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I'm new to recommender system and trying to understand the fundamental difference between standard collaborative filtering (CF) and hybrid methods like LightFM. As I researched online, most of the posts mentioned hybrid method combines both CF and content-based method. But from a matrix/math standpoint, LightFM also learns item-user interaction embedding, like CF. How are they different?

Thank you so much in advance.

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Based on Kula's [paper](https://arxiv.org/pdf/1507.08439.pdf, LightFM starts from a CF matrix factorization algorithm while also learning both users and items embeddings in the process (if such data available). However, if no user/item features are provided to the model, its behaviour will be that of a MF (Matrix Factorization) method.