How to Analyze the Distribution of Data with KDE Plots in EDA

Kernel Density Estimation (KDE) plots are a powerful tool in Exploratory Data Analysis (EDA) for visualizing the distribution of data. They provide a smooth, continuous estimate of the probability density function (PDF) of a random variable, helping us better understand the underlying distribution of the data. Unlike histograms, which display data in discrete bins, KDE plots give a more refined, smoothed view, making it easier to detect patterns, trends, and anomalies.

What is a KDE Plot?

A KDE plot is a non-parametric way to estimate the probability density function of a continuous random variable. It works by placing a kernel (usually a Gaussian) on each data point and then summing the contributions from all points. The result is a smooth curve that estimates the probability distribution of the data.

Why Use KDE Plots in EDA?

• Smooth Representation: KDE plots smooth out the sharp edges of histograms, offering a more natural look at the distribution.

• Identifying Patterns: They can reveal important features of the data like skewness, multi-modal distributions, and outliers.

• No Binning: Unlike histograms, KDEs do not require you to specify the number of bins, which can be subjective and affect the interpretation.

Steps to Create KDE Plots in EDA

To perform effective EDA using KDE plots, the following steps are generally involved:

1. Import Necessary Libraries

The first step is to import the necessary libraries for data manipulation and visualization.

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import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

2. Load the Dataset

Typically, a dataset is loaded into a pandas DataFrame. For this example, we’ll use a dataset with a continuous numerical feature.

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# Load sample dataset
data = sns.load_dataset('iris')  # Example dataset

3. Choose a Column for Analysis

For KDE, you need to pick a continuous numerical variable. In this example, we’ll analyze the distribution of the sepal_length column from the Iris dataset.

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# Choose the variable for analysis
column = 'sepal_length'

4. Plot the KDE

The seaborn library makes it easy to generate a KDE plot using the sns.kdeplot() function. This function creates the plot by default using a Gaussian kernel, but other kernel types can also be used.

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# Plot KDE for the chosen column
sns.kdeplot(data[column], shade=True)
plt.title(f'Distribution of {column}')
plt.xlabel(column)
plt.ylabel('Density')
plt.show()

In the above code:

• shade=True fills the area under the KDE curve with color.

• plt.title(), plt.xlabel(), and plt.ylabel() are used for labeling the plot.

5. Adjust Bandwidth for Smoothing

The bandwidth parameter controls the smoothness of the KDE curve. A smaller bandwidth will result in a more sensitive plot with more peaks and valleys, while a larger bandwidth will smooth out the curve more.

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# Adjust bandwidth
sns.kdeplot(data[column], shade=True, bw_adjust=0.5)  # More sensitive curve
plt.title(f'Distribution of {column} (Smoothed)')
plt.xlabel(column)
plt.ylabel('Density')
plt.show()

The bw_adjust parameter allows you to fine-tune the bandwidth. Lower values make the plot more sensitive (more peaks), and higher values smooth it out.

6. Overlay Multiple Distributions

KDE plots are also useful when comparing distributions. You can overlay multiple distributions on the same plot to see how they differ. For instance, comparing sepal_length for different species in the Iris dataset:

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# KDE for different species
sns.kdeplot(data=data[data['species'] == 'setosa'][column], shade=True, label='Setosa')
sns.kdeplot(data[data['species'] == 'versicolor'][column], shade=True, label='Versicolor')
sns.kdeplot(data[data['species'] == 'virginica'][column], shade=True, label='Virginica')

plt.title(f'Distribution of {column} by Species')
plt.xlabel(column)
plt.ylabel('Density')
plt.legend()
plt.show()

This comparison gives us a clearer view of how the distributions of sepal_length differ across the three species.

7. KDE for Bivariate Data

In addition to univariate distributions, KDE plots can be used for bivariate data (two variables). A 2D KDE plot can help visualize the relationship between two continuous variables.

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# KDE for bivariate data
sns.kdeplot(data=data, x='sepal_length', y='sepal_width', cmap='Blues')
plt.title('2D KDE Plot for Sepal Length and Sepal Width')
plt.show()

This allows you to explore how two variables are related in terms of density.

Interpreting KDE Plots

When analyzing the KDE plot, keep an eye out for the following features:

• Peaks: A peak in the plot represents regions where data points are concentrated. Multiple peaks suggest a multi-modal distribution.

• Skewness: If the distribution is not symmetric, the plot will show skewness (left or right).

• Outliers: Outliers may show up as areas with sparse data, far away from the main concentration of points.

• Spread: The width of the KDE curve indicates the spread of the data. A wider curve suggests more variability.

When to Use KDE Plots in EDA

• Understanding Distribution: KDE plots are ideal for understanding the underlying distribution of continuous data.

• Visualizing Skewness: They are particularly useful for identifying skewed data, where histograms might not provide a clear picture.

• Comparing Distributions: KDE plots excel at comparing the distribution of different groups or categories.

• Detecting Multi-modality: If your data is multi-modal (i.e., it has multiple peaks), KDE plots can easily reveal this.

Best Practices for KDE Plots

• Choosing the Right Bandwidth: The bandwidth parameter can significantly affect the appearance of the KDE plot. Make sure to experiment with different values to find the most appropriate one for your data.

• Overlaying KDEs: When comparing different distributions, overlaying KDE plots can be more informative than plotting separate histograms.

• Handling Large Datasets: KDE plots can become computationally expensive for very large datasets. You may need to sample or downsample the data before plotting.

• Plot Customization: Customize your plot with appropriate labels, legends, and color schemes to enhance readability and convey the right insights.

Conclusion

KDE plots are a powerful and flexible tool for understanding the distribution of continuous data in EDA. They offer several advantages over histograms, such as smoother curves and the ability to reveal multi-modal distributions, skewness, and other underlying patterns. By understanding how to create and interpret KDE plots, you can gain deeper insights into your data and make more informed decisions about further analysis or modeling.