How To Normalise The Histogram Height In Matplotlib

Understanding Histogram Normalization

Histogram normalization is a technique used to adjust the frequency distribution of a dataset, resulting in a clearer representation of data features. The primary purpose of normalization is to scale the heights of the histogram bars such that the overall distribution can be interpreted more consistently across various datasets. This process is particularly useful in bioinformatics, where the distribution of values can vary widely due to biological variability.

Setting Up Your Environment

To begin visualizing and normalizing histograms in Python, the essential library to use is Matplotlib. Additionally, NumPy is often utilized for generating sample data and performing numerical operations. Make sure to install these libraries if they are not already installed:

pip install matplotlib numpy

Creating a Basic Histogram

Before delving into normalization, it is important to understand how to create a basic histogram in Matplotlib. The following code demonstrates how to generate and plot a histogram using randomly generated data:

import matplotlib.pyplot as plt
import numpy as np

# Generating random data
data = np.random.randn(1000)

# Creating the histogram
plt.hist(data, bins=30)
plt.title('Basic Histogram')
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.show()

Normalizing Histogram Heights

To normalize the heights of the histogram, utilize the density parameter available in the plt.hist() function. When this parameter is set to True, it adjusts the area of the histogram to sum to one, allowing for the probability density of the data to be represented rather than absolute frequency.

Here is how to implement this:

# Creating a normalized histogram
plt.hist(data, bins=30, density=True)
plt.title('Normalized Histogram')
plt.xlabel('Value')
plt.ylabel('Probability Density')
plt.show()

Understanding the Output

After running the above code snippets, the normalized histogram will showcase a probability density function (PDF) instead of raw frequency counts. This allows for better comparison between distributions of different datasets, especially when the total number of observations varies.

The area under the histogram (sum of the heights of the bars multiplied by the bin widths) equals one, making it a useful representation when comparing how different datasets behave in relation to one another.

Adding Customization

Customizing your histogram enhances clarity and visual appeal. You may adjust the number of bins, color, transparency, and edge color of the bars. The example below illustrates how to apply these customizations:

plt.hist(data, bins=30, density=True, alpha=0.7, color='blue', edgecolor='black')
plt.title('Customized Normalized Histogram')
plt.xlabel('Value')
plt.ylabel('Probability Density')
plt.grid(axis='y', alpha=0.75)
plt.show()

Frequently Asked Questions

1. Why normalize a histogram?
Normalizing a histogram is valuable because it allows for the comparison of datasets with different absolute frequencies. It enables users to understand the relative distribution of probabilities, making it easier to interpret variations across different datasets or experimental conditions.

2. What does the density parameter control?
The density parameter in Matplotlib’s histogram function controls whether the histogram is plotted with counts or as a probability density function. If set to True, the total area of the histogram will equal one, transforming raw counts into proportions.

3. Can I normalize histograms of multi-dimensional data?
Normalizing histograms for multi-dimensional data is more complex but feasible. When dealing with multi-dimensional distributions, consider techniques such as multidimensional histograms or kernel density estimation, which convey a richer story about the data dimensionality.