CnGAN: Generative Adversarial Networks for Cross-network User Preference Generation for Non-overlapped Users

CnGAN is trained using target network interactions of each user at each time interval and their corresponding source network interactions. We used topic modeling to capture user interactions on a continuous topical space since CnGAN is a GAN based model and requires inputs in a continuous space. Let $u_{o}\in U=[Tn_{u}^{t},Sn_{u}^{t}]$ denote an overlapped user at time $t$, where $Tn_{u}^{t}$ and $Sn_{u}^{t}$ are target and source network interactions spanned over $T=[1,\dots,t]$ time intervals. A non-overlapped user $u_{no}\in U=[Tn_{u}^{t}]$ is denoted only using target network interactions. We used YouTube as the target and Twitter as the source network to conduct video recommendations on YouTube. Therefore, $Tn_{u}^{t}$ is the set of interacted videos (i.e., liked or added to playlists) and $Sn_{u}^{t}$ is the set of tweets. We assumed that each interaction (video or tweet) is associated with multiple topics, and extracted the topics from the textual data associated with each interaction (video titles, descriptions and tweet contents). We used the Twitter-Latent Dirichlet Allocation (Twitter-LDA) (Zhao et al., 2011) for topic modeling since it is most effective against short and noisy contents. Based on topic modeling, each user $u$ on the target network is represented as a collection of topical distributions $tn_{u}=\{\boldsymbol{tn_{u}^{1}};\dots;\boldsymbol{tn_{u}^{t}}\}\in\mathbb{R}^{T\times K^{t}}$ over $T$ time intervals, where $K^{t}$ is the number of topics. Each vector $\boldsymbol{tn_{u}^{t}}=\{tn_{u}^{t,1};\dots;tn_{u}^{t,K^{t}}\}\in\mathbb{R}^{K^{t}}$ is the topical distribution at time $t$, where $tn_{u}^{t,k}=\hat{tn}_{u}^{t,k}/\sum_{c=1}^{K^{t}}\hat{tn}_{u}^{t,c}$ is the relative frequency of topic k, and $\hat{tn}_{u}^{t,k}$ is the absolute frequency of the corresponding topic. Similarly, on the source network, interactions are represented as $sn_{u}=\{\boldsymbol{sn_{u}^{1}};\dots;\boldsymbol{sn_{u}^{t}}\}\in\mathbb{R}^{T\times K^{t}}$. The resultant topical frequencies indicate user preference levels towards corresponding $K^{t}$ topics. Therefore, $u=\{tn_{u},sn_{u}\}\in\mathbb{R}^{T\times 2K^{t}}$ represents user preferences over $T$ time intervals on a continuous topical space, and forms the input to the proposed model.

User preferences captured as topical distribution vectors $(\boldsymbol{tn_{u}^{t}}$ and $\boldsymbol{sn_{u}^{t}})$ become sparse when $\boldsymbol{K^{t}}$ is set to a sufficiently large value to capture finer level user preferences, and/or the number of interactions at a time interval is low. One of the most effective methods to train machine learning models with highly sparse data is to model interactions between input features (Blondel et al., 2016) (e.g., using neural networks (He et al., 2017)). Therefore, we used two neural encoders $E_{tn}$ and $E_{sn}$ for target and source networks to transform the input topical distributions to dense latent encodings. The resultant encodings are represented as $E_{tn}(tn_{u})$ $\in\mathbb{R}^{T\times En}$ and $E_{sn}(sn_{u})\in\mathbb{R}^{T\times En}$, where $En$ is the dimensionality of the latent space. These encodings form the input to the generator task.

For a non-overlapped user $u$, let $E_{tn}(\boldsymbol{tn_{u}^{t}})$ denote the target network encoding at time interval $t$. The generator task aims to synthetically generate the mapping source network encoding that closely reflects the missing source network encoding $E_{sn}(\boldsymbol{sn_{u}^{t}})$. Hence, $G$ uses target encoding $E_{tn}(\boldsymbol{tn_{u}^{t}})$ and attempts to generate the mapping source encoding to fool $D$. Similarly, $D$ tries to differentiate between real source encoding $E_{sn}(\boldsymbol{sn_{u}^{t}})$ and generated encoding $G(E_{tn}(\boldsymbol{tn_{u}^{t}}))$. Note that, we refer to the actual and generated target and source network encodings of non-overlapped users $\big{(}E_{tn}(\boldsymbol{tn_{u}^{t}}),G(E_{tn}(\boldsymbol{tn_{u}^{t}}))\big{)}$ as synthetically mapped data and the actual target and source network encodings of overlapped users $\big{(}E_{tn}(\boldsymbol{tn_{u}^{t}}),E_{sn}(\boldsymbol{sn_{u}^{t}})\big{)}$ as real mapping data.

