Recently, I read some papers about matrix completion with side information. I found that if I want to use this model, I have to get good estimators of the feature space. The following optimization problem pops up: $$ \hat{X},\hat{Y}=\arg\min\limits_{X\in \mathbb{R}^{n\times k},Y\in \mathbb{R}^{k\times n}}\|B-XAY\|_{F}^{2}+pen_1(X)+pen_2(Y), $$ a loss function with two penalty items.
I think this model has been well researched. If I want to get the properties of this model, what keywords can I enter in google scholar to get related papers?
This is a matrix factorization problem, you are factorizing a matrix $B\in \mathbb{R}^{n\times n}$ into the form $XAY$ with $X\in\mathbb{R}^{n\times k}$, $A\in\mathbb{R}^{k\times k}$ and $Y\in\mathbb{R}^{k\times n}$. The penalty functions represent some inductive biases you want to place on $X$ and $Y$, e.g., sparsity, low-rank, nonnegativity, etc.