GS²-RS: Generating Self-Serendipity Preference in Recommender Systems for Addressing Cold Start Problems

Given a recommender system, which contains $M$ users and $N$ items, the user-item rating matrix $R$ is a $M\times N$ low-rank sparse matrix, where its entity $r_{ij}$ stands for the rating that user $i$ marked for item $j$, ranging from [1,2,3,4,5]. Note that in real-world scenarios, $R$ is usually extremely sparse (more than 90% data is unknown to learning models), meaning there are many “?” in $R$.

We focus on original rating-based RS, which means that for achieving a Top-K recommendation task, the input of our model is only the original user-item rating matrix $R$. However, the sparsity of $R$ usually leads to the cold-start (CS) problem and the filter-bubble (FB) problem (Chae et al. 2020), as shown in Figure 2. Cold-start problem: The extreme sparsity may confuse the RS models to infer inaccurate preferences of users on candidate items, which causes item- and user-based CS problems. Filter-bubble problem: Some models pay so much attention to existing ratings that the more ratings an item has, the more chances it can be recommended to users. In Figure 2, as a FB problem, the item with rating [1,4,4] dominate other items to be recommended in some existing models, like CF models (Chen et al. 2020a). Both the problems affect recommender systems’ performance and affect users’ shopping experience.

To tackle the problem above, we are inspired by (Chae et al. 2020), which utilizes GANs to generate users’ virtual neighbors for enhancing CF models. However, this model can not consider the FB problem because it directly generates the virtual neighbors’ rating without inferring users’ preferences. Along with this line, we first introduce users’ two type perferences: interest and satisfaction preferences: Interest: for a user $u$ and an item $i$ in a candidate itemset $i\in I_{u}^{\text{can}}$, if $r_{ui}\neq?$, which means that $u$ has the interest to buy $i$, we define user’ interest preference $r^{\text{in}}_{ui}=1$, $r^{\text{in}}_{ui}\in R^{\text{in}}$, $i\in I_{u}^{\text{in}}$. Satisfaction: for a user $u$ and an item $i\in I_{u}^{\text{in}}$, if $r_{ui}\geq\alpha_{ui}$, we define user’s satisfaction preference $r^{\text{sa}}_{ui}=1$, $i\in I_{u}^{\text{sa}}$; else $r^{\text{sa}}_{ui}=0$, $r^{\text{sa}}_{ui}\in R^{\text{sa}}$. Note that the threshold $\alpha_{ui}$ can be defined as either $u$ or $i$’s average rating, or other contextual values. In our proposed model, we first extract users’ historical preferences, as shown in Figure 3.

Meanwhile, we analyze users’ preferences at a fine-grained level. We introduce users’ serendipity items: the items with high relevance but low shopping purpose (Yang et al. 2018). For common situations, these items can produce a wonderful purchasing experience once the users buy them. So recommend serendipity items can achieve better diversity and satisfaction. By considering serendipity items, the filter-bubble problem can be relieved effectively.

This section introduces how we deduce users’ multiple preferences, including users’ virtual interest and satisfaction preferences, based on Conditional Generative Adversarial Nets (CGAN) (Mirza and Osindero 2014), a framework to train generative models with complicated, high-dimensional real-world data such as images. Specifically, CGAN is an extension to the original GAN (Goodfellow et al. 2014): it allows a generative model $\mathcal{G}$ to produce date according to a specific condition vector c by treating the desired condition vector as an additional input with the random noise input z. Thus, CGAN’s objective function is formulated as follows:

where x is a ground truth data from the data distribution $p_{\text{data}}$, $z$ is a noise input vector sampled from known prior $p_{\textbf{z}}$. $\mathcal{G}(\textbf{z})$ is a synthetic data from the generator distribution $p_{\textbf{g}}$. $c$ corresponds to a condition vector such as a one-hot vector of a specifc class label. With the optimal objective $\mathop{\min}\limits_{\mathcal{G}}\mathop{\max}\limits_{\mathcal{D}}V(\mathcal{D,G})$. Ideally, the completely trained $\mathcal{G}$ is expected to generate realistic data that the discriminative model $\mathcal{D}$ evaluates the possibility that the data came from the ground truth rather than from $\mathcal{G}$ equals 0.5.

