Factorizations for data analysis

We can find structure in data by factoring it into building blocks, which should be interpretable for the context at hand. A classical example is principal component analysis (PCA), which uses the eigendecomposition of the covariance matrix to find axes of variation in a dataset. Starting from PCA, I will discuss matrix and tensor factorizations for data analysis, and the linear and multilinear algebra that underpins their theoretical properties. We will see examples from causal inference, independent component analysis, and dimensionality reduction.