Thinking in Low-Rank

This talk introduced the concept of low-rank approximation for tensors and matrices, which utilizes algebraic decompositions like Singular Value Decomposition (SVD) to represent high-dimensional data using a minimal set of essential components. The core method is a geometric approach to dimensionality reduction that identifies eigenvectors and eigenvalues to isolate principal directions of variance within a linear transformation. A visualization-driven intuition for coordinate scaling and space reshaping was also presented, providing information about how high-rank data can be compressed into lower-dimensional subspaces without significant information loss. Overall, low-rank approximations solve challenges in data redundancy and computational complexity, such as in text vectorization (e.g., RETVec) or image processing, more efficiently and robustly than standard full-rank representations. Notebook.