【GCN-RS】Region or Global? A Principle for Negative Sampling in Graph-based Recommendation (TKDE‘22)

Region or Global? A Principle for Negative Sampling in Graph-based Recommendation (TKDE’22)

Middle zone

stay GCN-RS in , Negative sampling should choose distance user In the middle , Areas that are too close are usually items aggregated by users , It's too far away to have much information , Samples that are not far or near can be regarded as difficult samples with a large amount of information .

Define the distance user k The item of the stage is the middle area $R_{med}$, You can use the breadth first search layer by layer to get $R_{med}$.

From the middle area $R_{med}$ choice M Negative samples form Negative sample candidate set $C_u$, And then from $C_u$ Two strategies are used to get hard negative samples .

The author claims that the intermediate region $R_{med}$ Much smaller than the entire item set , But my statistics on the data set is just 3-hop, most $R_{med}$ It contains almost the entire data set ：

A strategy ： Positive sample assistance

Be similar to MixUp technology , In order to get user Hard negative sample , Not only with user $u$ of , And also user A positive sample of $v$ of , For a pair of positive samples $(u,v)$,$C_u$ Medium negative sample $v_n^p$ The probability of being picked is ：
$$p_n\left(v_n^p\mid (u,v)\right)=\frac{\sigma \left(\alpha \left({\mathbf{e}}_u^{\ast }\cdot {\mathbf{e}}_{v_n^p}^{\ast }\right)+(1-\alpha )\left({\mathbf{e}}_v^{\ast }\cdot {\mathbf{e}}_{v_n^p}^{\ast }\right)\right)}{{\sum }_{v_i\in {\mathcal{C}}_u}\sigma \left(\alpha \left({\mathbf{e}}_u^{\ast }\cdot {\mathbf{e}}_{v_i}^{\ast }\right)+(1-\alpha )\left({\mathbf{e}}_v^{\ast }\cdot {\mathbf{e}}_{v_i}^{\ast }\right)\right)}$$
among $\alpha$ It's a super parameter. , Used to balance the impact of users and items . Intuitively understand the meaning of this formula ：$C_u$ in ,embedding Distance from users $u$ And positive samples $v$ The closer the object , The greater the probability of being a negative sample . from $p_n$ Zhongcai k Negative samples form a negative sample set ：${\mathcal{P}}_k=\left\{v_n^p\right\}$

10% Pseudo label .

10~20% Hard negative sample .

Strategy two ： The exposure did not click

You can't choose more , Because exposure without clicking contains a strong bias Information , Only select exposure without clicking **“ The hardest one ”**：
$$v_n^e=\underset{v_i\in {\mathcal{M}}_u}{\mathrm{argmax}}\sigma \left(\beta \left({\mathbf{e}}_u^{\ast }\cdot {\mathbf{e}}_{v_i}^{\ast }\right)\right)$$

$$\beta =\{\begin{array}{lr}1,& \text{ if }{v}_e\text{ not in }{\mathcal{C}}_u\\ \text{ number of exposed items, }& \text{ if }{v}_e\text{ in }{\mathcal{C}}_u\end{array}$$

${\mathcal{M}}_u$ Is the exposure of the UN clicked collection ,$\beta$ Cumulative score , But if it's not in the middle area , No count .

Negative sample fusion

because GCN-RS The essence is iteratively to the user - In the commodity map embedding Spread the message , So combine these negative sample strategies into embedding Space , among k It's the number of negative samples ：
$$\begin{array}{c}{\mathbf{e}}_{v_n}^{\ast }=\underset{v_n^p\in {\mathcal{P}}_k}{\mathrm{merge}}\left({\mathbf{e}}_{v_n^e}^{\ast },{\mathbf{e}}_{v_n^p}^{\ast }\right)\\ \mathrm{merge}\left({\mathbf{e}}_{v_n^e},{\mathbf{e}}_{v_n^p}\right)=\frac{1}{k}\cdot {\mathbf{e}}_{v_n^e}+\left(1-\frac{1}{k}\right)\cdot {\mathbf{e}}_{v_n^p}\end{array}$$
So finally, for a positive sample , Create a negative sample , And then use margin hinge loss Train this sample ：
$$\mathcal{L}=\max \left(0,{\mathbf{e}}_u^{\ast }\cdot {\mathbf{e}}_{v_n}^{\ast }-{\mathbf{e}}_u^{\ast }\cdot {\mathbf{e}}_v^{\ast }+\gamma \right)$$