Raccomender engines use content-based and collaborative filtering approaches to make recommendations. Content-based filtering recommends items based on a comparison of item characteristics to a user's profile, while collaborative filtering builds models from users' past behaviors and preferences to identify similar users and predict interests. The document then provides examples of how matrix factorization models are used for both content-based and collaborative filtering to learn latent representations of users and items from rating data through iterative optimization.
2. Index
• Content based
Its approaches utilize a series of discrete characteristics of an item in
order to recommend additional items with similar properties.
• Collaborative filtering
Its approaches building a model from a user's past behavior (items
previously purchased or selected and/or numerical ratings given to
those items) as well as similar decisions made by other users. This
model is then used to predict items (or ratings for items) that the user
may have an interest in.
3. Content based
Content-based filtering, also referred to as cognitive filtering, recommends items
based on a comparison between the content of the items and a user profile.
9. nu = 4 number of users
nm = 5 number of movies
f = 2 number of features
𝑥0 = 1 bias
𝑥(1) = [ 𝑥0 𝑥1 𝑥2 ]' = [ 1 0,7 0,5 ]' Movie features
𝑥(2) = [ 1 1 0,5 ]'
𝑥(3) = [ 1 0 1 ]'
𝑥(4) = [ 1 0,2 1,02 ]'
𝑥(5) = [ 1 1 0 ]'
For each user j, learn a parameter θ(j) ∈ ℝ3.
Predict user j as rating movie i with (θ(j))' 𝑥(i)
11. For each user j, learn a parameter θ(j) ∈ ℝ3.
Predict user j as rating movie i with (θ(j))' 𝑥(i)
θ(1) = [ 0 5 1 ]' User n.1
𝑥(3) = [ 1 0 1 ]' Movie n.3
User 1 gives to movie 3: 0×1 + 5×0 + 1×1 = 1 ✭
Compute θ(j) ,basically, it's a linear regression problem.
12. r(i,j) = 1 when user i rated movie j, 0 elsewhere
x(i) movie i feature vector
y(i,j) user i rating for movie j if set
n number of movies
m number of users
Learn θ(j) ( user j profile )
min
θ
( 𝑗) = 0.5 ∑i:r(i,j)=1 ( (θ(j) )'𝑥(i) - 𝑦(i,j) )2 + 0.5 λ ∑k=1..n (θ(j)
k)2
Learn θ(1) ... θ(m) ( for every user )
min
θ
(1)
... θ
(m) = 0.5 ∑ j=1..m ∑i:r(i,j)=1 ( (θ(j) )'𝑥(i) - 𝑦(i,j) )2 +
0.5 λ ∑j=1..m ∑k=1..n (θ(j)
k)2
13. 𝑥 → θ
• Cost is minimized on the single user preferences.
• User's profile depends on the product features.
17. The underlying assumption of the collaborative filtering approach is that if a
person A has the same opinion as a person B on an issue, A is more likely
to have B's opinion on a different issue x than to have the opinion on x of a
person chosen randomly.
Women often exclaim,
"All men are the same!"
18. Are we all the same ?
• Yes, we are.
• 16 base types
• 4 cognitive functions
Extraversion/Introversion,
INtuiting/Sensing,
Thinking/Feeling,
Perceiving/Judging.
31. 1. Product's features depend on all users ratings
2. User's profile depends on product's features
3. 1),2) ⇒ User's profile depents on all users ratings
4. Similar products depends on users' ratings and users'
profiles
5. Similar user profiles are defined by similar products
