Notation standards, ReferencesΒΆ

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 \(i\).
  • \(\sigma_u\) : the standard deviation of all ratings given by user \(u\).
  • \(\sigma_i\) : the standard deviation 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.

References

Here are the papers used as references in the documentation. Links to pdf files where added when possible. A simple Google search should lead you easily to the missing ones :)