TramoTDA

TramoTDA is a Python package designed for trajectory analysis using Topological Data Analysis (TDA). This package includes functionalities for generating, visualizing, and classifying trajectory data, as well as creating persistence diagrams, lifetime diagrams, and persistence images.

Project Structure

TramoTDA/
├── repo/
│   ├── src/
│   │   ├── __init__.py
│   │   ├── analysis.py
│   │   ├── data.py
│   │   ├── plotting.py
│   │   └── utils.py
│   │   └── main.py
│   ├── test/
│   │   ├── test.py
│   │   ├── Figures
├── pyproject.toml
└── README.md  
├── LICENSE

File Descriptions

• LICENSE: Contains the legal terms under which the project is licensed, outlining permissions and restrictions for use and distribution.

• repo/: Directory containing all the source code and relevant files for the project.

  • src/: Main source code directory.

    • tramoTDA/: Core functionality package.

      • __init__.py: Marks the directory as a Python package.

      • analysis.py: Implements data analysis methods.

      • data.py: Loads and processes data.

      • plotting.py: Contains functions for visualizations.

      • utils.py: Utility functions for various tasks.

    • main.py: Entry point for executing the project.

• pyproject.toml: Configuration file for project metadata, dependencies, and build system requirements.

• README.md: Overview and documentation for the project, including installation and usage instructions.

Installation

Prerequisites

Ensure you have Python installed. It's recommended to use a virtual environment to manage dependencies.

Clone the Repository

git clone https://github.com/MiriamEsteve/tramoTDA.git
cd tramoTDA

Install dependencies

Install the required dependencies using pip.

pip install numpy matplotlib scipy scikit-learn persim ripser gudhi giotto-tda POT

Project Setup

Ensure your directory structure looks like the above structure.

Usage

To run the entire analysis workflow, navigate to the project directory and execute:

python test.py

This will execute each step of the analysis independently and save the corresponding images in the project directory.

This repository contains the supplementary material for the TramoTDA project. The document provides detailed descriptions, mathematical formulations, and additional data supporting the main findings of the project.

Functions

Step 1: Plot Trajectory Data

    
    # Step 1: Plot Trajectory Data
    data_gen = SimulatedTrajectoryData()
    brownian_data = data_gen.brownian_motion()
    levy_data = data_gen.levy_flight()
    spiral_data = data_gen.spiral_trajectory()
    circular_data = data_gen.circular_trajectory()

    # Plotting example trajectories
    plot_trajectories(brownian_data, 'Trajectory_Brownian_Motion', '1_Load_Trajectory_Brownian_Motion.png')
    plot_trajectories(levy_data, 'Trajectory_Levy_Flight', '1_Load_Trajectory_Levy_Flight.png')
    plot_trajectories(spiral_data, 'Trajectory_Spiral', '1_Load_Trajectory_Spiral.png')
    plot_trajectories(circular_data, 'Trajectory_Circular', '1_Load_Trajectory_Circular.png')
    ```

#### Step 2: Generate Persistence Diagrams
```python
# Initialize the TrajectoryAnalysis class
analysis = TrajectoryAnalysis()
    
diagrams = generate_persistence_diagrams(analysis.datas)
plot_persistence_diagrams(diagrams, '2_Persistence_Diagrams.png')

Step 3: Calculate and Plot Lifetime Diagrams

lifetimes = calculate_lifetime_diagrams(diagrams)
plot_lifetime_diagrams(lifetimes, '3_Lifetime_Diagram.png')

Step 4: Generate Persistence Images

rips_instance = ripser.Rips(maxdim=1, coeff=2)
diagrams_h1 = [rips_instance.fit_transform(data)[1] for data in analysis.datas]
plot_persistence_images(diagrams_h1, '4_Persistence_Images.png')

Step 5: Compute and Plot Barycenter

compute_gudhi_barycenter(diagrams_h1, '5_Calculate_Barycenter.png')

Step 6: Perform Classification with Different Models

classifiers = {
    'Logistic Regression': LogisticRegression(max_iter=1000),
    'Support Vector Machine': SVC(),
    'Random Forest': RandomForestClassifier(),
    'Neural Network': MLPClassifier(max_iter=2000)  # Increased max_iter to 2000
}

for name, clf in classifiers.items():
    X, y, report = perform_classification(clf)
    plot_classification(X, y, f'6_Classification_{name.replace(" ", "_")}.png', name)
    plot_evaluation_and_refinement(report, f'7_Evaluation_and_Refinement_{name.replace(" ", "_")}.png', name)

Step 7: Create Flowchart

create_flowchart()

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

• The TDA tutorial for inspiration on using Gudhi for barycenter calculations.
• The Scikit-learn library for providing powerful machine learning tools.
• A. Falco and M. Esteve thank the grant TED2021-129347B-C22 funded by Ministerio de Ciencia e Innovación/ Agencia Estatal de Investigación