NLMF: NonLinear Matrix Factorization Methods for
Top-N Recommender Systems

Santosh Kabbur and George Karypis

Department of Computer Science, University of Minnesota Twin Cities, USA

ICDMW'14

Motivation

• Traditional MF-based models assumption
  • User preference is consistent across all the items that he/she has rated.
• Traditional MF-based models do not put emphasis on fitting the preference diversity of a given user preference.
• However, many users can have multiple interests and their preferences can vary with each such interest.

Background (1/3)

• Top-N recommendation Problem
  • Recommend the most appealing N items for users (Not necessary to be the exactly top N).
  • Ranking metrics (e.g. Precision) are the better measures of top-N task.
  • Conventional MF-based models which minimizes RMSE does not translate into performance improvements of top-N task.
  • Few top popular items can skew the top-N performance.

Background (2/3)

• MaxMF proposed by Weston et al.
  • Represent user with multiple latent vectors, each corresponding to a different interest.
  • Have more power to fit user's preference if user’s interests are diverse.
  • Only choose the maximum scoring interest as the final recommendation score.

Background (3/3)

• MaxMF proposed by Weston et al.
  • Weaknesses
    • Only interest-specific component is considered.
    • May fail in two cases
      • Users who have not provided enough preferences.
      • Users do not have enough diversity in their itemsets.

MaxMF

• Represent user by T interest vectors.
• The set of items is partitioned into T partitions for each user.
• If an item is ranked higher in the top-N list, at least one of the user's interests must provide a high score for that item.

Modification-NLMF

• Number of items for every interest may not be sufficient if only interest-specific preference component is learned.
• Learn user preferences as a combination of global preference and interest-specific preference components.
• Strike a balance between the two.

NLMFi

• The item vectors is independent between global preference and interest-specific preference components.
• The embedding sizes of the two components need not to be the same.

SGD for top-N task

• It is a common practice to do negative sampling in top-N task.
• Both positive feedbacks and missing entries are updated.
• ρ * (# of positive feedbacks) missing entries are sampled and are regarded as zeros.
• Usually ρ is small (in the range of 3-5).

NLMFs

• The item vectors is shared between global preference and interest-specific preference components.

Experiment (1/9)

• Dataset
  • Netflix
  • Flixster
• Extract a subset of the original dataset.
• Remove the top 5% of the frequently rated items.
• Binarize the Rating to make implicit feedbacks.
  • Rated => 1
  • Non-rated => 0

Experiment (2/9)

Experiment (3/9)

• 5-fold Leave-One-Out-Cross-Validation (LOOCV)
  • Randomly select one item per user from the dataset and place it in the test set.
  • Repeat to create 5 different folds.
• Evaluation Metric
  • Hit rate
     
  • Average Reciprocal Hit Rank = MRR in this case

=1

Experiment (4/9)

• Competitors
  • State-of-the-art for top-N recommendation problem
    • UserKNN
    • PureSVD
    • BPRMF
    • SLIM
    • MaxMF

Experiment (5/9)

Experiment (6/9)

• Effect of Number of Interests​
  • Peak values happen at T=3 or 4.
  • Further increasing the value of T, the performance starts to decrease.
    • Since the number of items for each interest decreases, less meaningful interest vectors are learned.

Experiment (7/9)

Experiment (8/9)

Experiment (9/9)

• All hyperparameters of these models are tuned to maximize Hit rate.
• NLMFi (independent) outperforms NLMFs (shared).
  • Item vectors are learned separately in NLMFi, which makes it have more power of striking a balance between global preference and interest-specific components.

Conclusion

• Contribution
  • A MF-based method (NLMF) which solves the top-N recommendation problem by considering user's preference diversity.
  • The recommendation score is computed as a combination of global preference and interest-specific user preference.
• Future works
  • Test on much sparser dataset.
  • Extend to rating prediction task.