Neighbor interaction-based personalised transfer for cross-domain recommendation

Abstract

Mapping-based cross-domain recommendation (CDR) can effectively tackle the cold-start problem in traditional recommender systems. However, existing mapping-based CDR methods ignore data-sparse users in the source domain, which may impact the transfer efficiency of their preferences. To this end, this paper proposes a novel method named Neighbor Interaction-based Personalized Transfer for Cross-Domain Recommendation (NIPT-CDR). This proposed method mainly contains two modules: (i) an intra-domain item supplementing module and (ii) a personalised feature transfer module. The first module introduces neighbour interactions to supplement the potential missing preferences for each source domain user, particularly for those with limited observed interactions. This approach comprehensively captures the preferences of all users. The second module develops an attention mechanism to guide the knowledge transfer process selectively. Moreover, a meta-network based on users' transferable features is trained to construct personalised mapping functions for each user. The experimental results on two real-world datasets show that the proposed NIPT-CDR method achieves significant performance improvements compared to seven baseline models. The proposed model can provide more accurate and personalised recommendation services for cold-start users.

Keywords:

• Cross-domain recommendation
• data sparsity
• attention mechanism
• meta-learning
• cold-start users

1. Introduction

Cross-domain recommendation (CDR) (P. Li & Tuzhilin, 2021; Q. Zhang et al., 2017) is a potential solution to address the cold-start issue in recommender systems. The essence of this model is to enhance the recommendation accuracy of the target domain by transferring knowledge from the source domain (Anwar & Uma, 2022; H. Liu et al., 2021; Sahu & Dwivedi, 2020). To accomplish knowledge transfer, previous works encoded user knowledge into embeddings and then trained a common mapping function to bridge user embeddings between the source and target domains (Man et al., 2017; T. Wang, Zhuang, et al., 2021). In practice, the preference relationship between different users in source and target domains is not entirely consistent. Consequently, CDR approaches based on common mapping functions ignore users' personalised preferences. Recently, a work utilised pre-trained embedding and meta-learning techniques to construct mapping functions for each user, considering the different preference relationships of different users (Y. Zhu et al., 2022). However, these methods ignore data-sparse users within the source domain, potentially hindering the transfer efficiency of their preferences.

The above CDR method based on personalised mapping (Y. Zhu et al., 2022) has substantially improved over the traditional CDR methods based on common mapping (Man et al., 2017; T. Wang, Zhuang, et al., 2021). However, there are still two main areas for improvement in these works. Firstly, these methods only consider users' historical interaction information to construct personalised mapping functions, as shown in Figure 1(a). Different from these methods, the method in this paper considers neighbour interaction information in addition to individual interaction information when learning personalised mapping functions, as illustrated in Figure 1(b). Secondly, these methods cannot effectively extract users' transferable preferences from their interaction information. Various interaction items contribute differently to users' transferable preferences. Consequently, the method in this paper adopts an effective attention mechanism to evaluate each item's importance automatically.

Figure 1. A simple illustration of model comparison. (a) Existing mapping-based CDR methods learn personalised mapping functions only considering the user's interactions. (b) The proposed NIPT-CDR considers the user's interactions, together with neighbour users' interactions when learning personalised mapping functions.

Based on the aforementioned analysis, we propose NIPT-CDR, a novel CDR framework for cold-start users. First, we design an intra-domain item supplementing module for users in the source domain. This module utilises a nearest-neighbour retrieval algorithm to find neighbour users with similar preferences and use their interaction items to compensate for users with sparse interaction information. Then, an attention network is adopted for adjusting the weight of various interaction items to the user's transferable preferences. Finally, we learn a meta-network that takes user preference features in the source domain as input and generates parameters for personalised mapping functions. In this way, the personalised mapping function based on user interactions differs from user to user, indicating that the preference transfer process is personalised. Overall, this paper makes the following main contributions:

• We devise an intra-domain item supplementing module to augment users' short sequences by introducing neighbour interaction information, which can fully capture users' preferences even if their observed interactions are limited.

• We develop a personalised feature transfer module with an attention mechanism, which can effectively extract users' transferable features from the source domain to enhance the efficiency of knowledge transfer.

The advantage of the proposed NIPT-CDR model is that it can capture user transferable preferences more comprehensively, especially when the user's historical interaction data in the source domain is very sparse. This is achieved by supplementing neighbour interactions and employing an efficient attention mechanism. Therefore, the model can more accurately construct personalised mapping functions to enhance the transfer efficiency of user preferences. Additionally, experimental results reveal that this approach can enhance recommendation accuracy.

The remaining sections of this paper are organised as follows. Section 2 presents a summary of several related studies. In Section 3, we introduce the notation of this work and present the specifics of the NIPT-CDR framework. Section 4 illustrates the better results of our NIPT-CDR compared to some baselines by performing experiments on real-world cross-domain scenarios. Finally, in Section 5, we discuss conclusions and further research.

