CUR Decomp
From the book
Chapter 9: Matrix Decompositions and Beyond. In the chapter mind map this icon labels CUR Decomp: $A \approx CUR$. The discussion below is excerpted and lightly edited from § Theorem: CUR Decomposition in Mathematics for AI and Machine Learning.
For a matrix $A \in \mathbb{R}^{M \times N}$ with $\mathrm{rank}(A) = r$, there exist $r$ row indices $\mathcal{R} \subset \{0, 1, \ldots, M-1\}$ and $r$ column indices $\mathcal{C} \subset \{0, 1, \ldots, N-1\}$ such that $A(\mathcal{R}, \mathcal{C}) \in \mathbb{R}^{r \times r}$ is invertible and
with $C = A(:, \mathcal{C})$ the selected columns, $R = A(\mathcal{R}, :)$ the selected rows, and $U = A(\mathcal{R}, \mathcal{C})^{-1}$ the inverse of their intersection.
What this drawing shows
What you see. Mindmap icon: `A = C @ U @ R` (CUR / skeleton), coloured like the chapter figure.
In the mind map. Chapter 9 — CUR Decomp. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 9: Matrix Decompositions and Beyond — see the mind-map node CUR Decomp.
