search
HomeBackend DevelopmentPython TutorialDetailed explanation of Gaussian Mixture Model (GMM) algorithm in Python

Gaussian Mixture Model (GMM) is a commonly used clustering algorithm. It models a group of data by dividing it into multiple normal distributions, each distribution representing a subset of the data. In Python, the GMM algorithm can be easily implemented using the scikit-learn library.

1. Principle of GMM algorithm

The basic idea of ​​GMM algorithm is: assuming that each data point in the data set comes from one of multiple Gaussian distributions. That is, each data point in the data set can be represented as a linear combination of many Gaussian distributions. The Gaussian distribution here refers to the normal distribution.

Given a data set, we want to find a set of Gaussian distributions whose combination forms the original data. Specifically, we need to find K Gaussian distributions (where K is a preset fixed value), as well as the mean and variance of each Gaussian distribution.

So, how to determine the number of Gaussian distributions? It is usually determined using the Bayesian Information Criterion (BIC) or the Akaik Information Criterion (AIC). Both methods estimate the predictive power of a selected model for unknown data and give a model quality score. The lower the final quality score, the smaller the number of Gaussians.

2. Implementation of GMM algorithm

The implementation of GMM algorithm is mainly divided into two steps: parameter estimation and label clustering.

Parameter estimation

Parameter estimation is the first step in the training process, which is used to find the mean and variance of the Gaussian distribution.

Before parameter estimation, we need to choose an initial value. It is usually initialized using k-means clustering algorithm. In the k-means clustering algorithm, K center points are first selected. Each point is assigned to the nearest center point. Then, the position of each center point is recalculated and each point is redistributed. This process is repeated until the clusters no longer change. Finally, we use the center point of each cluster to initialize the mean of the Gaussian distribution.

Next, we use the expectation maximization (EM) algorithm to estimate the mean and variance of the Gaussian distribution. The EM algorithm is an optimization algorithm that, given a set of observation data, uses a probabilistic model to estimate the distribution to which these data belong.

The specific process is as follows:

  • Step E: Calculate the probability that each data point belongs to each Gaussian distribution.
  • M step: Calculate the mean and variance of each Gaussian distribution.

Repeat the above steps until convergence. In scikit-learn, parameter estimation can be achieved through the following code:

from sklearn.mixture import GaussianMixture

model = GaussianMixture(n_components=k)
model.fit(X)

Among them, k is the predetermined number of Gaussian distributions, and X is the data set.

Label clustering

After parameter estimation is completed, we can use the K-means algorithm to complete label clustering. Label clustering is the process of dividing the data in a dataset into different labels. Each label represents a cluster. In scikit-learn, label clustering can be achieved by the following code:

from sklearn.cluster import KMeans

kmeans = KMeans(n_clusters=k, random_state=0)
kmeans. fit(X)

Where, k is the predetermined number of clusters, and X is the data set.

3. GMM algorithm application

The GMM algorithm can be applied to a variety of data modeling problems. One common application scenario is to represent a set of multidimensional data (such as images, audio, or video) as a probability distribution. This process is called data dimensionality reduction.

Data dimensionality reduction is usually done to reduce the dimensions of the data set and capture important information in the original data. By representing multidimensional data as probability distributions, we can compress important information into a small number of probability distributions. This process is similar to PCA and LDA. However, unlike PCA and LDA, GMM can better capture the characteristics of multi-modal distributions.

In addition, the GMM algorithm is also widely used in image processing, pattern recognition, natural language processing and other fields. In image processing, GMM can be used for background modeling, image segmentation and texture description. In pattern recognition, GMM can be used for feature extraction and classification.

In short, the GMM algorithm is a powerful modeling technology that can be applied in a variety of fields to help us better understand data characteristics and patterns. The scikit-learn library in Python provides us with a simple and practical tool to easily implement the GMM algorithm.

The above is the detailed content of Detailed explanation of Gaussian Mixture Model (GMM) algorithm in Python. For more information, please follow other related articles on the PHP Chinese website!