2. Related work

This section analyses previous relevant research, containing basic cross-domain recommendations, attention mechanisms, and meta-learning.

2.1. Cross-domain recommendation

The cold-start problem in recommender systems has long been very challenging (Herce-Zelaya et al., 2020; S. Li, Lei, et al., 2021; Natarajan et al., 2020). One promising solution is cross-domain recommendation (CDR), which can utilise more information from the auxiliary (source) domain to enhance recommendation accuracy compared to single-domain recommendation methods. G. Ma et al. (2021) and B. Wang et al. (2022). Typical CDR models are based on single-domain recommendation models. At the beginning, Singh and Gordon (2008) and Lian et al. (2017) proposed jointly factorising rating matrices across multiple domains to construct representations of overlapping users' shared preferences.

With the widespread adoption of deep learning (L. Yu, Duan, et al., 2021; Zhou et al., 2019), various deep learning-based approaches have been developed for enhancing knowledge transfer. Man et al. (2017) first proposed to employ a multilayer perceptron to learn the mapping of latent user features from source to target domains. This mapping approach has since become a widely adopted classic CDR method. Zhao et al. (2020) extended the mapping-based model to exploit auxiliary information, like item descriptions and user reviews, to capture cross-domain aspect-level correlations. Some researchers have also explored alternative approaches to improving the mapping function. For example, S. Kang et al. (2019) utilised semi-supervised learning for training mapping functions to solve the problem for a small portion of overlapping users. P. Li and Tuzhilin (2020) constructed an orthogonal mapping function to transfer user preferences across domains. Gupta and Bedathur (2022) utilised meta-learning and twin graph attention model to achieve cross-region transfer. The approach integrates social and location information and captures the inter-dependence between users and locations, allowing for effective recommendation even in regions with limited data. Different from the above methods, Y. Zhu et al. (2022) presented a personalised transfer model. The author leverages a meta-network to construct personalised bridging functions based on each user's interaction items. However, most of these methods neglect users with sparse historical interaction data. In particular, learning a personalised mapping function for each user requires sufficient user-item interaction data.

2.2. Attention mechanism

Attention mechanisms (J. Liu et al., 2019; Vaswani et al., 2017; S. Zhang et al., 2022) have been extensively utilised in a variety of fields, including image processing, natural language processing, and recommender systems. The structural model founded on the attention mechanism can evaluate the significance of various information features depending on the information's weight. It makes relevant and irrelevant decisions on information features, establishing dynamic weight parameters that enhance valuable information and decrease redundant information. This overcomes some limitations of traditional deep learning technology.

Attention mechanisms have been utilised in different manners in recommendation systems. W. C. Kang and McAuley (2018, November) adopted self-attention to dynamically attend to relevant items in the user's historical behaviour sequence. Similarly, Xu et al. (2021) developed a dual self-attention model that can extract short-term dynamics and long-term interests separately. The final representation is formed by integrating the learned long- and short-term representations. After that, Salamat et al. (2021) proposed a novel graph neural network model equipped with an attention mechanism that can effectively combine information from all sources for better social recommendation performance. Besides, Y. Li, Wu, et al. (2022) constructed an innovative dual attention mechanism that involves intra-domain and inter-domain attention components, which transfers user knowledge to accomplish cross-domain feature fusion. Inspired by the success of attention mechanisms in recommender systems, this study adopts an efficient attention network to automatically balance the contribution of various items to the user's transferable preferences.

2.3. Meta-learning

In general, meta-learning refers to learning how to learn (Hospedales et al., 2021), aimed at rapidly learning new tasks by training on similar tasks (Tian et al., 2022; W. Wang, Duan, et al., 2021). The field of meta-learning currently comprises three relatively independent research directions: parameter generation-based meta-learning approaches (T. Li, Su, et al., 2022), gradient-based meta-learning approaches (C. Yu et al., 2020), and metric-based meta-learning approaches (Snell et al., 2017). As meta-learning methods have been intensively investigated in various fields, including computer vision (X. Li, Sun, et al., 2021) and natural language processing (J. Li et al., 2020), these fields have achieved significant progress.

Recently, researchers have attempted to apply meta-learning techniques to improve recommender systems' performance. R. Yu, Gong, et al. (2021) suggested meta-learning with an adaptive learning rate to mitigate the cold-start challenge. Similarly, Zheng et al. (2021, May) investigated a gradient-based meta-learning approach for the sequential scenarios to resolve the item's cold-start issue. The method effectively captures users' preference knowledge from sparse interactions and matches target items with potential users. Additionally, Y. Zhu et al. (2021) utilised a task-oriented meta-network technique in the mapping stage, which alleviates the issue of limited overlapping users in CDR scenarios. This paper's proposed NIPT-CDR model belongs to the parameter generation-based meta-learning approach, which leverages the meta-network to predict the parameters.

