docs: add types of feedback

docs/introduction/data.rst

@@ -2,20 +2,83 @@
 Data
 ====
 
-
-In this page, settings of recommendation models will be discussed.
-
 There are typically two kinds of available feedbacks from users: **explicit feedback** and **implicit feedback**.
 
 Explicit Feedback
 =================
 
 **For explicit feedback, users give their preferences by ratings**. For example, a user gives 5 stars to a movie he likes and 1 star to a movie that he dislikes. A user's taste could be represented by ratings that he gives.
 
+The dataset of explicit feedback is defined as:
+
+.. math::
+
+    D = \{ <u,i,r_{ui}> \}
+
+There are multiple tuples :math:`<u,i,r_{ui}>` in the dataset. A tuple is consisted of a user ID :math:`u`, a item ID :math:`i` and a rating :math:`r_{ui}`. The table of a dataset should be:
+
+==== ==== ======
+User Item Rating
+==== ==== ======
+0    1    5
+0    2    4
+1    1    3
+1    2    4
+==== ==== ======
+
+Example: [MovieLens]_ 
+
 Implicit Feedback
 =================
 
-**For implicit feedback, only positive feedbacks are collected.** For example, implicit feedback represents that a user watched a movie. However, there is no feedback that represents a user dislikes a movie. It's even worse that implicit feedback couldn't show that the user likes the movie. Implicit feedbacks are naturally noisy but it is the most situations in practice.
+**For implicit feedback, only positive feedbacks are collected.** For example, implicit feedback represents that a user watched a movie. However, there is no feedback that represents a user dislikes a movie. It's even worse that implicit feedback couldn't show that the user likes the movie. Implicit feedbacks are naturally noisy but it is the common situation in practice.
+
+The dataset of implicit feedback is defined as:
+
+.. math::
+
+    D = \{ <u,i> \}
+
+There are multiple tuples :math:`<u,i>` in the dataset. A tuple is consisted of a user ID :math:`u` and a item ID :math:`i`. The table of a dataset should be:
+
+==== ====
+User Item
+==== ====
+0    1   
+0    2   
+1    1   
+1    2   
+==== ====
+
+Example: [Last.FM]_
 
 Weighted Implicit Feedback
 ==========================
+
+**For weighted implicit feedback, positive feedbacks and their weights are collected.** For example, a user :math:`u` played a game :math:`i` for :math:`r_{ui}` hours. There is no rating that represents this user likes or dislikes this game. The weight :math:`r_{ui}` is a score of confidence rather than preference.
+
+The definition is almost the same as explicit feedback:
+
+.. math::
+
+    D = \{ <u,i,r_{ui}> \}
+
+There are multiple tuples :math:`<u,i,r_{ui}>` in the dataset. A tuple is consisted of a user ID :math:`u`, a item ID :math:`i` and a weight :math:`r_{ui}`. The table of a dataset should be:
+
+==== ==== ======
+User Item Weight
+==== ==== ======
+0    1    100
+0    2    20
+1    1    5
+1    2    50
+==== ==== ======
+
+Example: [SteamVideoGames]_
+
+Datasets
+========
+
+.. [MovieLens] https://grouplens.org/datasets/movielens/
+.. [Last.FM] https://grouplens.org/datasets/hetrec-2011/
+.. [SteamVideoGames] https://www.kaggle.com/tamber/steam-video-games