Statistical Computing in Clojure: Functional Approaches to Unsupervised Learning

Author: Jaryt Salvo
Course: CS 7300 Unsupervised Learning
Term: Fall 2024

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Project Documentation and Results

Project Overview

This work implements fundamental statistical algorithms using functional programming paradigms. The implementation leverages Clojure's immutable data structures and pure functions to develop a mathematically rigorous framework for numerical computing. Our approach emphasizes computational efficiency while maintaining mathematical precision through careful algorithm selection and implementation.

Core Implementation

The project consists of three primary computational modules:

1. Statistical Foundations

• Implementation of numerically stable algorithms for variance and covariance computation
• Robust central tendency measures optimized for large-scale data processing
• Matrix operations designed for efficient statistical analysis

2. Eigenvalue Decomposition

• Power iteration methods for computing dominant eigenvalues
• Complete eigendecomposition through QR algorithm implementation
• Specialized inverse iteration techniques for eigenvector computation

3. Principal Component Analysis

• Covariance-based PCA implementation with mathematical rigor
• Optimized matrix transformations for dimensionality reduction
• Comparative analysis against established implementations

Technical Implementation

The codebase utilizes modern Clojure libraries and practices:

• Neanderthal for high-performance numerical computations
• Systematic validation through property-based testing
• Integrated documentation with mathematical derivations

Development Environment

The project uses containerized development environments to ensure computational reproducibility across systems. This approach eliminates environment-specific issues and maintains consistent behavior across different operating systems.

System Requirements

• Docker Desktop
• Visual Studio Code with Dev Containers extension

Environment Setup

1. Install the required software:

   • Docker Desktop
   • Visual Studio Code
   • Dev Containers Extension

2. Clone and initialize the repository:

   git clone https://github.com/adabwana/f24-cs7300-final-project.git
   cd f24-cs7300-final-project
   code .
   

3. Select development environment:

   • Primary Container: Clojure environment for core implementation
   • Validation Container: Python environment for comparative analysis

The container configuration automatically:

• Configures language-specific toolchains
• Installs project dependencies
• Establishes consistent development environments
• Isolates project-specific configurations

This containerized approach ensures that all computational results are reproducible and that the development environment remains consistent across different systems and users.