CS660 - Project 2

Overview

This repository contains the codebase for Project 2 in CS660: Mathematical Foundations of Analytics (CRN# 71425), Fall 2024 at Pace University. The project involves implementing Python scripts to compute Eigenvalues, Eigenvectors, Principal Components, and Singular Values of a matrix, and comparing the execution time of our code with Python’s built-in libraries.

Course Information

• Course: CS660/71425 Mathematical Foundations of Analytics
• Instructor: Prof. Tassos Sarbanes
• Group-1: Will Torres, Mike Griffin, Watson Blair, Syed Abdul Mubashir
• Semester: Fall 2024
• Project #: 2
• Due Date: 04-Nov-2024

Project Requirements

1. Eigenvalues and Eigenvectors Computation:

   • Compute the eigenvalues and corresponding eigenvectors of a matrix.
   • Compare the runtime with Python’s built-in function numpy.linalg.eig.
   • Documentation

2. Principal Components Computation:

   • Calculate the principal components of a matrix.
   • Compare runtime with sklearn.decomposition.PCA.
   • Documentation

3. Singular Values Computation:

   • Perform Singular Value Decomposition (SVD) to find the singular values of a matrix.
   • Compare runtime with numpy.linalg.svd.
   • Documentation

Each task includes creating independent computation modules and analyzing runtime performance.

Approach

The core of our implementation consists of the following helper functions, designed to handle computations and execution timing:

• pca: Computes the principal components of a given matrix.
• eigen: Calculates eigenvalues and eigenvectors.
• svd: Performs Singular Value Decomposition.
• run_timer: Measures and records the execution time for each function.
• process_matrix: Organizes data preparation and initiates computations on matrices of various sizes.

These functions are combined within presentation.ipynb to execute each calculation and gather runtime data for comparison.

Efficiency Analysis

To analyze computation efficiency, we test each function with randomly generated matrices of different sizes:

# Define sample sizes for analysis
matrix_sizes = [10, 25, 50, 75, 100, 250, 400]
data_list = [np.random.rand(n, n) for n in matrix_sizes]
labels = [f'{n}x{n}' for n in matrix_sizes]

# Initialize BenchmarkUtility to iterate through matrices and benchmark
processor = BenchmarkUtility(labels=labels)
processor.batch_benchmark(data_list)

This setup allows us to evaluate how each implementation scales with matrix size and to benchmark our code against standard libraries.

How to Run

1. Open presentation.ipynb in Jupyter Notebook.
2. Run the notebook to execute computations, collect runtime data, and view analysis results.