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PCA from First Principles

this year hard (>1 hr) | linear-algebra PCA dim-reduction eigenvalues eigenvectors

Principal Component Analysis (PCA) is a fundamental dimensionality reduction technique. It works by transforming the data into a new coordinate system such that the greatest variance by any...
SVD for Image Compression

this year hard (>1 hr) | compression linear-algebra dim-reduction SVD image-processing

Singular Value Decomposition (SVD) is a powerful matrix factorization technique with numerous applications, including dimensionality reduction, noise reduction, and data compression. Any real $m...