Knowledge Graph Context-Enhanced Diversified Recommendation

We introduces the two data structures: user-item interaction graph, knowledge graph and the formulated problem.

User-Item interactions graph. We consider a collection of users denoted as $\mathcal{U}$, and a set of items represented by $\mathcal{I}$, where $m$ and $n$ correspond to the number of users and items, respectively. We establish a user-item bipartite graph $\mathcal{G}=\{\mathcal{V},\mathcal{E}\}$, where $\mathcal{V}=\{\mathcal{U},\mathcal{I}\}$ denotes the node set, and $\mathcal{E}$ represents the edge set. An edge $(u,i)\in\mathcal{E}$ signifies that the user $u$ purchased the item $i$ before.

Knowledge graph. Knowledge graph is defined as $\mathcal{G}_{K}=\{(h,r,t)\}$, where each triplet represents a relation $r\in\mathcal{R}$ from the head entity $h\in\mathcal{E}$ to the tail entity $t\in\mathcal{E}$. Here, $\mathcal{E}$ and $\mathcal{R}$ represent the sets of entities and relations within KG, respectively. Notably, the entity set $\mathcal{E}$ comprises both items ($\mathcal{I}$) and non-item entities ($\mathcal{E}\textbackslash\mathcal{I}$).

Task Description. Given the $\mathcal{G}$ and $\mathcal{G}_{K}$, the goal of knowledge-aware recommendation is to recommend top $k$ items to each user. Moreover, the diversified recommendation task in KG encourages more entities (or relations) covered by recommended items.

KG is a multi-relational graph comprising entities and relations, denoted by a set of triplets, i.e., $(h,r,t)$. To facilitate understanding, we denote $N_{i}=\{(r,v)|(i,r,v)\in\mathcal{G}_{K}\}$ to represent the corresponding relations and entities connected to the item $i$. A single entity may participate in multiple KG triplets, and it possesses the ability to adopt the linked entities as its attributes, thus revealing content similarity among items. Take an example in Figure 1, the star Chris Evans involves in multiple KG triplets, i.e., (actor, The Avengers), (actor, Before We Go), and (director, Before We Go). Then, we perform an aggregation technique to integrate the semantic information from $N_{i}$ to generate the representation of item $i$:

where $\textbf{e}_{i}^{(l-1)}$ and $\textbf{e}_{v}^{(l-1)}$ represent the embedding of item $i$ and entity $v$ after $l-1$ layers aggregation respectively, and $\textbf{e}_{r}$ is the embedding of relation $r$. $\textbf{e}_{i}^{(l)}$ is the aggregated representation obtained by $f(\cdot)$ which is the aggregation function that integrates information from ego-network $N_{i}$ of item $i$. Regarding the function $f(\cdot)$, prior research efforts (Wang et al., 2019) predominantly focus on incorporating the relation $r$ solely into the weight factors during propagation. Nevertheless, it is vital to acknowledge that the combination of connected relation and entity $(r,v)$ holds distinct contextual implications. For instance, consider the star Chris Evans, who is linked twice to the film Before We Go in KG triplets, each time in a different role (director and actor). To address this contextual difference effectively, it becomes imperative to integrate relational contexts into the aggregator $f(\cdot)$. It not only facilitates discerning the diverse effects of relational nuances but also augments the overall diversity of relations within the model. Therefore, we model the relation into the aggregation function $f(\cdot)$ following (Wang et al., 2021a):

where $\odot$ is the element-wise product. The relational message $\textbf{e}_{r}\odot\textbf{e}_{v}^{(l-1)}$ is propagated by modeling the relation $r$ as either a projection or rotation operator (Sun et al., 2019). This design allows the relational message to effectively unveil distinct meanings inherent in the triplets.

