Notation standards, References
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.
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 :)
| [KBV09] | Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques for recommender systems. 2009. |
| [LZXZ14] | Xin Luo, Mengchu Zhou, Yunni Xia, and Qinsheng Zhu. An efficient non-negative matrix factorization-based approach to collaborative filtering for recommender systems. 2014. |
| [RRSK10] | Francesco Ricci, Lior Rokach, Bracha Shapira, and Paul B. Kantor. Recommender Systems Handbook. 1st edition, 2010. |