Matrix Completion I | The Optimization Formula
Given a partially observed matrix $ A \in \mathbb{R}^{m \times n} $, where only entries $ A_{ij} $ for $ (i, j) \in \Omega \subseteq [m] \times [n] $ are known, the goal is to recover the missing values and construct a full matrix $ \hat{A} \in \mathbb{R}^{m \times n} $. For example, think of known entries of $A_{ij}$ as observation of $m$ consumers’ past ratings on $n$ products. The goal is to make predictions....