📊 EM Algorithm: Gaussian Mixture Modeling for Height Data

This project implements the Expectation-Maximization (EM) algorithm to estimate parameters of a Gaussian Mixture Model (GMM) applied to height data. The goal is to model the height distribution as a mixture of two normal distributions, typically representing male and female groups.

📁 Project Structure

EMAlgorithm/
├── Data_handler.py             # Main script to run the EM algorithm and plot results
├── Em_engine.py             # Main script to run the EM algorithm and plot results
├── EmAlgorithm.py             # Main script to run the EM algorithm and plot results
├── height.xlsx                # Input dataset (height values)
└── README.md                  # Project documentation

📦 Dependencies

Make sure you have the following Python libraries installed:

pip install numpy pandas matplotlib openpyxl

openpyxl is required for reading .xlsx Excel files.

🚀 How to Run

1. Place your height data in the height.xlsx file.
2. Execute the script:

python EmAlgorithm.py

This will:

• Load the data from Excel,
• Run the EM algorithm to estimate GMM parameters,
• Plot the overall mixture and individual distributions,
• Print the mean, standard deviation, and weight for each Gaussian component.

📈 Output

The script produces two plots:

• Mixture Gaussian Distribution – Shows the combined GMM and individual distributions.
• Separate Components – Displays each Gaussian component with labels and statistics.

It also prints:

Male mean height: 174.22, standard deviation: 4.51, proportion: 0.88
Female mean height: 162.40, standard deviation: 3.89, proportion: 0.12

📊 Dataset

• File: height.xlsx
• Data Range: rows 3 to 95, column 2 (zero-indexed)
• Assumption: the dataset is a mixture of two Gaussian distributions.

🧠 EM Algorithm Overview

The Expectation-Maximization algorithm iteratively estimates the parameters of a mixture model:

1. Initialization: Start with initial guesses for means, variances, and mixing weights.
2. E-Step: Estimate the probability that each data point belongs to each distribution.
3. M-Step: Update the parameters to maximize the expected log-likelihood.
4. Repeat until convergence.

💡 Use Cases

• Unsupervised clustering with continuous data
• Modeling population subgroups in statistics
• Educational demonstration of the EM algorithm

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Feel free to open issues or contribute if you'd like to improve the code or add more features!