After obtaining item embedding representation $\textbf{e}_{i}^{(l)}$ from $l$-th layer of knowledge graph, we leverage it to generate diversified user embedding. We denote $\mathcal{N}_{u}=\{i|(u,i)\in\mathcal{E}\}$ to represent the $u$’s interacted items. Then, we formulate the temporary user representation by applying mean pooling on the interacted items:

In this way, the user representation is expressed by the representation of adopted items. The motivation of conventional RecSys revolves around aligning the representations of users and their purchased items. For example, in the left part of Figure 2, the user $u$ interacted with $i_{1}$, $i_{2}$, and $i_{3}$. A common approach involves driving the vector representation of user $u$ to approximate the vectors of items $i_{1}$ and $i_{2}$, as these two items display high similarity due to their overlapping connections on the KG. However, it localizes the representation of $u$ in the surrounding area of $i_{1}$ and $i_{2}$ with their connected entities in KG (i.e., $v_{1}$, $v_{2}$, and $v_{3}$), which makes it hard to be exposed to the diverse items and entities around $i_{3}$ (i.e., $i_{4}$ and $v_{5}$). Hence, we devise the user diversified embedding learning layer with the intent of liberating the user representation from localization constraints and fostering diversity. The temporary user representation $\textbf{e}^{(l)}_{u_{\text{temp}}}$, where temp is short for temporary, is utilized to measure the dissimilarities with $\textbf{e}_{i}^{(l)}$ in the $l$-th layer:

Here, we utilize the Euclidean distance to compute dissimilarity, as it serves as a reliable measure to gauge the level of diversity. A higher distance value implies a greater potential for diversity in the resulting outcomes. The abundance of similar items may confine the user representation, resulting in a resemblance to these item representations. To counteract this, we mitigate the issue while preserving the intrinsic preference by generating diversity-aware embedding for the user through the following step:

Consequently, the user representation is emancipated from the constraints of localization, which often result from an abundance of similar items. For instance, $\textbf{e}_{u}$ will be compelled to distance itself from $\textbf{e}_{i}$ and $\textbf{e}_{2}$, while drawing nearer to $\textbf{e}_{3}$, thereby facilitating access to novel entities and items (e.g., $i_{4}$ and $v_{5}$). Moreover, stacking multiple layers has been empirically demonstrated to effectively exploit high-order connectivity (Wang et al., 2019, 2021a). Therefore, the $\textbf{e}_{u}^{(l)}$ can capture diverse information from $l$-hop neighbors of linked items, thereby enhancing exposure to diverse entities explicitly. We further sum up the embeddings obtained at each layer to form the final user and item representation, respectively:

where $L$ is the number of knowledge graph propagation layers.

To effectively encode KG in RecSys, we design a novel conditional alignment on KG entity embedding to preserve the semantic information between two similar items. Consider item $i_{1}$ and item $i_{2}$, both sharing the entities $v_{1}$ and $v_{2}$. Rather than a straightforward alignment (Wang et al., 2022b; Yang et al., 2023a), the item representations $\textbf{e}_{i_{1}}$ and $\textbf{e}_{i_{2}}$ should be aligned based on the shared information of entity representations $\textbf{e}_{v_{1}}$ and $\textbf{e}_{v_{2}}$. We define conditional embedding as follows:

where $O_{i_{1},i_{2}}$ is the set of entities shared by item $i_{1}$ and item $i_{2}$ in KG and $\textbf{e}_{v_{\text{overlap}}}=\frac{1}{|O_{i_{1},i_{2}}|}\sum_{v\in O_{i_{1},i_{2}}}\textbf{e}_{v}$ is the average embedding of the overlapping entities between item $i_{1}$ and item $i_{2}$. After modeling the overlapping entities as the projection or rotation on two items, we then perform the alignment loss:

This design plays an essential role in pulling two similar items closer according to their connectivity on KG. Furthermore, the uniformity loss (Yu et al., 2022) is also applied to scatter the embedding uniformly:

After performing $L$ propagation layers in KG, we further employ convolutional operation to capture collaborative signals from user-item interaction. Due to the effectiveness and simple architecture of LightGCN (He et al., 2020), where feature transformation and activation function are removed, we adopt its Light Graph Convolution layer (LGC) to encode the collaborative signals from user-item interactions:

where $\mathbf{e}_{u}^{(k)}$ and $\mathbf{e}_{i}^{(k)}$ are the embedding of user $u$ and item $i$ at the $k$-th LGC layer, respectively. Meanwhile, $\mathbf{e}_{u}^{(0)}$ and $\mathbf{e}_{i}^{(0)}$ are the embedding obtained by Eq. 7. Following $K$ layers of propagation, we integrate the embeddings acquired at each layer into the ultimate embeddings for both users and items:

The embeddings produced by different LGC layers stem from distinct receptive fields, which also facilitates diversity from high-order neighbors. We choose the BPR loss (Rendle et al., 2012) for the optimization:

where $\mathcal{O}=\{(u,i,j)|(u,i)\in\mathcal{E},(u,j)\in\mathcal{E}^{-}\}$. $\mathcal{E}^{-}$ is the set of unobserved interactions, and the $j$ is sampled from items that user $u$ has not interacted. Finally, the overall loss function is defined as:

where $\lambda_{1}$ and $\lambda_{2}$ decide the weight of alignment and uniformity loss, respectively, and $\lambda_{3}$ denotes the parameter regularizing factor.

We explore the effects of each module in KG-Diverse on the Amazon-book dataset, including (1) KG propagation layer for item representation learning, (2) Relation encoding into item representation in Eq. 2, (3) Diversified Embedding Learning (DEL) module in generating user diversity-aware representations, and (4) Conditional Alignment and Uniformity (CAU) that regularizes KG embedding learning. The results are shown in Table 3:

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  After removing the KG propagation layer, the knowledge within entities and relations will not be incorporated to enrich the item representations, and there is a single layer to generate user diversified representation without KG. Even though there are 2.7% and 5.5 % improvements on R@20 and N@20, respectively, the performance on EC@20 decreased by 7.1%. It shows the effectiveness of learning entity-aware item representation via Eq. 2.

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  Upon removing relation encoding, the item representation in $l$-th layer is obtained by averaging the embeddings of its connected entities in the previous layer. The results indicate significant decreases in all evaluation metrics, particularly a 5.9% drop in RC@20. It indicates the crucial role of relations in enriching item representations. The presence of relations in the encoding process allows the model to capture and leverage the semantic connections between items and entities, contributing to more accurate and diverse recommendations.

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  In the $l$-th KG propagation layer, the user diversity-aware embedding $\textbf{e}_{u}^{(l)}$ in Eq. 6 is replaced by $\textbf{e}^{(l)}_{u_{\text{temp}}}$ in Eq. 3 if DEL is removed. The declines in all four metrics: R@20 decreased by 4.3%, N@20 decreased by 7.0%, EC@20 decreased by 3.4%, and RC@20 decreased by 2.1%, underscores our model’s advantage in enabling user representations to transcend localization constraints.

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  Without conditional alignment and uniformity, there are substantial drops in R@20, N@20, and EC@20 metrics. This underscores the crucial role played by the regularization on KG embedding learning, as it serves as the foundational prerequisite for KG application. We find that the similarity and distinctions among items in the KG significantly influence the overall framework.

Additional exploratory experiments are conducted to comprehensively understand the KG-Diverse structure and investigate the underlying reasons for its effectiveness. We explore the effects of four essential hyper-parameters in KG-Diverse on Last.FM dataset, including the number of KG propagation layers $L$, the coefficient $\lambda_{1}$ on alignment loss, and the weight decay $\lambda_{2}$ on uniformity loss.

