Multivariate Normal Distribution Normalization | Python Matplotlib

Introduction

This lab explores various normalizations on a multivariate normal distribution using Python Matplotlib. In this lab, you will learn about linear normalization, power law normalization, and how to use Matplotlib to visualize the multivariate normal distribution.

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Skills Graph

%%%%{init: {'theme':'neutral'}}%%%% flowchart RL matplotlib(("`Matplotlib`")) -.-> matplotlib/BasicConceptsGroup(["`Basic Concepts`"]) python(("`Python`")) -.-> python/ControlFlowGroup(["`Control Flow`"]) python(("`Python`")) -.-> python/DataStructuresGroup(["`Data Structures`"]) python(("`Python`")) -.-> python/ModulesandPackagesGroup(["`Modules and Packages`"]) python(("`Python`")) -.-> python/PythonStandardLibraryGroup(["`Python Standard Library`"]) python(("`Python`")) -.-> python/DataScienceandMachineLearningGroup(["`Data Science and Machine Learning`"]) python(("`Python`")) -.-> python/FunctionsGroup(["`Functions`"]) matplotlib/BasicConceptsGroup -.-> matplotlib/importing_matplotlib("`Importing Matplotlib`") matplotlib/BasicConceptsGroup -.-> matplotlib/figures_axes("`Understanding Figures and Axes`") python/ControlFlowGroup -.-> python/for_loops("`For Loops`") python/ControlFlowGroup -.-> python/list_comprehensions("`List Comprehensions`") python/DataStructuresGroup -.-> python/lists("`Lists`") python/DataStructuresGroup -.-> python/tuples("`Tuples`") python/ModulesandPackagesGroup -.-> python/importing_modules("`Importing Modules`") python/ModulesandPackagesGroup -.-> python/using_packages("`Using Packages`") python/ModulesandPackagesGroup -.-> python/standard_libraries("`Common Standard Libraries`") python/PythonStandardLibraryGroup -.-> python/math_random("`Math and Random`") python/DataScienceandMachineLearningGroup -.-> python/numerical_computing("`Numerical Computing`") python/DataScienceandMachineLearningGroup -.-> python/data_visualization("`Data Visualization`") python/FunctionsGroup -.-> python/build_in_functions("`Build-in Functions`") subgraph Lab Skills matplotlib/importing_matplotlib -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} matplotlib/figures_axes -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/for_loops -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/list_comprehensions -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/lists -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/tuples -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/importing_modules -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/using_packages -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/standard_libraries -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/math_random -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/numerical_computing -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/data_visualization -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} python/build_in_functions -.-> lab-48881{{"`Multivariate Normal Distribution Visualizations`"}} end

Import Libraries

In this step, you need to import the necessary libraries which are Matplotlib, NumPy, and Multivariate_normal from NumPy.random.

import matplotlib.pyplot as plt
import numpy as np
from numpy.random import multivariate_normal

Set Random State

In this step, you need to set the random state for reproducibility.

np.random.seed(19680801)

Create Data

In this step, you need to create data using multivariate_normal(). This function generates a random sample from a multivariate normal distribution.

data = np.vstack([
    multivariate_normal([10, 10], [[3, 2], [2, 3]], size=100000),
    multivariate_normal([30, 20], [[3, 1], [1, 3]], size=1000)
])

Create Histogram

In this step, you need to create a histogram using hist2d(). The hist2d() function is used to create a two-dimensional histogram.

plt.hist2d(data[:, 0], data[:, 1], bins=100)

Create Power Law Normalization

In this step, you need to create power law normalization using PowerNorm().

plt.hist2d(data[:, 0], data[:, 1], bins=100, norm=mcolors.PowerNorm(gamma))

Create Subplots

In this step, you need to create subplots using subplots().

fig, axs = plt.subplots(nrows=2, ncols=2)

Create Linear Normalization

In this step, you need to create linear normalization.

axs[0, 0].hist2d(data[:, 0], data[:, 1], bins=100)

Create Power Law Normalization

In this step, you need to create power law normalization with different gamma values.

for ax, gamma in zip(axs.flat[1:], gammas):
    ax.hist2d(data[:, 0], data[:, 1], bins=100, norm=mcolors.PowerNorm(gamma))

Set Title

In this step, you need to set the title of each plot.

axs[0, 0].set_title('Linear normalization')

for ax, gamma in zip(axs.flat[1:], gammas):
    ax.set_title(r'Power law $(\gamma=%1.1f)$' % gamma)

Tight Layout

In this step, you need to adjust the spacing between subplots.

fig.tight_layout()

Show Plot

In this step, you need to display the plot using show().

plt.show()

Summary

This lab explored various normalizations on a multivariate normal distribution using Python Matplotlib. You learned about linear normalization, power law normalization, and how to use Matplotlib to visualize the multivariate normal distribution.

Multivariate Normal Distribution Visualizations

Introduction

VM Tips

Skills Graph

Import Libraries

Set Random State

Create Data

Create Histogram

Create Power Law Normalization

Create Subplots

Create Linear Normalization

Create Power Law Normalization

Set Title

Tight Layout

Show Plot

Summary

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