Comparative Analysis of Ensemble and Traditional Classification Methods on the MNIST Dataset

Project Description

This project compares the performance of various classification algorithms on the MNIST dataset, a benchmark for machine learning. It focuses on four methods: AdaBoost, Classification Trees, Quadratic Discriminant Analysis (QDA), and Bagging. Each method is implemented from scratch, using only NumPy and Matplotlib for numerical computations and data visualization. The study evaluates the accuracy, computational efficiency, and robustness of these models, providing insights into their strengths and weaknesses for image recognition tasks.

Table of Contents

• Introduction
• Installation
• Dataset
• Methodology
  • AdaBoost
  • Classification Trees
  • Quadratic Discriminant Analysis (QDA)
  • Bagging
• Results
• Conclusion
• Future Work
• References

Introduction

The MNIST dataset is a collection of 70,000 handwritten digits, widely used for training and testing image processing systems. In this project, we implement and compare four classification algorithms from scratch, highlighting their effectiveness and efficiency for digit recognition.

Installation

To run this project, you need to have Python installed along with the following libraries:

• NumPy
• Matplotlib

You can install the necessary libraries using pip:

pip install numpy matplotlib

Dataset

Download the MNIST dataset from the official MNIST database. Save the dataset files in the data directory of the project.

Methodology

AdaBoost

AdaBoost (Adaptive Boosting) is an ensemble learning method that combines multiple weak classifiers to create a strong classifier. It adjusts the weights of incorrectly classified instances, improving the overall accuracy.

Classification Trees

Classification Trees, or Decision Trees, use a tree-like model of decisions and their possible consequences. They are simple yet powerful tools for classification tasks.

Quadratic Discriminant Analysis (QDA)

QDA is a statistical classifier that assumes each class has a Gaussian distribution. It models the decision boundary as a quadratic function, making it suitable for complex datasets.

Bagging

Bagging (Bootstrap Aggregating) is an ensemble method that improves the stability and accuracy of machine learning algorithms. It reduces variance by averaging multiple models trained on different subsets of the data.

Results

The results of the classification algorithms will be evaluated based on:

• Accuracy
• Computational efficiency
• Robustness

Detailed results and comparisons will be provided in the report.

Conclusion

This project provides a comprehensive comparison of AdaBoost, Classification Trees, QDA, and Bagging for digit recognition using the MNIST dataset. The insights gained from this study will help in selecting appropriate models for similar image recognition tasks.

Future Work

Future work could involve:

• Implementing additional classification algorithms.
• Exploring the impact of different hyperparameters.
• Applying the methods to other datasets.
• Enhancing the implementations for better performance.

References

• MNIST Database
• Freund, Y., & Schapire, R. E. (1997). A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 55(1), 119-139.
• Breiman, L. (1996). Bagging predictors. Machine Learning, 24(2), 123-140.