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What is: Field Embedded Factorization Machine?

SourceField-Embedded Factorization Machines for Click-through rate prediction
Year2000
Data SourceCC BY-SA - https://paperswithcode.com

Field Embedded Factorization Machine, or FEFM, is a factorization machine variant. For each field pair, FEFM introduces symmetric matrix embeddings along with the usual feature vector embeddings that are present in FM. Like FM, v_iv\_{i} is the vector embedding of the ithi^{t h} feature. However, unlike Field-Aware Factorization Machines (FFMs), FEFM doesn't explicitly learn field-specific feature embeddings. The learnable symmetric matrix W_F(i),F(j)W\_{F(i), F(j)} is the embedding for the field pair F(i)F(i) and F(j).F(j) . The interaction between the ithi^{t h} feature and the jthj^{t h} feature is mediated through WF(i),F(j).W_{F(i), F(j)} .

ϕ(θ,x)=ϕ_FEFM((w,v,W),x)=w_0+_i=1mwixi+_i=1m_j=i+1mv_iTW_F(i),F(j)v_jx_ix_j\phi(\theta, x)=\phi\_{F E F M}((w, v, W), x)=w\_{0}+\sum\_{i=1}^{m} w_{i} x_{i}+\sum\_{i=1}^{m} \sum\_{j=i+1}^{m} v\_{i}^{T} W\_{F(i), F(j)} v\_{j} x\_{i} x\_{j}

where W_F(i),F(j)W\_{F(i), F(j)} is a k×kk \times k symmetric matrix ( kk is the dimension of the feature vector embedding space containing feature vectors v_iv\_{i} and v_jv\_{j} ).

The symmetric property of the learnable matrix W_F(i),F(j)W\_{F(i), F(j)} is ensured by reparameterizing W_F(i),F(j)W\_{F(i), F(j)} as U_F(i),F(j)+U\_{F(i), F(j)}+ U_F(i),F(j)TU\_{F(i), F(j)}^{T}, where U_F(i),F(j)TU\_{F(i), F(j)}^{T} is the transpose of the learnable matrix U_F(i),F(j).U\_{F(i), F(j)} . Note that WF(i),F(j)W_{F(i), F(j)} can also be interpreted as a vector transformation matrix which transforms a feature embedding when interacting with a specific field.