Principal Component Analysis (PCA) for Feature Reduction and Model Improvement

Introduction

In this data analysis project, I will explore the application of Principal Component Analysis (PCA) to reduce the dimensionality of a dataset and enhance the performance of a machine learning model. The dataset used in this analysis pertains to telescope data. It was generated by a Monte Carlo program, Corsika, described in D. Heck et al., CORSIKA, A Monte Carlo code to simulate extensive air showers, Forschungszentrum Karlsruhe FZKA 6019 (1998).

The primary goals of this project are as follows:

1. Data Loading and Preprocessing: We will initiate the project by loading the telescope dataset and ensuring data cleanliness by eliminating any null or NaN values.

2. Exploratory Data Analysis (EDA): An initial phase of data exploration will involve displaying the first few rows of the dataset and generating a correlation matrix heatmap to visualize feature correlations.

3. PCA using NumPy: We will perform PCA using NumPy to gain insights into the dataset's variances and principal components. This will encompass the computation of eigenvalues, eigenvectors, and the visualization of explained variance ratios through scree plots.

4. PCA using scikit-learn: The scikit-learn PCA module will be leveraged to carry out PCA on the dataset. Steps will include data standardization, determination of principal components, and extraction of explained variances.

5. Using PCA Features in a Machine Learning Model: The dataset will be transformed into a reduced feature space incorporating two principal components (PC1 and PC2) utilizing scikit-learn's PCA functionality. The distribution of data points based on these components will be visualized, and class labels will be converted for machine learning.

6. Model Comparison: A Linear Support Vector Classifier (LinearSVC) will be trained using both the two PCA features and two original features selected from the dataset. The accuracy of the models will be compared to assess the impact of PCA on model performance.

7. Summary of Results: The results will be succinctly summarized, with a focus on highlighting the improvement in accuracy achieved by employing PCA features in comparison to original features.

This project aims to underscore the efficacy of PCA in dimensionality reduction and exemplify how it can bolster the accuracy of a machine learning model. By juxtaposing the performance of models with PCA features against those with original features, we will elucidate the information retained by PCA components.

Let's proceed with the code to delve into the details of these methods.