【GCN-RS】MCL: Mixed-Centric Loss for Collaborative Filtering (WWW‘22)

MCL: Mixed-Centric Loss for Collaborative Filtering (WWW’22)

Pointwise and pairwise The information of loss function mining is too little , Just take samples , Then update the weights

In order to mine more signals from the available preference information , Consider difficult samples and global information .

Collect difficult samples first

$E$ It's European distance .

Hard to correct sample Is the distance ratio of the correct sample The distance minus threshold of the negative sample with the smallest distance And a large sample .
$$E_{uj}>\underset{k\in N_u}{\min }{E}_{uk}-ϵ$$
Hard negative sample It refers to the distance ratio of negative samples The distance from the largest positive sample plus the threshold Even smaller samples .
$$E_{uk}<\underset{j\in P_u}{\max }{E}_{uj}+ϵ$$

Mixing Center loss (CML)

The positive and negative sample sets collected are ：${\mathrm{P}}_{\mathrm{u}}^{\mathrm{s}},{\mathrm{N}}_{\mathrm{u}}^{\mathrm{s}}$. In the process of training , Given a batch B（ contain m Users ）, Define the loss function ：
$$\begin{array}{rl}{L}_{MCL}& =\frac{1}{\alpha }\log \left[1+\frac{1}{m}\sum _{u\in B}\sum _{j\in P_u^s}{e}^{\alpha \left(E_{uj}+{\lambda }_p\right)}\right]\\ & +\frac{1}{\beta }\log \left[1+\frac{1}{m}\sum _{u\in B}\sum _{k\in N_u^s}{e}^{-\beta \left(E_{uk}+{\lambda }_n\right)}\right]\end{array}$$
Explain why you designed this loss, This loss For a pair of positive samples ：
$$\begin{array}{rl}\frac{\partial L}{\partial E_{uj}}=w_{uj}^{+}& =\frac{1}{m}\cdot \frac{e^{\alpha E_{uj}}}{e^{-\alpha {\lambda }_p+\frac{1}{m}}{\sum }_{u^{\prime }\in B}{\sum }_{i\in P_{u^{\prime }}^s}{e}^{\alpha E_{u^{\prime }i}}}\\ & =\frac{1}{m}\cdot \frac{1}{w_1^{+}(u,j)+w_2^{+}(u,j)+w_3^{+}(u,j)}\end{array}$$

• user - Item Center （$w_1^{+}$）: Only with users - The distance of the object , The farther $w_1$ The smaller it is ,loss The bigger it is .
• Center of the same type （$w_2^{+}$）： Calculate the current positive sample items $j$ Relationship with other difficult samples of users . If the sample article $j$ The distance from the user is greater than that of other difficult samples , be $w_1$ The smaller it is ,loss The bigger it is . This is similar to the object embedding Space plus a constraint , We hope that the distance between the same type of items and users is similar （ stay embedding Space , Items interacted with the same user , Around the user .）
• Same batch Center （$w_3^{+}$）： And the same batch Compare with other users in , Provides additional consistency across users , It is hoped that each user is the same distance from its positive sample .