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## Intro to Gaussian Mixture Model

In this fascinating tutorial, you will learn about a novel unsupervised learning model calls Gaussian Mixture Model (GMM). You will learn how to synthesis GMM from several normal density functions using spreadsheet. We will use well-known Expectation-Maximization (EM) algorithm to analyze the fitness of the Gaussian Mixture Model. We will start with the concepts to introduce you with the terminologies, and then we will proceed with numerical examples that you can use paper with a calculator. We will use merely Microsoft Excel spreadsheet without programming to give you better understanding on the full numerical computation. You will see the connection between EM algorithm and Gaussian Mixture Model and k-means clustering. By the end of this tutorial, you will also learn how to solve clustering problem, probability density estimation and maximum likelihood estimation numerically. All of those terminologies seems to be difficult jargons to be understood at first. Don't worry. Through step by step workshop style tutorial, you will learn deeper knowledge of Gaussian Mixture Model and Expectation-Maximization (EM) algorithm with comprehensive numerical example from start to a complete solutions. There is no need for a special software aside from Microsoft Excel spreadsheet. There is no need for macro programming because all of these steps are done in the spreadsheet.

This GMM/EM method has been widely used for data analysis in the field Data Mining, Machine learning, and Pattern recognition, Image Processing, Business Intelligence, Speech recognition, Medical Imaging and many other fields. You will see in this tutorial why this unsupervised learning technique is very powerful.

## Contents

Probability Distribution
Mixture of Distributions
Density Estimation
Gaussian Mixture Model
Maximum Likelihood
EM algorithm
Numerical Example of GMM/EM
Building Excel Worksheet for Gaussian Mixture Model
Connection GMM and K Means Clustering
Evaluating GMM/EM