According to the analysis of the above-related works, it is necessary for the method to consider neighbour interaction information. Furthermore, combining an attention mechanism with a meta-network approach is feasible for building personalised mapping functions. First, the model supplements users' historical interaction data with the interaction records of their neighbours. Subsequently, the attention mechanism and meta-network are utilised to generate dynamic parameters. The main innovation of this paper is the design of an intra-domain item supplementing module that obtains sufficient interaction data for users in the source domain.

3. Methodologies

This section introduces the problem definition for the single-target cross-domain recommendation. Then, the framework of NIPT-CDR is presented. Next, the detailed components of the model are introduced in a sequential manner. Finally, we discuss the algorithm of this model.

3.1. Problem formulation

Consider two domains: the source domain $D^s$, and the target domain $D^t$. The user and item sets in the two domains are represented as ${\mathcal{U}}^s$, ${\mathcal{I}}^s$, ${\mathcal{U}}^t$ and ${\mathcal{I}}^t$. In numerous real-world scenarios, there is a partial overlap between ${\mathcal{U}}^s$ and ${\mathcal{U}}^t$. Thus, $\mathcal{O}={\mathcal{U}}^s\cap {\mathcal{U}}^t$ denotes the set of overlapping users. However, there are no overlapping items between ${\mathcal{I}}^s$ and ${\mathcal{I}}^t$. In $D^s$, the user-item interaction matrix ${\mathcal{R}}^s$ is decomposed into two sub-matrices $\{U^s,I^s\}$. Similarly, the user-item interaction matrix ${\mathcal{R}}^t$ is decomposed into two sub-matrices $\{U^t,I^t\}$ in $D^t$. For each user $u_i$, we denote by $H_{u_i}^s=\{I_1^s,I_2^s,\dots ,I_n^s\}$ the list of her interaction items in $D^s$, where n represents the total number of interaction items, and $N_{u_i}^s=\{u_1^s,u_2^s,\dots ,u_k^s\}$ represents the set of similar users, where k denotes the number of similar users.

For quick reference, Table 1 provides a list of the notations along with their descriptions.

Table 1. Summary of notations.

Notations	Descriptions
${\mathcal{U}}^s,{\mathcal{U}}^t$	set of users in the source (target) domain
${\mathcal{V}}^s,{\mathcal{V}}^t$	set of items in the source (target) domain
$\mathcal{O}$	set of overlapping users
${\mathcal{R}}^s,{\mathcal{R}}^t$	interaction matrix from the source (target) domain
$U^s,U^t$	user embedding matrix of the source (target) domain
$I^s,I^t$	item embedding matrix of the source (target) domain
$H_{u_i}^s$	list of interaction items for user $u_i$ in the source domain
n	number of interaction items
k	number of similar users
m	maximum number of interaction items

3.2. Model architecture

This paper proposed NIPT-CDR aims to mitigate the problem of data sparsity and enhance recommendation accuracy in the target domain. Figure 2 depicts our model architecture, which consists of three key components. The first component is single-domain latent factor modeling, which utilises matrix factorisation to obtain the intra-domain embeddings of each user and item. The second component is the intra-domain item supplementing module. The FAISS algorithm retrieves the top-K neighbour users, and then their interaction items are integrated into the query user's interaction sequence. The third component mainly completes the personalised feature transfer. The attention network is utilised to automatically modulate the importance of different items to user preference features. The meta-network then takes these features as input to generate personalised mapping function parameters. Finally, for users who lack prior interaction data in the target domain, their source domain embeddings are bridged to the target domain using the trained personalised mapping function, thus achieving the goal of recommendation.

Figure 2. An illustrative figure of the NIPT-CDR framework.

3.3. Single-domain latent factor modeling

In the latent factor modeling stage, this paper employs a matrix factorisation model to obtain embeddings of users and items in each domain. The embeddings of user $u_i^s$ and item $i_j^s$ in the source domain are represented as $U_i^s\in {\mathbb{R}}^d$ and $I_j^s\in {\mathbb{R}}^d$, respectively. Similarly, the embeddings of user $u_i^t$ and item $i_j^t$ in the target domain are represented as $U_i^t\in {\mathbb{R}}^d$ and $I_j^t\in {\mathbb{R}}^d$, where d denotes the dimensionality of the embeddings. Taking the source domain as an example, the preference score of user $u_i^s$ for item $i_j^s$ is computed as the inner product between their embeddings, $U_i^s{I}_j^s$. The formula for the loss function is as follows: (1) $\underset{U,I}{min}\frac{1}{\left|R^s\right|}\sum _{r_{ij}\in R^s}{(r_{ij}-U_i^s{I}_j^s)}^2$(1) where $|R^s|$ denotes the number of ratings in the source domain, and $r_{ij}$ represents the true labels.

