User-Based Collaborative Filtering

User-based collaborative filtering finds users whose rows in the utility matrix resemble the target user’s row, then recommends what those neighbors liked. It is the most literal form of collaborative filtering: “people with histories like yours also liked this.”

User-user prediction

With similarity $w_{uv}$, a rating-style prediction is

$${\hat{r}}_{ui}={\bar{r}}_u+\frac{{\sum }_{v\in N(u)}{w}_{uv}(r_{vi}-{\bar{r}}_v)}{{\sum }_{v\in N(u)}|w_{uv}|}.$$

For binary interactions, the numerator is often just a weighted sum of neighbor item indicators. Item-based collaborative filtering flips the similarity computation to columns.

Worked example

For target user U0 with ratings $(5,4,0,0)$, cosine similarity compares U0’s rating vector with each other user’s vector:

User	Ratings	Similarity to U0	Contribution to unseen items
U0	$(5,4,0,0)$	1.000	Target user; already-seen items are filtered.
U1	$(4,5,1,0)$	0.964	Strong neighbor; contributes to item 2.
U2	$(0,1,5,4)$	0.096	Weak neighbor; contributes little.
U3	$(0,0,4,5)$	0.000	No overlap with U0’s rated items.

After filtering items 0 and 1, item 2 receives the strongest neighbor-weighted support because the nearest user rated it. Matrix factorization can be viewed as replacing this local neighbor lookup with a global low-rank model.

Caveats

User neighborhoods are unstable when users have few interactions or rapidly changing tastes. Computing user-user similarities is expensive in systems with many users. New users need onboarding, content-based recommendation, or exploration before neighbor scores are meaningful.

References

• scikit-learn documentation: cosine_similarity
• Adomavicius and Tuzhilin, 2005, Toward the Next Generation of Recommender Systems

Nav

Section — Recommendation Systems and Personalization

← Collaborative Filtering Item-Based Collaborative Filtering →