# Notation standards¶

In the documentation, you will find the following notation:

• $$R$$ : the set of all ratings.
• $$R_{train}$$, $$R_{test}$$ and $$\hat{R}$$ denote the training set, the test set, and the set of predicted ratings.
• $$U$$ : the set of all users. $$u$$ and $$v$$ denotes users.
• $$I$$ : the set of all items. $$i$$ and $$j$$ denotes items.
• $$U_i$$ : the set of all users that have rated item $$i$$.
• $$U_{ij}$$ : the set of all users that have rated both items $$i$$ and $$j$$.
• $$I_u$$ : the set of all items rated by user $$u$$.
• $$I_{uv}$$ : the set of all items rated by both users $$u$$ and $$v$$.
• $$r_{ui}$$ : the true rating of user $$u$$ for item $$i$$.
• $$\hat{r}_{ui}$$ : the estimated rating of user $$u$$ for item $$i$$.
• $$b_{ui}$$ : the baseline rating of user $$u$$ for item $$i$$.
• $$\mu$$ : the mean of all ratings.
• $$\mu_u$$ : the mean of all ratings given by user $$u$$.
• $$\mu_i$$ : the mean of all ratings given to item $$i$$.
• $$N_i^k(u)$$ : the $$k$$ nearest neighbors of user $$u$$ that have rated item $$i$$. This set is computed using a similarity metric.
• $$N_u^k(i)$$ : the $$k$$ nearest neighbors of item $$i$$ that are rated by user $$u$$. This set is computed using a similarity metric.