3.4. Intra-domain item supplementing module

Through the latent factor model, we can obtain the embedding vectors of each user and item in the source domain. The similarity between users' embedding vectors reflects their statistical co-occurrence relationships. In other words, if two users have a high degree of overlap in their preferences for items, the training process will result in highly similar embedding vectors for these users. Thus, this study employs the FAISS algorithm (Johnson et al., 2019), a powerful library designed for efficient similarity search on large-scale datasets, to quickly and accurately retrieve users with similar preferences in the user embedding layer. The algorithm's workflow can be broken down into two main steps: indexing and searching. During the indexing phase, FAISS preprocesses user embedding vectors to construct an index structure optimised for rapid similarity retrieval. The design of this index aims to minimise the subsequent distance computations during the search phase, enhancing overall search efficiency. In the searching phase, FAISS performs queries on the index to identify the nearest neighbours of a given query user. To assess the similarity between users, FAISS includes various distance metrics, such as the Euclidean distance or Dot product. For this study, dot products were selected as the metric for determining the similarity between user vectors. The formula for the dot product between user $u_i$ and $u_j$ is as follows: (2) $DotProduct(u_i,u_j)=U_i\odot U_j=\sum _{l=1}^d{U}_{il}{U}_{jl}$(2) where d represents the dimension of user embedding vectors and ⊙ represents the dot product operation. $U_{il}$ and $U_{jl}$ denote the corresponding elements of user vectors $U_i$ and $U_j$ at index l, respectively. Specifically, user vectors that have the highest dot product values with the query vector are considered similar. By skillfully utilising the dot product similarity measure and effectively navigating the index, FAISS quickly identifies the top-K most similar users to the query user.

This module defines the maximum length of users' interaction sequences as m. We consider that a user's preferences can be influenced by the interaction items of users with similar interests. Therefore, when a query user $u_i$ in the source domain has interacted with fewer than m items, we supplement her interaction list with interaction items from neighbouring users. This approach can provide more useful information, particularly for users with observed sparse interactions. The supplementing number is denoted as k, where k = m−n. In practice, it is known that each user has at least one interaction. Therefore, this module proposes to utilise the FAISS algorithm to return the top-K similar neighbour users $N_{u_i}^s=\{u_1^s,u_2^s,\dots ,u_k^s\}$, as shown in Figure 3. Subsequently, the interaction lists of all neighbour users are concatenated to form a long sequence using the formula: (3) $H_{u_{1\cdots k}}^s=\mathrm{concat}(H_{u_1}^s,H_{u_2}^s,\dots ,H_{u_k}^s)=\{I_1^s,I_2^s,\dots ,I_x^s\}$(3) where $H_{u_{1\cdots k}}^s$  represents concatenated interaction list, $H_{u_k}^s$ represents the interaction list of the neighbour user $u_k^s$, and x represents the total number of interaction items. We then select k consecutive items from $H_{u_{1\cdots k}}^s$, denoted as $H_{nbr}^s=\{I_1^s,I_2^s,\dots ,I_k^s\}$. Finally, the interaction lists of query users and neighbour users are concatenated to form the final interaction list. Therefore, for each query user $u_i$, we represent her final interaction list by $Z_i^s=\{I_1^s,I_2^s,\dots ,I_m^s\}$. For convenience, the embedding matrix $Z_i^s$ is defined as follows: (4) $Z_i^s=\mathrm{concat}(H_{u_i}^s,H_{nbr}^s)={\left[z_{i,j}^s\right]}_{j=1}^m$(4) where $Z_i^s\in {\mathbb{R}}^{d\times m}$, and d represents the dimensionality of item embeddings. $H_{u_i}^s$ represents the list of items interacted with by user $u_i$, while $H_{nbr}^s$ represents the list of items interacted with by neighbouring users. $z_{i,j}^s$ is the jth column, also known as the embedding vector for the jth item. Subsequently, we can leverage each embedding matrix $Z_i^s$ as a feature to help construct the personalised mapping function.

Figure 3. Intra-domain item supplementing module process.

3.5. Personalized feature transfer module

We cannot estimate a proper embedding for cold-start users without auxiliary data. Mapping-based CDR methods involve introducing knowledge from the source domain, which essentially trains a mapping function. Ideally, this mapping should be personalised. In other words, since each user's preferences are different, the parameters of the mapping function should also be different. Therefore, we leverage the attention network and meta-network to generate the parameters of the personalised mapping function from the embedding matrix $Z_i^s$.