After we extract users’ interest and satisfaction preferences $R^{\text{in}},R^{\text{sa}}$, we build two CGANs for each type of preferences, respectively. The training procedure is shown in Figure 4. Note that we apply the same CGAN framework on interest and satisfaction preferences, respectively. For the sake of simplicity, we take interest preferences as the example and briefly introduce how this framework can be properly deployed on satisfaction preferences. Formally, we train our two CGANs as follows:

where $\textbf{c}_{u}^{\text{in}}$ denotes $u$’s interest condition vector, $\textbf{z}_{u}^{\text{in}}$ denotes $u$’s noise vector, $\textbf{r}_{u}^{\text{in}}$ denotes $u$’s interest vector, $\textbf{f}_{u}^{\text{in}}$ denotes the interest indicator vector. Note that $\textbf{f}_{u}^{\text{in}}$ is in the same dimension as $\textbf{r}_{u}^{\text{in}}$, and each entity $f_{ui}^{\text{in}}$ of $\textbf{f}_{u}^{\text{in}}$ is $1/0$ to indicate that there is/not an interest value for item $i$.

In Formula 2, $\mathcal{G}_{\text{r}}^{\text{in}}$ and $\mathcal{G}_{\text{f}}^{\text{in}}$ are employed to produce $u$’s synthetic interest vector and interest indicator vector, denoted as $\overline{\bf{r}}_{u}^{{\rm{in}}}$, $\overline{\bf{f}}_{u}^{{\rm{in}}}$. While $\mathcal{D}_{\text{r}}^{\text{in}}$ and $\mathcal{D}_{\text{f}}^{\text{in}}$ are employed to distinguish real interest vector ${\bf{r}}_{u}^{{\rm{in}}}$, indicator vector ${\bf{f}}_{u}^{{\rm{in}}}$ from synthetic vectors $\overline{\bf{r}}_{u}^{{\rm{in}}}$, $\overline{\bf{f}}_{u}^{{\rm{in}}}$, respectively. Specifically, there are two designs in this framework: first, each $\mathcal{G}$’s outputs’ value are restricted to the range of (0 1) for computing with a Layer Normalization; second, a masking operation is employed to avoid useless computations: ${({\bf{z}}_{u}^{{\rm{in}}}|{\bf{c}}_{u}^{{\rm{in}}})\bullet{\rm{f}}_{u}^{{\rm{in}}}}$. This element-wise dot operation forces the discriminators to focus on the values $r^{\text{in}}_{ui}$ in interest vector ${\bf{r}}_{u}^{{\rm{in}}}$, which contributes to the computing results. Besides, the masking operation relieves the data sparsity issue. All $\mathcal{D},\mathcal{G}$ are co-trained and deployed by DNN where the stochastic gradient descent (SGD) with minibatch and the back-propagation algorithm are employed.

Similar as interest preferences, satisfaction preferences can be modeled as follows:

After the training of our CGANS, we are ready to generate users’ virtual preferences, including interest and satisfaction. With these virtual preferences, we aim at deducing users’ self-serendipity preferences for an accurate recommendation.

The usage of GS²-RS is shown in Figure 5. With four well-trained generators $\mathcal{G}_{\text{r}}^{\text{in}}$, $\mathcal{G}_{\text{f}}^{\text{in}}$, $\mathcal{G}_{\text{r}}^{\text{sa}}$, $\mathcal{G}_{\text{f}}^{\text{sa}}$, we feed objective user $u$’s condition vectors $\textbf{c}_{u}^{\text{in}}$, $\textbf{c}_{u}^{\text{sa}}$, and noise vectors $\textbf{z}_{u}^{\text{in}}$, $\textbf{z}_{u}^{\text{sa}}$, we can achieve the synthetic vectors $\overline{\bf{r}}_{u}^{{\rm{in}}}$, $\overline{\bf{f}}_{u}^{{\rm{in}}}$, $\overline{\bf{r}}_{u}^{{\rm{sa}}}$, $\overline{\bf{f}}_{u}^{{\rm{sa}}}$, which are formulated as follows:

where ^∗ denotes either ${}^{\text{in}}$ or ${}^{\text{sa}}$. For each objective user, our propose model can generate several synthetic ${\overline{\rm{\textbf{r}}}_{u}^{*}}{\rm{,}}{\overline{\rm{\textbf{f}}}_{u}^{*}}$ pairs. Generally, we treat each vector pairs as a virtual user $u^{\prime}$ for the objective user $u$, named self neighbors. And each virtual user $u^{\prime}$’s preferences can be formulated as follows:

