Recommendation systems rely on various definitions of similarities.These definitions while having numerous design factors in different domains help identify and recommend relevant content. For example, similarity between users, or items, are measured based on, but not limited to, explicit feedback such as ratings, thumbs up; or/and implicit feedback such as clicks, views etc; or/and based on composition of item such as tags, metadata etc. In this paper, we explore a similarity model while very intuitive to find similar items using a very common natural law of attraction between bodies, that is gravitational law. We show how the two attributes, relative mass and distance between the bodies, of gravitation law can be interpreted for an effective personalized recommendations; in both spatial and non-spatial domains. Finally, we illustrate the use of distance and mass in a non-spatial domain and we exhibit the accuracy in recommendations against popular baselines.

1. The Force Within: Recommendation via
Gravitational Attraction Between Items
Vikas Kumar (University of Minnesota)
Saeideh Bakhshi (Facebook)
Lyndon Kennedy (FutureWei Tech)
David A. Shamma (CWI Amsterdam)
This research was performed when the authors worked at Yahoo Inc!

2. Many Similarity Models

3. Observation:
● Using Flickr data, we determined similarity between cities based on photo tags.
● We found that bigger cities like San Francisco and New York are more similar to each other.
● Smaller cities, like Berkeley, have more influence from their closest bigger city.

4. MovieLens Example:
A popular Mafia movie. A popular “thought-provoking”* movie.
* based on tags applied by users
http://movielens.org

5. MovieLens Example:
A popular Mafia movie. A popular “thought-provoking”* movie.
* based on tags applied by users
Highly similar; alike users rate
both movies.
http://movielens.org

6. MovieLens Example:
Other mafia movies arguably influenced from
“The Godfather” but not as popular.
Other “thought-provoking” movies influenced
from “The Shawshank Redemption” but not as
popular.
http://movielens.org

7. Movies Example:
Other mafia movies arguably influenced from
“The Godfather” but not as popular.
Other “thought-provoking” movies influenced
from “The Shawshank Redemption” but not as
popular.
http://movielens.org
planet
planet

8. Movies Example:
Other mafia movies arguably influenced from
“The Godfather” but not as popular.
Other “thought-provoking” movies influenced
from “The Shawshank Redemption” but not as
popular.
http://movielens.org
planet
planet
moon
moon
moon
moon
moon
moon
moon

9. Movies Example:
Other mafia movies arguably influenced from
“The Godfather” but not as popular.
Other “thought-provoking” movies influenced
from “The Shawshank Redemption” but not as
popular.
http://movielens.org
planet
planet
moon
moon
moon
moon
moon
moon
moon

10. Gravitational Law of Attraction:
● Determines force of attraction between two bodies:
○ Bigger bodies (with more mass) attracts more.
○ Bodies closer to each other attracts more.

11. Gravitational Law of Attraction:
• Determines force of attraction between two bodies.
• Bigger bodies (with more mass) attracts more.
• Bodies closer to each other attracts more.
• Why this model?
• This model resonates with our observation.
• It is easy, intuitive, and has an adaptable definition.
• Mass and distance can provide interpretation in various
contexts.

12. Gravitational Law in RecSys
Two important factors:
1.Mass
a. Scalar or vector form that determines relative size or mass of an item.
b. Example: #ratings, #views, #photos_at_location etc.
2.Distance
a. Scalar or vector form that suggests relative content dissimilarity.
b. Example: Spatial domain - Geodesic distance between items, or semantic dissimilarity based on
content (ex: tags) or composition of item.

13. Experiment: Movie Recommendations
● Predicting rating of item (m) for user (u) using gravitational similarity:

14. Experiment: Movie Recommendations
● Predicting rating of item (m) for user (u) using gravitational similarity:

15. Experiment Details
● MovieLens 10M rating dataset*
○ 10 million ratings, 100K tags, 10K movies, and 72K users.
○ Prediction Task: 90% - 10% train-test split.
○ Recommendation Task: Sample users, hideout. (80%)
● Baselines: ItemItem, UserUser, MatrixF (Matrix Factorization)
● Metrics:
○ Prediction: RMSE
○ Recommendation: Precision@20, Recall@20, and Map@20
*available at grouplens.org/datasets/movielens

16. Results

17. Results Gravity-based recommender
stands out in recommendation
metrics!

18. Results Hard to beat MF
techniques on RMSE

19. Results
Achieves comparable
diversity and spread
within system.

20. Conclusion:
● Replicates natural form of attraction.
● Balances popularity and relevance of items in a very intuitive fashion.
● Definition adaptable to various domains and recommendation space.
● An exploratory work, more to come!

21. Thank You!
Questions?
vikas@cs.umn.edu; Twitter: @vikasnitr
saeideh@gatech.edu; Twitter: @sdhbkh