Firstly, we consider the difference in importance of different items to user preferences. To accomplish this, we employ an attention mechanism (Vaswani et al., 2017) to construct a feature-level attention layer, as shown in Figure 4. Given user embedding $U_i^s$ in the source domain, we generate its query vector $q_i^s\in {\mathbb{R}}^d$. Similarly, given user interaction item embedding $z_{i,j}^s$, we generate its key vector $k_{i,j}^s\in {\mathbb{R}}^d$, and value vector $v_{i,j}^s\in {\mathbb{R}}^d$, with the following transformations: (5) $Q_i^s={\left(U_i^s\right)}^{\mathrm{\top }}{W}_q^s,K_i^s={\left(Z_i^s\right)}^{\mathrm{\top }}{W}_k^s,V_i^s={\left(Z_i^s\right)}^{\mathrm{\top }}{W}_v^s$(5) where $Q_i^s=q_i^s\in {\mathbb{R}}^d$, $K_i^s=[k_{i,j}^s{]}_{j=1}^m,V_i^s=[v_{i,j}^s{]}_{j=1}^m\in {\mathbb{R}}^{m\times d}$, and $W_q^s,W_k^s,W_v^s\in {\mathbb{R}}^{d\times d}$ are the weight matrixes for query, key, and value in the attention network. Then the transferable feature representation $T_{u_i}$ of user $u_i$ is calculated by the following formula: (6) $T_{u_i}=\mathrm{Attention}(Q_i^s,K_i^s,V_i^s)=\mathrm{Softmax}\left(\frac{Q_i^s{K}_i^{s^{\mathrm{\top }}}}{\sqrt{d}}\right)V_i^s$(6) where $Q_i^s{K}_i^{s^{\mathrm{\top }}}$ utilises dot product operation to compute the similarity between the query and a key. In other words, the attention network uses the user's embedding $U_i^s$ to compute weights for each item in $Z_i^s$. The scale operation $\sqrt{d}$ is to avoid the dot product result being too large, resulting in 0 or 1 after normalisation. The activation function softmax normalises the result of the operation $\frac{Q_i^s{K}_i^{s^{\mathrm{\top }}}}{\sqrt{d}}$ to obtain a probability distribution, where the sum of weights is equal to 1.

Figure 4. Attention weight calculation process.

Secondly, we employ a meta-network to take the user's preference feature representation as input and generate the parameters of the personalised mapping function. The formula for the meta-network is presented as follows: (7) $w_{u_i}=g(T_{u_i};\epsilon )$(7) where the meta-network $g(\cdot )$ is a two-layer perceptron, and $\epsilon$ represents its parameters. The size of the vector $w_{u_i}$ varies according to the structure of the mapping function. Since users' feature representations are different, the generated meta-network outputs will also be different.

Finally, given a cold-start user $u_i$ on the target domain, her source domain embedding is mapped to the target domain by the personalised mapping function. We use $w_{u_i}$ as a parameter of the mapping function: (8) ${\hat{U}}_i^t=f_{u_i}(U_i^s;w_{u_i})$(8) where $f_{u_i}(\cdot )$ is the mapping function, which also adopts the structure of a two-layer perceptron. The parameter $w_{u_i}$ of the mapping function varies according to user preferences, thereby realising the personalised mapping of user embedding. ${\hat{U}}_i^t$ is the cold-start user's transferred embedding in the target domain. Subsequently, the predicted preference score of the cold-start user $u_i$ for the item in the target domain is computed as follows: (9) ${\hat{r}}_{i,j}^t={\hat{U}}_i^t\odot I_j^t$(9) where ⊙ represents the dot product operation and $I_j^t$ is the item embedding in the target domain. We recommend items from the target domain to cold-start users based on their predicted preference ratings.

3.6. Loss function

Most existing mapping-based methods commonly employ a mapping-oriented optimisation procedure to train their models. Specifically, these methods train the mapping function by minimising the distance between users' transferred embeddings and their embeddings in the target domain. Since the interactions of overlapping users between the two domains are usually very limited, the learned user embeddings may not be accurate. Therefore, we employ a task-oriented optimisation approach, directly utilising the final predicted score as the optimisation goal. The formulation of the task-oriented loss function is as follows: (10) $\underset{\epsilon }{min}\frac{1}{\left|R_{\mathcal{O}}^t\right|}\sum _{r_{ij}\in R_{\mathcal{O}}^t}{(r_{ij}-{\hat{r}}_{i,j}^t)}^2$(10) where $R_{\mathcal{O}}^t$ denotes the set of ratings from overlapping users in the target domain. This optimisation approach helps alleviate the impact of unreasonable embeddings and provides a larger set of training samples.

3.7. Algorithm analysis

The NIPT-CDR model training process consists of three stages: the pre-training stage, the intra-domain item supplementing stage, and the personalised feature transfer stage, as depicted in Algorithm 1. Steps 1–2 are the pre-training phase. This phase generates embeddings for users and items using the pre-trained model. Then, step 5 is the process of retrieving the top-K neighbour users for a given query user. Steps 6–11 supplement the query user's interaction sequence with the neighbour's interaction items, up to a maximum length of m. Finally, Steps 12–14 represent training the personalised feature mapping based on the interaction sequence supplemented in the previous step. Step 15 is the process of computing the rating ${\hat{r}}_{i,j}$ of the cold-start user $u_i$ for the item in the target domain. Assuming that the number of neighbour users is k, and the maximum number of user interaction items is m, the time complexity of the intra-domain item supplementing phase is $O(km)$. Considering that d is the dimensionality of embeddings, the time complexity of the personalised feature transfer stage is $O(dm)$.

