Core Concepts

Principal Component Analysis (PCA) is one of the most important dimensionality reduction algorithms in machine learning.

Statistics of Datasets

• Compute basic statistics of data sets
• Interpret the effects of linear transformations on means and (co)variances
• Compute means/variances of linearly transformed data sets
• Write code that represents images as vectors
• Write code that computes basic statistics of datasets

Inner Products

• Explain inner products
• Compute angles and distances using inner products
• Write code that computes distances and angles between images
• Demonstrate an understanding of properties of inner products
• Discover that orthogonality depends on the inner product

Orthogonal Projections

• Compute orthogonal projections using different inner products
• Relate projections to the reconstruction error and compute it
• Write code that projects image data onto a 2-dimensional subspace

Principal Component Analysis

• Summarize PCA
• Write code that implements PCA
• Assess the properties of PCA when applying to high-dimensional data