PRINCIPAL_COMPONENT_ANALYSIS

Core Machine Learning Concepts in the Principal Component Analysis Practical

This document explains the primary machine learning concepts demonstrated in the Principal Component Analysis (PCA) practical notebook. The notebook applies PCA to the Olivetti faces dataset to perform dimensionality reduction and visualize the principal components (eigenfaces).

1. Data Loading and Initial Visualization

• Dataset Acquisition:
  • The Olivetti faces dataset is loaded using fetch_olivetti_faces from sklearn.datasets.
  • The data contains images (64x64 pixels) of faces which are flattened into feature vectors.
• Basic Visualization:
  • A grid of sample images is displayed to provide an overview of the dataset.

2. Dimensionality Reduction with PCA

• PCA Initialization:
  • The PCA model is initialized with n_components=150 and whiten=True to standardize the influence of components.
• Transformation:
  • The dataset is transformed into its principal components using the PCA model. This reduces dimensionality while retaining the variance in the data.

3. Explained Variance Analysis

• Variance Reporting:
  • The notebook prints the percentage of total variance explained by each of the first 12 principal components.
• Cumulative Variance Visualization:
  • A cumulative variance plot is generated to illustrate how the variance accumulates with the addition of more principal components.
  • Dashed lines mark the variance explained by the first 12 components.

4. Visualization of Principal Components (Eigenfaces)

• Eigenfaces Display:
  • The first 12 principal components (eigenfaces) are reshaped back into the original image dimensions.
  • These eigenfaces are visualized in a grid format to show the key patterns captured from the original dataset.

This practical notebook serves as a comprehensive example of applying PCA to reduce dimensionality, analyze the variance captured by principal components, and visualize the eigenfaces, thereby demonstrating how fundamental machine learning techniques can be used for feature extraction and data visualization.