Referring to the LightFM model from paper Metadata Embeddings for User and Item Cold-start Recommendations, the model tries to learn $d$-dimensional user and item feature embeddings $e_f^U$ and $e_f^I$ for each feature $f$ ($U$ is the set of users, $I$ is the set of items).

The latent representation of user $u$ is given by the sum of its features' latent vectors: $$ \mathbf{q_u} = \sum_{j\in{f_u}}\mathbf{e_j^U} $$

The same holds for item $i$: $$ \mathbf{p_i} = \sum_{j\in{f_i}}\mathbf{e_j^I} $$

Does it really make sense to sum the latent embeddings to represent a set of features (user or item)?


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