PLS于RMLS

搜索中的PLS和RMLS matchPLS:partial least squaretwo space $X \in R^m$ and $Y \in R^n$training data ${(x_i, y_i, r_i)}{i=1}^N, r \in {+1,-1}$ or $r_i \in R $modeldot product as similarity:$f(x, y)=<L_X^Tx, L_Y^Ty>=x^TL_XL_Yy$$L_X, L_Y$ are two linear (and orthonormal) transformationsobjective function$$argmax{L_X, L_Y}\sum {r_i=+1} x_i^TL_XL_Y^Ty - \sum {r_i = -1} x_i^TL_XL_Y^Ty$$s.t. $L_X^TL_X=I{K*K}, L_Y^TL_Y=I{K*K}$RMLS:Regularized mapping to latent spacetwo space $X \in R^m$ and $Y \in R^n$training data ${(x_i, y_i, r_i)}{i=1}^N, r \in {+1,-1}$ or $r_i \in R $modeldot product as similarity:$f(x, y)=<L_X^Tx, L_Y^Ty>=x^TL_XL_Yy$$L_X, L_Y$ are two linear transformations with $l_1$ and $l_2$ regularizations(sparse transformations)objective function $$ argmax{L_X, L_Y}\sum _{r_i=+1} x_i^TL_XL_Y^Ty - \sum _{r_i = -1} x_i^TL_XL_Y^Ty $$s.t. $|L_X| \leq |\lambda_X|,|L_Y| \leq |\lambda_Y|,||L_X|| \leq v_X,||L_Y|| \leq v_X$