Statement
The content of this article is voluntarily contributed by netizens, and the copyright belongs to the original author. This site does not assume corresponding legal responsibility. If you find any content suspected of plagiarism or infringement, please contact admin@php.cn
详细讲解Python之Seaborn(数据可视化)详细讲解Python之Seaborn(数据可视化)Apr 21, 2022 pm 06:08 PM

本篇文章给大家带来了关于Python的相关知识,其中主要介绍了关于Seaborn的相关问题,包括了数据可视化处理的散点图、折线图、条形图等等内容,下面一起来看一下,希望对大家有帮助。

详细了解Python进程池与进程锁详细了解Python进程池与进程锁May 10, 2022 pm 06:11 PM

本篇文章给大家带来了关于Python的相关知识,其中主要介绍了关于进程池与进程锁的相关问题,包括进程池的创建模块,进程池函数等等内容,下面一起来看一下,希望对大家有帮助。

Python自动化实践之筛选简历Python自动化实践之筛选简历Jun 07, 2022 pm 06:59 PM

本篇文章给大家带来了关于Python的相关知识,其中主要介绍了关于简历筛选的相关问题,包括了定义 ReadDoc 类用以读取 word 文件以及定义 search_word 函数用以筛选的相关内容,下面一起来看一下,希望对大家有帮助。

归纳总结Python标准库归纳总结Python标准库May 03, 2022 am 09:00 AM

本篇文章给大家带来了关于Python的相关知识,其中主要介绍了关于标准库总结的相关问题,下面一起来看一下,希望对大家有帮助。

Python数据类型详解之字符串、数字Python数据类型详解之字符串、数字Apr 27, 2022 pm 07:27 PM

本篇文章给大家带来了关于Python的相关知识,其中主要介绍了关于数据类型之字符串、数字的相关问题,下面一起来看一下,希望对大家有帮助。

分享10款高效的VSCode插件,总有一款能够惊艳到你!!分享10款高效的VSCode插件,总有一款能够惊艳到你!!Mar 09, 2021 am 10:15 AM

VS Code的确是一款非常热门、有强大用户基础的一款开发工具。本文给大家介绍一下10款高效、好用的插件,能够让原本单薄的VS Code如虎添翼,开发效率顿时提升到一个新的阶段。

详细介绍python的numpy模块详细介绍python的numpy模块May 19, 2022 am 11:43 AM

本篇文章给大家带来了关于Python的相关知识,其中主要介绍了关于numpy模块的相关问题,Numpy是Numerical Python extensions的缩写,字面意思是Python数值计算扩展,下面一起来看一下,希望对大家有帮助。

python中文是什么意思python中文是什么意思Jun 24, 2019 pm 02:22 PM

pythn的中文意思是巨蟒、蟒蛇。1989年圣诞节期间,Guido van Rossum在家闲的没事干,为了跟朋友庆祝圣诞节,决定发明一种全新的脚本语言。他很喜欢一个肥皂剧叫Monty Python,所以便把这门语言叫做python。

See all articles

Hot AI Tools

Undresser.AI Undress

Undresser.AI Undress

AI-powered app for creating realistic nude photos

AI Clothes Remover

AI Clothes Remover

Online AI tool for removing clothes from photos.

Undress AI Tool

Undress AI Tool

Undress images for free

Clothoff.io

Clothoff.io

AI clothes remover

AI Hentai Generator

AI Hentai Generator

Generate AI Hentai for free.

Hot Article

Hot Tools

Zend Studio 13.0.1

Zend Studio 13.0.1

Powerful PHP integrated development environment

mPDF

mPDF

mPDF is a PHP library that can generate PDF files from UTF-8 encoded HTML. The original author, Ian Back, wrote mPDF to output PDF files "on the fly" from his website and handle different languages. It is slower than original scripts like HTML2FPDF and produces larger files when using Unicode fonts, but supports CSS styles etc. and has a lot of enhancements. Supports almost all languages, including RTL (Arabic and Hebrew) and CJK (Chinese, Japanese and Korean). Supports nested block-level elements (such as P, DIV),

Notepad++7.3.1

Notepad++7.3.1

Easy-to-use and free code editor

ZendStudio 13.5.1 Mac

ZendStudio 13.5.1 Mac

Powerful PHP integrated development environment

VSCode Windows 64-bit Download

VSCode Windows 64-bit Download

A free and powerful IDE editor launched by Microsoft