Item-Based Collaborative Filtering

Item-based collaborative filtering computes similarity between item columns, then recommends items similar to those a user already consumed. Compared with user-based collaborative filtering, item similarities can be more stable because item catalogs often change slower than user histories.

Item-item similarity

For item vectors $x_i$ and $x_j$ over users,

$$w_{ij}=\frac{x_i^{\top }{x}_j}{\Vert x_i\Vert \Vert x_j\Vert }.$$

A user score for unseen item $j$ is

$$s(u,j)=\sum _{i\in I_u}{w}_{ij}.$$

This is often a fast candidate generation source before richer ranking.

Worked example

Assume the target user already consumed items 0 and 3. Candidate scores sum item-item similarities from the consumed set and then filter already-seen items:

Candidate item	Similarity to item 0	Similarity to item 3	Unseen score	Decision
Item 0	1.000	0.408	filtered	already consumed
Item 1	0.816	0.000	0.816	candidate
Item 2	0.408	0.500	0.908	top candidate
Item 3	0.408	1.000	filtered	already consumed

Item 2 receives support from both consumed items and becomes the top unseen recommendation. Matrix factorization can compress a similar item-item structure into latent factors.

Caveats

Popular items are similar to many items unless similarities are normalized or shrinkage is used. Item-item tables can be large for huge catalogs, so approximate nearest-neighbor indexes and pruning are common. Pure item similarity still has cold-start problems for brand-new inventory.

References

• Linden, Smith, and York, 2003, Amazon.com Recommendations: Item-to-Item Collaborative Filtering
• Sarwar et al., 2001, Item-based Collaborative Filtering Recommendation Algorithms

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Section — Recommendation Systems and Personalization

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