DeepCF

prior research

• DMF Xue, H. J., Dai, X., Zhang, J., Huang, S., & Chen, J. (2017, August). Deep matrix factorization models for recommender systems. In IJCAI (Vol. 17, pp. 3203-3209).
  • 표현 학습(Representation Learning)은 사용자와 아이템의 관계가 쌍선형(Bilinear)이라는 단순 가정 하에 엔티티들의 의미론적(Basis) 유사도를 반영하는 의미 체계(Linear Space, Latent Space)를 학습하는 데 강점이 있음
• NCF He, X., Liao, L., Zhang, H., Nie, L., Hu, X., & Chua, T. S. (2017, April). Neural collaborative filtering. In Proceedings of the 26th international conference on world wide web (pp. 173-182).
  • 매칭 함수 학습(Matching Function Learning)은 사용자와 아이템의 관계를 단순 가정으로 사전 제약하지 않고 데이터로부터 학습하여 데이터에 적합한 관계 구조를 모사하는 데 강점이 있음

idea

• CFNet(Collaborative Filtering Networks): 표현 학습 모듈(Representation Learning Networks)과 매칭 학습 모듈(Matching Function Learning Networks)을 병렬 결합하는 앙상블 모형

  

notation

• $u=1,2,\cdots,M$: user idx
• $i=1,2,\cdots,N$: item idx
• $\mathbf{Y} \in \mathbb{R}^{M \times N}$: user-item interaction matrix
• $\mathbf{u}_{u} \in \mathbb{R}^{K}$: user latent factor vector
• $\mathbf{v}_{i} \in \mathbb{R}^{K}$: item latent factor vector
• $\mathbf{z}_{u,i}$: predictive vector of user $u$ and item $i$
• $\hat{y}_{u,i}$: interaction probability of user $u$ and item $i$

function

• CFNet is RLNet & MLNet Ensemble

  \[\begin{aligned} \hat{y}_{u,i} &= \sigma\left(\mathbf{W}\cdot \left[\mathbf{z}_{u,i}^{\mathrm{(rl)}} \oplus \mathbf{z}_{u,i}^{\mathrm{(ml)}}\right]\right) \end{aligned}\]

representation learning networks

• user latent factor vector representation learning:

  \[\begin{aligned} \mathbf{u}_{u} &=\mathrm{mlp}_{\mathrm{ReLU}}\left(\mathbf{Y}_{u*}\right) \end{aligned}\]

• item latent factor vector representation learning:

  \[\begin{aligned} \mathbf{v}_{i} &=\mathrm{mlp}_{\mathrm{ReLU}}\left(\mathbf{Y}_{*i}\right) \end{aligned}\]

• bilinear interaction between user $u$ and item $i$:

  \[\begin{aligned} \mathbf{z}_{u,i} &=\mathbf{u}_{u}\odot\mathbf{v}_{i} \end{aligned}\]

• if use CFNet-rl as a single prediction module:

  \[\begin{aligned} \hat{y}_{u,i} &=\sigma\left(\mathbf{W}\cdot\mathbf{z}_{u,i}\right) \end{aligned}\]

matching function learning networks

• generate user latent factor vector through linear transformation:

  \[\begin{aligned} \mathbf{u}_{u} &=\mathbf{W}\cdot\mathbf{Y}_{u*} \end{aligned}\]

• generate user latent factor vector through linear transformation:

  \[\begin{aligned} \mathbf{v}_{i} &=\mathbf{W}\cdot\mathbf{Y}_{*i} \end{aligned}\]

• predictive vector of user $u$ and item $i$:

  \[\begin{aligned} \mathbf{z}_{u,i} &=\mathrm{mlp}_{\mathrm{ReLU}}\left(\mathbf{u}_{u}\oplus\mathbf{v}_{i}\right) \end{aligned}\]

• if use CFNet-ml as a single prediction module:

  \[\begin{aligned} \hat{y}_{u,i} &=\sigma\left(\mathbf{W}\cdot\mathbf{z}_{u,i}\right) \end{aligned}\]