Introduction

This article explores violin plots, a powerful visualization tool that combines box plots with density plots. It explains how these plots can reveal patterns in data, making them useful for data scientists and machine learning practitioners. The guide provides insights and practical techniques for using violin plots, enabling informed decision-making and confident communication of complex data stories. It also includes practical Python examples and comparisons.

Learning objectives

• Understand the fundamental components and features of violin plots.
• Learn the differences between violin plots, box plots, and density plots.
• Explore the role of violin plots in machine learning and data mining applications.
• Gain hands-on experience with Python code examples for creating and comparing these graphs.
• Recognize the importance of violin plots in EDA and model evaluation.

This article was published as part of the Data Science Blogathon.

Understanding Violin Plots

As mentioned above, violin plots are a cool way to display data. They combine two other types of plots: box plots and density plots. The key concept behind violin plots is kernel density estimation (KDE), a nonparametric way to estimate the probability density function (PDF) of a random variable. In violin plots, KDE smoothes the data points to provide a continuous representation of the data distribution.

KDE computations include the following core concepts:

The kernel function

A kernel function smoothes the data points by assigning weights to the data points based on their distance from a target point. The further away the point, the lower the weights. Typically, Gaussian kernels are used; however, other kernels, such as linear and Epanechnikov, can be used if necessary.

Bandwidth

Bandwidth determines the width of the kernel function. Bandwidth is responsible for controlling the smoothness of the KDE. Larger bandwidth makes the data too smooth, leading to underfitting, while small bandwidth makes the data overfit with more peaks and valleys.

Estimation

To calculate the KDE, place a kernel on each data point and sum them to obtain the overall density estimate.

Mathematically speaking,

In violin plots, the KDE is mirrored and placed on either side of the box plot, creating a violin-like shape. The three main components of violin plots are:

• Central boxplot: Displays the median value and interquartile range (IQR) of the dataset.
• Density plot: Displays the probability density of the data, with regions of high data concentration highlighted by peaks.
• Axles: The x-axis and y-axis represent the category/group and data distribution, respectively.

By placing these components together, you can gain insight into the underlying shape of the data distribution, including multimodality and outliers. Violin Plots are very useful, especially if you have complex data distributions, whether this is due to many groups or categories. They help identify patterns, anomalies, and potential areas of interest within the data. However, due to their complexity, they may be less intuitive for those unfamiliar with data visualization.

Applications of violin plots in data analysis and machine learning

Violin plots are applicable in many cases. Below are the most important ones:

• Functional analysis: Violin plots help to understand the feature distribution of the dataset. They also help to categorize outliers, if any, and compare distributions across categories.
• Model evaluation: These graphs are very valuable for comparing predicted and actual values, allowing for the identification of biases and variance in model predictions.
• Hyperparameter tuning: Selecting the one with optimal hyperparameter settings when working with multiple machine learning models is a challenge. Violin plots help compare model performance with different hyperparameter settings.

Comparison of violin plot, box plot and density plot

Seaborn is a standard Python library with a built-in function for creating violin plots. It is easy to use and offers the ability to customize the aesthetics, colors, and styles of the plot. To understand the strengths of violin plots, we compare them with box and density plots on the same dataset.

Step 1: Install the libraries

First, we need to install the necessary Python libraries to create these plots. By setting up libraries like Seaborn and Matplotlib, you will have the tools needed to generate and customize your visualizations.

The command for this is:

!pip install seaborn matplotlib pandas numpy
print('Importing Libraries...',end='')
import seaborn as sns
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
print('Done')

Step 2: Generate a synthetic dataset

# Create a sample dataset
np.random.seed(11)
data = pd.DataFrame({
    'Category': np.random.choice(('A', 'B', 'C'), size=100),
    'Value': np.random.randn(100)
})

We generate a synthetic dataset with 100 samples to compare the plots. The code generates a data frame named data using the Pandas Python library. The data frame has two columns namely Category and Value. Category contains random choices from ‘A’, ‘B’ and ‘C’; while Value contains random numbers drawn from a standard normal distribution (mean = 0, standard deviation = 1). The above code uses a seed for reproducibility. This means that the code will generate the same random numbers in each successive run.

Step 3: Generate a data summary

Before diving into the visualizations, let’s summarize the dataset. This step provides an overview of the data, including basic statistics and distributions, and sets the tone for effective visualization.

# Display the first few rows of the dataset
print("First 5 rows of the dataset:")
print(data.head())

# Get a summary of the dataset
print("\nDataset Summary:")
print(data.describe(include="all"))

# Display the count of each category
print("\nCount of each category in 'Category' column:")
print(data('Category').value_counts())

# Check for missing values in the dataset
print("\nMissing values in the dataset:")
print(data.isnull().sum())

It is always a good practice to view the contents of the dataset. The above code shows the first five rows of the dataset to preview the data. Then the code shows the basic data statistics such as count, mean, standard deviation, minimum and maximum values, and quartiles. We also check for missing values ​​in the dataset, if any.

Step 4: Generate plots using Seaborn

This code snippet generates a visualization with violin, box, and density plots for the synthetic dataset we generated. The plots show the distribution of values ​​across different categories in a dataset: Category A, B, and C. In violin and box plots, the category and its values ​​are
plotted on the x-axis and y-axis respectively. In the case of the density plot, the value is plotted on the x-axis and the corresponding density on the y-axis. These plots are available in the figure below, which provides a comprehensive overview of the data distribution, allowing for easy comparison of the three types of plots.

# Create plots
fig, axes = plt.subplots(1, 3, figsize=(18, 6))

# Violin plot
sns.violinplot(x='Category', y='Value', data=data, ax=axes(0))
axes(0).set_title('Violin Plot')

# Box plot
sns.boxplot(x='Category', y='Value', data=data, ax=axes(1))
axes(1).set_title('Box Plot')

# Density plot
for category in data('Category').unique():
    sns.kdeplot(data(data('Category') == category)('Value'), label=category, ax=axes(2))
axes(2).set_title('Density Plot')
axes(2).legend(title="Category")

plt.tight_layout()
plt.show()

Output:

Conclusion

Machine learning is all about data visualization and analysis; that is, at its core, machine learning is a data processing and visualization task. This is where violin plots come in handy, as they provide a better understanding of how the features are distributed, which improves feature engineering and selection. These plots combine the best of both, box and density plots with exceptional simplicity, and provide incredible insights into the patterns, shapes, or outliers of a dataset. These plots are so versatile that they can be used to analyze different data types, such as numerical, categorical, or time series data. In short, by revealing hidden structures and anomalies, violin plots enable data scientists to communicate complex information, make decisions, and generate hypotheses effectively.

Key Points

• Violin plots combine the detail of density plots with the summary statistics of box plots, providing a richer picture of the data distribution.
• Violin charts work well with a variety of data types, including numeric, categorical, and time series data.
• They help in understanding and analyzing feature distributions, evaluating model performance, and optimizing various hyperparameters.
• Standard Python libraries such as Seaborn support violin plots.
• They effectively convey complex information about data distribution, making it easier for data scientists to share insights.

Frequently Asked Questions

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