4. Experiments

This section provides the experimental settings and subsequently performs comprehensive experiments in three cross-domain scenarios to respond to the following six research questions:

1. How does NIPT-CDR perform in comparison to other methods in various cold-start CDR scenarios?

2. Is NIPT-CDR a general approach that is applicable to different base pre-training models?

3. How does the hyperparameter affect NIPT-CDR?

4. How do the intra-domain item supplementing module and attention network in NIPT-CDR improve recommendation accuracy?

5. How is the classification performance of NIPT-CDR?

6. How does NIPT-CDR perform on different cross-domain datasets?

4.1. Experimental settings

4.1.1. Datasets

This study uses the Amazon dataset. The dataset contains information from various domains, and we select three domains: Movie, Music, and Book. For each scenario, the domain with the most interactions is chosen as the source domain, while the other is the target domain. We classify three cross-domain scenarios: Scenario 1: Movie $\mathrm{\&}$ Music, Scenario 2: Book $\mathrm{\&}$ Movie, and Scenario 3: Book $\mathrm{\&}$ Music. Unlike many existing works that filter out a portion of users and items with less interaction, we use full data to simulate real-world scenarios. The statistics are shown in Table 2.

Table 2. Statistics of different cross-domain scenarios on the Amazon dataset.

	Dataset		Item		User			Inter
Scenario	Source	Target	Source	Target	Source	Target	Overlap	Source	Target
Scenario1	Movie	Music	50,052	64,443	123,960	75,258	18,031	1,697,533	1,097,592
Scenario2	Book	Movie	367,982	50,052	603,668	123,960	37,388	8,898,041	1,697,533
Scenario3	Book	Music	367,982	64,443	603,668	75,258	16,738	8,898,041	1,097,592

In each cross-domain scenario, a small subset of overlapping users is randomly selected, and their ratings on the target domain are removed to simulate cold-start users (test users). Subsequently, we utilise the remaining overlapping users to train the mapping function. In this experiment, to simulate more scenarios, overlapping users are set to form the test set according to a certain ratio of 80%, 50%, and 20%.

4.1.2. Evaluation metrics

Consistent with previous research, this paper employs MAE and RMSE as evaluation metrics to assess the performance of the proposed model. MAE and RMSE are calculated using the following formulas: (11) $\begin{array}{rl}\mathrm{MAE}& =\frac{1}{N}\sum _{i=1}^N|{\hat{y}}_i-y_i|\end{array}$(11) (12) $\begin{array}{rl}\mathrm{RMSE}& =\sqrt{\frac{\sum _{i=1}^N{({\hat{y}}_i-y_i)}^2}{N}}\end{array}$(12) where N represents the sample size, ${\hat{y}}_i$ represents the predicted score obtained in the model, and $y_i$ denotes the true score. Lower MAE and RMSE values indicate superior model performance.

4.1.3. Baseline methods

We contrast our results with various methods, including both traditional baselines and innovative approaches. Table 3 shows the comparison between our method and the CDR baselines.

Table 3. The comparison of the baselines and our method.

Model	Training Data	Transfer Strategy	Technology Adoption or Basic Idea
CMF	Rating	Shared embedding	Multiple relations
DCDCSR	Rating	Common mapping	DNN mapping
SSCDR	Rating	Common mapping	Semi-supervised learning
EMCDR	Rating	Common mapping	MLP-based nonlinear mapping
CATN	Rating, content	Common mapping	Aspect correlation learning
PTUPCDR	Rating	Personalized mapping based on user interaction	Meta-network
NIPT-CDR	Rating	Personalized mapping based on user and neighbour interactions	Attention mechanism, meta-network, nearest neighbour search algorithm

• TGT represents the target matrix factorisation model, which utilises only the knowledge of the target domain during training.

• CMF (Singh & Gordon, 2008): An extended method of the matrix factorisation model. The embedding of overlapping users is shared between all domains.

• DCDCSR (F. Zhu et al., 2018): A mapping-based method that employs matrix factorisation models and fully connected deep neural networks to develop benchmark factors from target and source domains.

• SSCDR (S. Kang et al., 2019): A semi-supervised mapping-based approach that utilises unshared user data within the domain to enhance the robustness of the mapping function.

• EMCDR (Man et al., 2017): A cross-domain recommendation embedding and mapping framework that factorises user rating matrices and captures cross-domain nonlinear mappings with multi-layer perceptrons.

• CATN (Zhao et al., 2020): A review-based cross-domain recommendation method that transfers user preference by extracting aspects from review documents and finding correlations from a global aspect representation with attention.

• PTUPCDR (Y. Zhu et al., 2022): A personalised transfer learning method is proposed for cross-domain recommender systems, which leverages a meta-learner to construct personalised preference bridges based on user characteristics extracted from their historical interactions in the source domain.