In this case study, we randomly selecte a user, $u_{52279}$, from the Amazon-book dataset to compare the entity and relation coverages of two recommendation models: KGIN and KG-Diverse. The visualization of their performance comparison is illustrated in Figure 5. From both models, we retrieved the top-5 recommendations for $u_{52279}$, with $i_{4079},i_{4075},i_{1153},i_{3613}$ being common items recommended by both models. To simplify the analysis, we focus on two distinct recommended items: $i_{6583}$ from KGIN and $i_{1041}$ from KG-Diverse. We have the following observations:

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  The item $i_{6583}$ with the name The Affair covers only a few entities and relations, namely $N_{\text{The Affair}}$ = ((Genre, Noval), (Author, Lee Child)). Remarkably, the item $i_{1041}$ recommended by our model, KG-Diverse, also includes these two pairs of entities and relations. It exemplifies the strong relevance and effectiveness of KG-Diverse in providing relevant recommendations.

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  In addition to the strong relevance, the item $i_{1041}$ titled Echo Burning covers a significantly broader range of entities and relations in the KG compared to $i_{6583}$. The entities and relations covered by $i_{1041}$ include (Genre, Suspense), (Genre, Fiction), (Subjects, Adventure), (Subjects, Texas). It underscores the substantial capacity of KG-Diverse in enhancing the diversity of recommendations. By recommending items like Echo Burning, which encompass a wide variety of entities and relations, KG-Diverse successfully introduces diversity and enriches the user experience by offering a more varied and engaging selection of recommendations.

CKE (Zhang et al., 2016) model enriches the item representation by incorporating (1) structural embedding learned from items’ structural knowledge via TransR, (2) textual and visual representations extracted by applying two different auto-encoders on textual and visual knowledge separately. DKN (Wang et al., 2018), a news recommendation model, fuses semantic-level and knowledge-level information to news embedding by a multi-channel and word-entity-aligned knowledge-aware convolutional neural network (KCNN) (Kim, 2014). The user’s vector is aggregated from the attention-weighted sum of news he/she clicked. KGIN (Wang et al., 2021a) models a finer-grained level of each intent by a combination of KG relations and designs a relational path-aware aggregation scheme that integrates information from high-order connectivities. KGAT (Wang et al., 2019) is designed to update embeddings by recursive propagation to capture high-order connectivities and compute the attention weights of a node’s neighbors which aggregate information from high-order relations during propagation. KGCL (Yang et al., 2022) defines knowledge graph structure consistency score to identify items less sensitive to structure variation and tolerate noisy entities in KG. MetaKRec (Wang et al., 2022a) extracts KG triples into direct edges between items via prior knowledge and achieves improved performance with graph neural network.

While the mentioned works primarily concentrate on enhancing the accuracy of recommendations by leveraging KG, our work distinguishes itself by focusing on elevating the diversity of recommendations at a fine-grained level while ensuring accuracy.

Diversified recommendation technique is used to provide users with a diverse set of recommendations rather than a narrow set of highly similar items. The concept of diversified recommendation was first proposed by Ziegler et al. (Ziegler et al., 2005). They performed a greedy algorithm to retrieve the diversified top-K items. DUM (Ashkan et al., 2015) designs the submodular function to select items by a greedy method and balance the utility of items and diversity in the re-ranking procedure. Determinantal point process (DPP) (Chen et al., 2018b), a post-processing method, retrieves the set of diverse items depending on the largest determinant of the item similarity matrix with MAP inference. DGCN (Zheng et al., 2021) stands as the initial diversified recommendation approach based on GNNs. It adopts the inverse category frequency to select node neighbors for diverse aggregation and employs category-boosted negative sampling and adversarial learning to enhance item diversity within the embedding space. DGRec (Yang et al., 2023c) is the current state-of-the-art model that produces varied recommendations through an enhanced embedding generation process. The proposed modules (i.e., submodular neighbor selection, layer attention, and loss reweighting) collectively aim to boost diversity without compromising accuracy. DivKG (Gan et al., 2020) learns knowledge graph embeddings via TransH (Wang et al., 2014) and designs a DPP kernel matrix to ensure the trade-off between accuracy and diversity. EMDKG (Gan et al., 2021) encodes the diversity into item representations by an Item Diversity Learning module to reflect the semantic diversity from KG.

The previous works study diversity as the covered categories, which is measured at the coarse-grained level. This paper first investigates the fine-grained diversity with KG context information.