Note that the number of virtual users can be tuned for better performance. We will discuss it in our experiment section. For the sake of simplicity, we only generate $t$=2 self neighbors here for explanations, as shown in Figure 5. Then we feed the virtual user $u^{\prime}$’s preference vectors and original user $u$’s preference vector $\textbf{r}^{*}$ into existing CF models to achieve self preference ${\bf{\bar{r}}}^{*}_{u}$ (Formula 6), for interest and satisfaction, respectively. This operation can generate two enhanced preference matrices ${\bar{R}^{\text{in}}}$, ${\bar{R}^{\text{sa}}}$. Note that we can achieve these two matrices with different operations among original vectors and their virtual neighbors, such as average, threshold mechanism, collaborative filtering, etc.

Then serendipity fusion operation is employed for marking each potential candidate item for objective users. First, we give a reminder of serendipity items: the items with high relevance but low shopping purpose (Yang et al. 2018). With this consideration, intuitively, we can deduce that the items with high satisfaction but low interest should be marked as serendipity items, which means that the objective user would achieve a much better experience after buying them. To achieve the serendipity item set, we set the thresholds $\theta^{*}$ for interest and satisfaction, respectively. The item with $r^{\text{sa}}\geq\theta^{\text{in}}$ but $r^{\text{in}}<\theta^{\text{in}}$ is marked as $s_{ui}$=1. For each user, there is an indicator $\textbf{s}_{u}$ to mark his serendipity items.

One of our contributions is to solve the cold-start problem. The reason for the cold-start issue is the sparsity of the user-item matrix. Thus we employ a zero matrix injection to relieve the sparsity issue. Unlike existing matrix injection methods, we do not inject the potential candidate items into the user-item matrix. Instead, we pick impossible items to filter the candidate items. The reason is that 1) the rating deduction from users’ preferences is usually tricky and inaccurate, with many uncontrollable factors. 2) In real-world scenarios, the potential items of an objective user take a relatively small partition from thousands or millions of unobserved items. So adding zeros for impossible items could relieve the sparsity issue greatly.

While we filter the items with two vectors ${{\bf{\bar{r}}}^{{\text{in }}}_{u}}$ and ${{\bf{\bar{r}}}^{{\text{sa}}}_{u}}$ for user $u$’s zero injections, there are several situations with different values (${{\bar{r}}^{{\text{in }}}_{ui}}$ and ${{\bar{r}}^{{\text{sa}}}_{ui}}$, $i$-th is the location index of both vectors), respectively. Note that the ${{\bf{\bar{r}}}^{{\text{in }}}_{u}}$ and ${{\bf{\bar{r}}}^{{\text{sa}}}_{u}}$ are computed by Formula 5, and the element value is [$\bar{r}^{*}_{ui}$, 0, ?], $0<\bar{r}_{ui}\leq 1$. Generally, we obey the following principles to inject $r^{\text{h}}_{ui}=0$ into enhanced matrix $\textbf{R}^{\text{h}}$:

• •

  If ${{\bar{r}}^{{\text{in}}}_{ui}}<\theta^{\text{in}}$ and ${{\bar{r}}^{{\text{sa}}}_{ui}}<\theta^{\text{sa}}$, inject $r^{\text{h}}_{ui}=0$;

• •

  If ${{\bar{r}}^{{\text{in}}}_{ui}}<\theta^{\text{in}}$/${{\bar{r}}^{{\text{sa}}}_{ui}}<\theta^{\text{sa}}$, and ${{\bar{r}}^{{\text{sa}}}_{ui}}/{{\bar{r}}^{{\text{in}}}_{ui}}=?$, inject $r^{\text{h}}_{ui}=0$;

• •

  Else, we set $r^{\text{h}}_{ui}=r_{ui}$.