4.2. Results and discussion

To demonstrate the effectiveness of the NIPT-CDR framework, we contrast the recommendation accuracy of NIPT-CDR and other models using two metrics: MAE and RMSE. Tables 4 and 5 show the MAE and RMSE obtained for the seven models on three cross-domain scenarios under $\mathit{\beta }\in \{20\mathrm{\%},50\mathrm{\%},80\mathrm{\%}\}$. Overall, the NIPT-CDR model outperforms the comparison model on all cross-domain scenarios and for different $\mathit{\beta }$ values. Several profound conclusions can be drawn from the experimental results: (1) TGT employs data from the target domain for training, while the rest of the baselines are CDR models. There is no doubt that TGT consistently performs the worst of all evaluations. In scenarios with sparse data, it is not enough to just use the data from a single domain. Therefore, exploiting information from the source domain can mitigate the data sparsity problem. (2) Compared with most CDR methods, the recommendation accuracy of CMF is slightly inferior. This is because CMF directly shares the overlapping users' embedding in different domains, ignoring the domain shift problem. In contrast, the mapping-based CDR model can transform source embedding to target latent space, thereby mitigating the impact of potential domain shift. (3) The NIPT-CDR model outperforms the CDR methods based on common mapping functions EMCDR, DCDCSR, SSCDR, and CATN, indicating that the personalised transfer strategy is effective in the transfer of user preference knowledge. (4) PTUPCDR is the closest approach to our proposed method NIPT-CDR. However, our method outperforms PTUPCDR both on MAE and RMSE metrics. This is because PTUPCDR does not focus on data-sparse users in the source domain and cannot capture user preferences more comprehensively from their interaction history, resulting in inferior transfer results. The intra-domain item supplementing and personalised feature transfer modules proposed in this paper can effectively compensate for this deficiency.

Table 4. Comparison of the model NIPT-CDR with other models in terms of the MAE.

	Scenario 1			Scenario 2			Scenario 3
Scenario	$20\mathrm{\%}$	$50\mathrm{\%}$	$80\mathrm{\%}$	$20\mathrm{\%}$	$50\mathrm{\%}$	$80\mathrm{\%}$	$20\mathrm{\%}$	$50\mathrm{\%}$	$80\mathrm{\%}$
TGT	4.4997	4.5127	4.5232	4.2195	4.2493	4.2456	4.5192	4.0591	4.5262
CMF	1.5399	1.7236	2.6086	1.4508	1.6032	2.1636	1.8624	2.1748	3.1326
DCDCSR	1.5012	1.8447	2.7991	1.4124	1.6895	2.3698	1.8718	2.2446	3.1903
SSCDR	1.3828	1.6562	1.9829	1.3061	1.2454	1.3291	1.5903	1.6891	2.1144
EMCDR	1.3641	1.6059	2.0857	1.1609	1.1876	1.3310	1.4812	1.7641	2.3084
CATN	1.2671	1.4890	1.8182	1.1249	1.1598	1.2672	1.3924	1.6023	1.9571
PTUPCDR	1.1828	1.2857	1.6057	1.0787	1.1141	1.2182	1.2330	1.3694	1.7843
NIPT-CDR	1.1098${}^{\ast }$	1.2398	1.5830${}^{\ast }$	1.0672${}^{\ast }$	1.1028${}^{\ast }$	1.2004	1.2281${}^{\ast }$	1.3568${}^{\ast }$	1.7673${}^{\ast }$

Notes: ${}^{\ast }$ denotes significance level at 0.05, paired t-test for best baseline and NIPT-CDR.

Table 5. Comparison of the model NIPT-CDR with other models in terms of the RMSE.

	Scenario 1			Scenario 2			Scenario 3
Scenario	$20\mathrm{\%}$	$50\mathrm{\%}$	$80\mathrm{\%}$	$20\mathrm{\%}$	$50\mathrm{\%}$	$80\mathrm{\%}$	$20\mathrm{\%}$	$50\mathrm{\%}$	$80\mathrm{\%}$
TGT	5.1814	5.1943	5.2018	4.7840	4.8592	4.8397	5.1855	5.1810	5.2055
CMF	2.1862	2.3561	3.3318	1.8447	2.1002	2.6941	2.4517	2.8411	3.9791
DCDCSR	2.0156	2.4497	3.6215	1.8137	2.0632	2.7786	2.3451	2.8908	3.8820
SSCDR	1.7847	2.0923	2.3108	1.6970	1.5844	1.7154	1.9736	2.2217	2.7003
EMCDR	1.6691	2.0155	2.4925	1.4742	1.5058	1.6454	1.9150	2.1223	2.6526
CATN	1.6468	1.9205	2.2991	1.4548	1.4826	1.6280	1.7399	2.0665	2.5623
PTUPCDR	1.5519	1.7443	2.2351	1.3945	1.4507	1.6215	1.6421	1.8548	2.4022
NIPT-CDR	1.4469${}^{\ast }$	1.6861	2.1801${}^{\ast }$	1.3785	1.4365${}^{\ast }$	1.6061	1.6320	1.8349${}^{\ast }$	2.3884${}^{\ast }$

Notes: ${}^{\ast }$ denotes significance level at 0.05, paired t-test for best baseline and NIPT-CDR.

