vstack([yy.ravel(), xx.ravel()]).T
    xy_train  = np.vstack([y, x]).T

    kde_skl = KernelDensity(bandwidth=bandwidth, **kwargs)
    kde_skl.fit(xy_train)

    # score_samples() returns the log-likelihood of the samples
    z = np.exp(kde_skl.score_samples(xy_sample))
    return xx, yy, np.reshape(z, xx.shape)

import numpy as np
import matplotlib.pyplot as plt

m1 = np.random.normal(size=1000)
m2 = np.random.normal(scale=0.5, size=1000)

x, y = m1 + m2, m1 - m2

xx, yy, zz = kde2D(x, y, 1.0)

plt.pcolormesh(xx, yy, zz)
plt.scatter(x, y, s=2, facecolor='white')
  1. Install the libraries using the pip install command
  2. Copy the code using the "Copy" button above, and paste it in a Python file in your IDE.
  3. Modify the values.
  4. Run the file and check the output.


I hope you found this useful. I have added the link to dependent libraries, version information in the following sections

Dependent Libraries

matplotlibby matplotlib

Python doticonstar image 17559 doticonVersion:v3.7.1doticon
no licences License: No License (null)

matplotlib: plotting with Python

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            matplotlibby matplotlib

            Python doticon star image 17559 doticonVersion:v3.7.1doticonno licences License: No License

            matplotlib: plotting with Python
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                      numpyby numpy

                      Python doticonstar image 23755 doticonVersion:v1.25.0rc1doticon
                      License: Permissive (BSD-3-Clause)

                      The fundamental package for scientific computing with Python.

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                                numpyby numpy

                                Python doticon star image 23755 doticonVersion:v1.25.0rc1doticon License: Permissive (BSD-3-Clause)

                                The fundamental package for scientific computing with Python.
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                                          scikit-learnby scikit-learn

                                          Python doticonstar image 54584 doticonVersion:1.2.2doticon
                                          License: Permissive (BSD-3-Clause)

                                          scikit-learn: machine learning in Python

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                                                    scikit-learnby scikit-learn

                                                    Python doticon star image 54584 doticonVersion:1.2.2doticon License: Permissive (BSD-3-Clause)

                                                    scikit-learn: machine learning in Python
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                                                              Environment Tested 

                                                              I tested this solution in the following versions. Be mindful of changes when working with other versions. 

                                                              1. The solution is created in Python3.11. 

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                                                              FAQ:  

                                                              1. What is the purpose of a Kernel Density Plot in Python?  

                                                              The purpose of a kernel density plot in Python is to visualize the probability function of a dataset. It provides an estimate of the density of the data points, allowing you to gain insights into the shape. Kernel density plots are particularly useful for exploring univariate or multivariate data.  

                                                               

                                                              2. How is Python's Density Estimation for Statistics and Data Analysis implemented?  

                                                              Density estimation is a technique used in analysis to estimate the probability. In Python, there are several libraries and methods available for implementing density estimation.  

                                                               

                                                              3. What are empirical cumulative density plots, and how do they relate to KDE plots?  

                                                              Empirical cumulative density plots, also known as cumulative distribution function plots. The graphical illustrations of the cumulative probability distribution of a dataset. They provide information about the distribution of the data and allow the probabilities.  

                                                               

                                                              4. What is a Probability Density Function (PDF), and how does it differ from a KDE plot?  

                                                              The Probability Density Function (PDF) is a mathematical function of a variable. It represents the probability distribution of the random variable. The PDF shows the relative likelihood of observed values within the variable range.  

                                                               

                                                              5. How can I import stats using SciPy when creating KDE plots with Python programming?  

                                                              Import the necessary modules from the SciPy library when creating KDE plots in Python. It needs to import the stats module from the SciPy library. Additionally, you'll need to import the Seaborn library for data visualization.  

                                                              • Seaborn: Seaborn is a data visualization library. It is built on top of Matplotlib. It provides a high-level interface for creating pleasing statistical graphics, including KDE plots.  
                                                              • matplotlib.pylot: Matplotlib is the foundational plotting library in Python. We import the pyplot module from Matplotlib to create, plot, and customize it.  
                                                              • scipy.stats: SciPy is a library that provides various statistical functions and distributions. We import the stats module from SciPy to access the kernel density function. 

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