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@jemoka / Jemoka Knowledge Base / raw/concept/kbhalternating_least_squares.md
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--- title: "Alternating Least Squares" source: https://www.jemoka.com/posts/kbhalternating_least_squares/ --- Alternating Least Squares is a method to Factoring a matrix into two components: \begin{equation} \mathcal{M}( R) \approx \mathcal{M}(U) \cdot \mathcal{M}(P) \end{equation} where, we want to come up matricies \(U\) and \(P\) with a certain side length \(k\) that we exdogenously come up with To perform Alternating Least Squares, we fix the values of either \(U\) or \(P\), then perform the least-squares optimization on (This is proven best-fit for “non-pathological matricies”)