Latent Vector

A Latent Vector is a vector of latent variables.

• Context:
  • It can (typically) come from a Latent Space.
• See: Latent Factor Model Fitting Algorithm, Eigenvector.

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References

2011

• (Wang & Blei, 2011) ⇒ Chong Wang, and David M. Blei. (2011). “Collaborative Topic Modeling for Recommending Scientific Articles.” In: Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ISBN:978-1-4503-0813-7 doi:10.1145/2020408.2020480
  • QUOTE: Among latent factor methods, matrix factorization performs well [13]. In matrix factorization, we represent users and items in a shared latent low-dimensional space of dimension [math]\displaystyle{ K }[/math] — user [math]\displaystyle{ i }[/math] is represented by a latent vector [math]\displaystyle{ u_j \in \mathbb{R}^K }[/math] and item [math]\displaystyle{ j }[/math] by a latent vector [math]\displaystyle{ v_j \in \mathbb{R}^K }[/math]. We form the prediction of whether user [math]\displaystyle{ i }[/math] will like item [math]\displaystyle{ j }[/math] with the inner product between their latent representations, [math]\displaystyle{ \hat{r}_{ij} = u^T_iv_j. \ (1) }[/math]

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