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Neural Collaborative Filtering Explanation & Implementation

The document proposes a neural collaborative filtering (NCF) model that uses a neural network to model user-item interactions in a latent space. It shows that NCF generalizes matrix factorization models. An evaluation on two real-world datasets shows that NCF outperforms state-of-the-art recommendation models.

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Steeve Huang
 1. Propose Neural Collaborative Filtering (NCF) which models the user and item interactions in the latent space effectively with a Neural Network.  2. Show that NCF is a generalization of Matrix Factorization.  3. Demonstrate that NCF outperforms the state-of-the-art models in two real- world datasets.
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 0 0 0 0 0 User 2 0 0 0 0 0 User 3 0 0 0 0 0 User 4 0 0 0 0 0
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 Observed Interaction Unobserved Interaction
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Multiplication
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Multiplication
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
Item 1 Item 2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
S23 > S12 > S13
S23 > S12 > S13 P1 P2 P3
S23 > S12 > S13 P1 P2 P3 S41 > S43 > S42
S23 > S12 > S13 P1 P2 P3 P4 S41 > S43 > S42
Multiplication Unit Matrix JKx1 L(x) = x
𝑦 𝑢𝑖 = 𝐿 𝑝 𝑢 ⊙ 𝑞𝑖 × 𝐽 𝐾𝑥1 𝑦 𝑢𝑖 = 𝐿 𝑝 𝑢 𝑇 ∙ 𝑞𝑖 𝑦 𝑢𝑖 = 𝑝 𝑢 𝑇 ∙ 𝑞𝑖
Neural Collaborative Filtering Explanation & Implementation
Neural Collaborative Filtering Explanation & Implementation
Neural Collaborative Filtering Explanation & Implementation
Neural Collaborative Filtering Explanation & Implementation
Neural Collaborative Filtering Explanation & Implementation
Neural Collaborative Filtering Explanation & Implementation

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In this document
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Steeve Huang introduces Neural Collaborative Filtering (NCF), describing it as a model for user-item interactions using Neural Networks, which generalizes matrix factorization and outperforms existing models.

Visualization of user-item interaction data: slides illustrate interaction matrices, showing both observed and unobserved interactions among 5 items for 4 users.

Detailing the construction of utility matrices through multiplication, with examples of user and item matrices alongside Mean Squared Error calculations.

Continued exploration of utility matrices with reference to Mean Squared Error, demonstrating mathematical formulations that further characterize the model.

Results comparison among different algorithms, highlighting performance rankings and the effectiveness of the proposed NCF model over identified comparative models.

Presentation of linear algebra concepts related to matrix multiplication and latent factors in collaborative filtering, reinforcing how user-specific utility values are computed.

Neural Collaborative Filtering Explanation & Implementation

  • 1.
  • 2.
     1. ProposeNeural Collaborative Filtering (NCF) which models the user and item interactions in the latent space effectively with a Neural Network.  2. Show that NCF is a generalization of Matrix Factorization.  3. Demonstrate that NCF outperforms the state-of-the-art models in two real- world datasets.
  • 3.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 0 0 0 0 0 User 2 0 0 0 0 0 User 3 0 0 0 0 0 User 4 0 0 0 0 0
  • 4.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0
  • 5.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 Observed Interaction Unobserved Interaction
  • 6.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix
  • 7.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Multiplication
  • 8.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Multiplication
  • 9.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication
  • 10.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
  • 11.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
  • 12.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
  • 13.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
  • 14.
    Item 1 Item2 Item 3 Item 4 Item 5 User 1 1 0 0 1 0 User 2 0 0 0 0 1 User 3 0 0 0 1 0 User 4 0 0 1 0 0 0 1.3 -0.6 0 0 0.9 -0.8 0 0 0 -0.8 0 -0.6 0.5 0 0 0.8 0 ≈ X Item MatrixUser MatrixUtility Matrix 0.7 0 0 1.1 0 0 0 0.5 0 0.4 0.5 0 0 0.7 0 0 0 0.6 0 0.5 Mean Squared Error Multiplication k
  • 16.
    S23 > S12> S13
  • 17.
    S23 > S12> S13 P1 P2 P3
  • 18.
    S23 > S12> S13 P1 P2 P3 S41 > S43 > S42
  • 19.
    S23 > S12> S13 P1 P2 P3 P4 S41 > S43 > S42
  • 21.
  • 22.
    𝑦 𝑢𝑖 =𝐿 𝑝 𝑢 ⊙ 𝑞𝑖 × 𝐽 𝐾𝑥1 𝑦 𝑢𝑖 = 𝐿 𝑝 𝑢 𝑇 ∙ 𝑞𝑖 𝑦 𝑢𝑖 = 𝑝 𝑢 𝑇 ∙ 𝑞𝑖