Once $D$ and $E$ are trained, they adversarially guide $G$ by effectively identifying real and synthetically generated data. Specifically, $G$ takes in a target network encoding $E_{tn}(\boldsymbol{tn_{u}^{t}})$ and synthetically generates the mapping source network encoding that resemble $E_{sn}(\boldsymbol{sn_{u}^{t}})$ drawn from real mapping data.

Let $E_{tn}(\boldsymbol{tn_{u}^{t}}),G(E_{tn}(\boldsymbol{tn_{u}^{t}}))$ denote a non-overlapped user $u$ at time $t$ based on synthetically mapped data, which reflects current preferences. To capture previous preferences, we used a previous interaction vector $R_{u}^{t-}\in\mathbb{R}^{M}$, where $M$ is the number of items. Each element $r_{{u},i}^{t-}\in\boldsymbol{R_{u}^{t-}}$ is set to 1 if the user had an interaction with item $i$ before time $t$, and 0 if otherwise. Thus, we formulated the recommender task as a time aware Top-N ranking task where, current and previous user preferences are used to predict a set of $N$ items that the user is most likely interact with, in the next time interval $t+1$.

Typically, BPR optimization is performed using Stochastic Gradient Descent (SGD) where, for each training instance $(u,i,j)$, parameter ($\Theta$) updates are performed as follows:

where $\alpha$ is the learning rate, $\hat{r}_{uij}=\hat{r}_{ui}-\hat{r}_{uj}$ is the pairwise loss for a given $(u,i,j)$ triplet and $\hat{r}_{ui}$ is the predicted rating for user $u$ and item $i$. Since BPR is a generic optimization criterion, $\hat{r}_{ui}$ can be obtained using any standard collaborative filtering approach (e.g., MF). Considering the rating prediction function in MF ($\hat{r}_{ui}=\sum_{f=1}^{K}\boldsymbol{w_{uf}}\cdot\boldsymbol{h_{if}}$, where $\boldsymbol{w_{uf}}\in\mathbb{R}^{K}$ and $\boldsymbol{h_{if}}\in\mathbb{R}^{K}$ are latent representations of user $u$ and item $i$), $\hat{r}_{uij}$ for MF based BPR optimization can be defined as $\hat{r}_{uij}=\sum_{f=1}^{K}w_{uf}\cdot(h_{if}-h_{jf})$.

For each $(u,i,j)$ instance, three updates are performed when $\Theta=w_{uf}$, $\Theta=h_{if}$ and $\Theta=h_{jf}$. For each update on the latent user representation ($w_{uf}$), two updates are performed on the latent item representations $(h_{if}$ and $h_{jf})$. Hence, the training process is biased towards item representation learning, and we term the standard BPR optimization function as an item-based pairwise loss function. Since our goal is to learn effective user representations to conduct quality recommendations, we introduce a user-based pairwise loss function ($R$ loss), which is biased towards user representation learning.

We used a fixed time-length sliding window approach in the training process where, at each time interval, the model is trained using the interactions within the time interval (see Section 3.2.1). Thus, we denote the training instances for the new user-based BPR at each time interval $t$ as $S^{t}=\{(u,v,i)|u\in U_{i+}^{t}\land v\in U\setminus U_{i+}^{t}\land i\in I\}$ where $U_{i+}^{t}$ is the set of users who have interactions with item $i$, at time $t$. Compared to $(u,i,j)$ in the standard item-based BPR, user-based BPR contains $(u,v,i)$ where, for item $i$ at time $t$, user $u$ has an interaction and user $v$ does not. Thus, intuitively, the predictor should assign a higher score for $(u,i)$ compared to $(v,i)$. Accordingly, we defined the user-based loss function to be minimized as follows:

where $\hat{r}_{uvi}^{t}=\hat{r}_{ui}^{t}-\hat{r}_{vi}^{t}=\sum_{f=1}^{K}(w_{uf}^{t}-w_{vf}^{t})h_{if}$. During optimization, $\Theta$ updates are performed as follows:

For different $\Theta$ values, the following partial derivations are obtained:

We used a Siamese network for the recommender architecture since it naturally supports pairwise learning (see Figure 2). Given a non-overlapped user $u$ with current preferences $E_{tn}(\boldsymbol{tn_{u}^{t}}),G(E_{tn}(\boldsymbol{tn_{u}^{t}}))$ and previous preferences $\boldsymbol{R_{u}^{t-}}$ at time $t$, we learned a transfer function $\Phi$, which maps the user to the latent user space $w_{u,f}^{t}$ for recommendations as follows:

The transfer function $\Phi$ is learned using a neural network since neural networks are more expressive and effective than simple linear models. Accordingly, for a non-overlapped user $u$ at time $t$, the predicted rating $\hat{r}_{ui}$ for any given item $i$ is obtained using the inner-product between the latent user and item representations as follows:

We used the sliding window approach and data from the first 16 months ($2T/3$) of overlapped users to learn the mapping from target to source network preferences for the generator task, the neural transfer function $(\Phi)$, and item latent representations $(h_{if})$ for the recommender task. At each training epoch, the generator task is learned first. Hence, $E$, $D$ and $G$ are trained using real mapping data and the trained $G$ is used to generate synthetically mapped data. The generated preferences are used as inputs to the recommender task to predict interactions at the next time interval. The ground truth interactions at the same time interval are used to propagate the recommender error from the recommender to the generator task and learn parameters of both processes.

We used data from the last 8 months ($2T/3$ onward) to test and retrain the model online in a simulated real-world environment. At each testing time interval $t$, first, mapping source network preferences are generated for non-overlapped users based on their target network preferences. Second, the synthetically mapped data for non-overlapped users are used as inputs to conduct Top-N recommendations for $t+1$ (see Equation 9). The entire model is then retrained online before moving to the next time interval, as follows: First, the recommender parameters $(\Phi$ and $\boldsymbol{h_{if}^{t}})$ are updated based on the recommendations for both overlapped and non-overlapped users. Second, the components of the generator task $(E$, $D$ and $G)$ are updated based on the real mapping data from overlapped users. Finally, to guide $G$ from the training signals of the recommender, the model synthesizes mapping data for overlapped users, which are used as inputs for recommendations. The error is back-propagated from the recommender task to $G$, and consequently, the parameters $G$, $\Phi$ and $\boldsymbol{h_{if}^{t}}$ are updated. This process is repeated at subsequent time intervals as the model continues the online retraining process. In line with common practices in sliding window approaches, the model is retrained multiple times before moving to the next time interval.

We evaluated CnGAN against single network, cross-network, linear factorization and GAN based baselines.

• •

  TimePop: Recommends the most popular $N$ items in the previous time interval to all users in the current time interval.

• •

  TBKNN (Campos et al., 2010): Time-Biased KNN computes a set of $K$ neighbors for each user at each time interval based on complete user interaction histories, and recommends their latest interactions to the target user at the next time interval. Similar to the original work, we used several $K$ values from 4 to 50, and the results were averaged.

• •

  TDCN (Perera and Zimmermann, 2017): Time Dependent Cross-Network is an offline, MF based cross-network recommender solution, which provides recommendations only for overlapped users. TDCN learns network level transfer matrices to transfer and integrate user preferences across networks and conduct MF based recommendations.

• •

  CRGAN: Due to the absence of GAN based cross-network user preference synthesizing solutions, we created Cross-network Recommender GAN, as a variation of our solution. Essentially, CRGAN uses the standard $D$ and $G$ loss functions and does not contain the $L_{mismatch}$ and $L_{content}$ loss components.

• •

  NUBPR-O and NUBPR-NO: Due to the absence of neural network based cross-network recommender solutions, we created two Neural User-based BPR solutions, as variations of our solution. Essentially, both models do not contain the generator task. NUBPR-O considers both source and target network interactions and NUBPR-NO only considers target network interactions to conduct recommendations.