# Notation standardsΒΆ

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`

.