Explore dimensionality reduction techniques for matrix- and tensor-coded data in this comprehensive lecture by Alex Williams from Stanford University. Delve into the theoretical foundations and practical applications of matrix and tensor factorizations, including PCA, non-negative matrix factorization (NMF), and independent components analysis (ICA). Focus on canonical polyadic (CP) tensor decomposition as an extension of PCA for higher-order data arrays. Learn about recent developments in the field, hands-on exercises, and practical advice for implementing these models. Cover topics such as the rotation problem, sparse PCA, Bayes rule, logistic PCA, loss functions, and cross-validation. Access additional resources, including slides, references, and exercises, to further enhance your understanding of these powerful data compression and analysis techniques.