动机
在推荐系统中,交叉特征(Cross Features)可以深入挖掘特征之间的潜在关系,提升模型效果。例如,把职业特征occupation={ banker,doctor}occupation=\left\{banker,doctor\right\}occupation={ banker,doctor}和性别特征gender={ M,F}gender=\left\{M,F\right\}gender={ M,F}进行交叉组合,可以得到新特征occupation_gender={ banker_M,banker_F,doctor_M,doctor_F}occupation\_gender=\left\{banker\_M,banker\_F,doctor\_M,doctor\_F\right\}occupation_gender={ banker_M,banker_F,doctor_M,doctor_F}
Factorization Machine(FM)是挖掘交叉特征有代表性的模型,它的表达式如下:
yFM(x)=w0+∑i=1nwixi+∑i=1n∑j=i+1nviTvj⋅xixj y_{FM}(x) = w_0+\sum^n_{i=1}w_ix_i+\sum^n_{i=1}\sum^n_{j=i+1}v_i^Tv_j·x_ix_j yFM(x)=w0+i=1∑nwixi+