# What is: Field Embedded Factorization Machine?

Source | Field-Embedded Factorization Machines for Click-through rate prediction |

Year | 2000 |

Data Source | CC 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, $v\_{i}$ is the vector embedding of the $i^{t h}$ feature. However, unlike Field-Aware Factorization Machines (FFMs), FEFM doesn't explicitly learn field-specific feature embeddings. The learnable symmetric matrix $W\_{F(i), F(j)}$ is the embedding for the field pair $F(i)$ and $F(j) .$ The interaction between the $i^{t h}$ feature and the $j^{t h}$ feature is mediated through $W_{F(i), F(j)} .$

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

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