Intuitively, the impossible item set for recommendations consists of low interest and low satisfaction (below the thresholds) items. Also, we inject 0s for the items with an unknown preference (?) and a low interest/satisfaction preference. As far as we know, these 0s can relieve the user-item matrix’s sparsity. Moreover, the enhanced user-item matrix $\textbf{R}^{\text{h}}$ can give more meaningful feedback to indicate users’ preferences on items and reduce the unknown feedbacks, which relieves the cold-start problem. While for the items/users with few or zero feedbacks (new items/users in recommender systems) in original user-item matrix R, our proposed model can inject some zeros as an initialization. It relieves the new user/item cold-start problem. Note that these zeros are temporary, not fixed. Once the original user-item matrix has been updated to a large extent (utilizes many new $r_{ui}$ to replace ?), We can employ GS²-RS again to update $\textbf{R}^{\text{h}}$.

With $\textbf{R}^{\text{h}}$ as input (replacing original R), and interest matrix ${{\bar{\textbf{R}}}}^{\text{in}}$, satisfaction matrix ${\bar{\textbf{R}}}^{\text{sa}}$ and self-serendipity matrix S as side information inputs, we can achieve different types (Top-k, CTR, or next purchase, etc) recommendation results L with different RS models:

The complete GS²-RS model is described in Algorithm 1:

This section introduces how our proposed model enhances the SOTA recommender systems and solves the filter-bubble problem.

The overall performance across two datasets is shown in Table 2. Generally speaking, GS²-RS outperforms all compared models on both datasets for all metrics. The improvement can be attributed to two aspects: 1) The improvement from two GAN-based models (AR-CF and GS²-RS) over other models indicates that the usage of GAN on sparse matrices is obvious for recommendations. 2) GS²-RS can enhance performance by generating their virtual preferences, which is effective than directly generating their virtual ratings on items, which can be indicated from GS²-RS’s improvement on AR-CF.

Moreover, as we claimed, GS²-RS can be applied as the preprocessing for SOTA RS models, which are shown in Figure 6. We observe that our proposed model can enhance the SOTA models’ Precision and NDCG performance on Movielens. GS²-RS universally and consistently provide the best accuracy, and we believe that the benefits are credited to GS²-RS’s characteristics that it can take advantage of the performance gains coming from the generated virtual (but plausible) users’ preferences as qualified training data.

The problem with the cold-start items is that they are challenging to be recommended. So we employ Exposure Ratio (ER) to evaluate the performance for solving the cold-start problem. We employ NCF, JoVA, AR-CF as baselines compared with GS²-RS, as shown in Figure 7. T$\%$denotes the bottom percentage of items that have interactions with users, and we treat these items as cold-start items. We observe that NCF and JoVA have difficulty solving the cold-start problem, and AR-CF and our model outperform them considerably. Meanwhile, because our proposed model generates users’ preferences, not ratings, GS²-RS performs better than AR-CF. Jointly considered with accuracy results in Figure 6, the results demonstrate the effectiveness of our model in solving cold-start issues with a stable recommendation performance.

We utilize Diversity and Serendipity to evaluate the performance for solving the filter-bubble problem, as shown in Figure 8. From the results, we observe that 1) GS²-RS can improve the diversity and serendipity significantly, especially on sparse dataset Amazon. 2) JoVA achieves a second-best accuracy performance but a relatively low diversity and serendipity compared with other baselines. With a high diversity and serendipity, we can offer users an attractive and exciting recommendation instead of a boring, repeated one, greatly relieving the filter-bubble problem.

We validate the effect of $\theta$, the most vital threshold of GS²-RS, ranging (0.0, 1,0) with step 0.1. Note that we set $\theta^{\text{in}}$=$\theta^{\text{sa}}$=$\theta$ for validation, as shown in Figure 9. From the results, we observe that GS²-RS achieves the best performance at $\theta$=0.5. When $\theta$ is descending to 0, GS²-RS can not filter any items, which fades to a basic GAN-based model. When $\theta$ is ascending to 1, GS²-RS drops every item and damages its performance.