4.3. Generalization experiments (RQ2)

Mapping-based CDR approaches emphasise the mapping function itself. For experimental evaluation, this study mainly uses Matrix Factorization (MF) (H. Ma et al., 2008) as the base model. However, MF is a simple non-neural model. To verify the compatibility of NIPT-CDR and other mapping-based CDR models, we change the base model to Generalized Matrix Factorization (GMF) (He et al., 2017). GMF generalises the traditional MF and has stronger learning and expression abilities. We consider three mapping-based CDR methods: EMCDR, PTUPCDR, and NIPT-CDR. For single-domain models MF and GMF, we train them with data from both domains. The MAE and RMSE results for the three scenarios with $\mathit{\beta }=20\mathrm{\%}$ are presented in Figures 5(a,b) and 6(a,b). The experimental findings reveal several important insights: (1) Mapping-based CDR methods can be applied to different base models and consistently outperform single-domain models in terms of MAE and RMSE. (2) The generalised NIPT-CDR model achieves optimal performance across various base models.

Figure 5. Based on the MF model, the NIPT-CDR compares with EMCDR and PTUPCDR. In (a), we employ MAE metric to evaluate the model's performance, and in (b), the metric is RMSE.

Figure 6. Based on the GMF model, the NIPT-CDR compares with EMCDR and PTUPCDR. In (a), we employ MAE metric to evaluate the model's performance, and in (b), the metric is RMSE.

4.4. Hyperparameter analysis (RQ3)

In this study, we employ the intra-domain item supplementing module to address the challenge of data sparsity. The degree of item supplementing affects recommendation accuracy. Figure 7 plots the effect of different $m\in \{10,20,30,40,50\}$ for NIPT-CDR across three cross-domain scenarios. In addition, to reflect the impact of m on the recommendation accuracy of NIPT-CDR as realistically as possible, given the same settings (i.e. $\mathit{\beta }=50\mathrm{\%}$) for all scenarios. The experiments show that the optimal value of m varies depending on the cross-domain scenario, possibly due to the varying data distribution across different scenarios. Specifically, for Scenario 1, NIPT-CDR demonstrates optimal performance when the number of items is 20, and the MAE and RMSE reach their minimum. Similarly, for Scenario 2 and Scenario 3, NIPT-CDR achieves optimal performance when the number of items is 30, with the MAE and RMSE reaching their minimum. On the contrary, when the number of items exceeds 20 or 30, the recommendation accuracy of NIPT-CDR decreases. One possible explanation is that excessive supplementation of interaction information may lead to the introduction of noise. Overall, the impact of different hyperparameter settings on model performance is relatively small, indicating that the NIPT-CDR model is robust to hyperparameter settings.

Figure 7. The influence of changing the total number m of interaction items on different cross-domain scenarios in NIPT-CDR. (a) the change curve of the MAE metric and (b) the change curve of the RMSE metric.

4.5. Ablation studies (RQ4)

To explore the significance of various components in NIPT-CDR, we implement ablation experiments on three cross-domain scenarios, where $\mathit{\beta }=20\mathrm{\%}$. We compare our solutions with the following variants:

• NIPT-CDR${}_{IS}$: This is a variant of NIPT-CDR that removes the intra-domain item supplementing module when capturing user preferences. As a result, it ignores the items that neighbour users interact with.

• NIPT-CDR${}_{ATT}$: This is another variant of NIPT-CDR that does not exploit the proposed attention network when aggregating user interaction items.

Table 6 summarises the performance comparison of NIPT-CDR components, with the optimal performance displayed in boldface. The values of the metrics MAE and RMSE are given. NIPT-CDR achieves a better result for each cross-domain scenario than NIPT-CDR${}_{IS}$, demonstrating the effectiveness of increasing neighbour behaviour. From this result, incorporating the intra-domain item supplementing module into NIPT-CDR helps capture more user preferences, thus improving recommendation accuracy in most cross-domain scenarios. Furthermore, NIPT-CDR performs better than NIPT-CDR${}_{ATT}$, denoting the importance of the proposed attention network in extracting user transferable preference features. Overall, the NIPT-CDR method achieves optimal performance and demonstrates impressive improvements in three cross-domain scenarios. These experimental findings also confirm the positive impact of the two proposed components on user preference transfer and their effectiveness in enhancing the performance of the target domain.

Table 6. The comparison results of ablations studies on three cross-domain scenarios.

	Scenario 1		Scenario 2		Scenario 3
Scenario	MAE	RMSE	MAE	RMSE	MAE	RMSE
NIPT-CDR	1.0863	1.4161	1.0775	1.3826	1.2548	1.6597
NIPT-CDR${}_{IS}$	1.1435	1.4916	1.0784	1.3831	1.2686	1.6710
NIPT-CDR${}_{ATT}$	1.1335	1.4864	1.1021	1.4031	1.2562	1.6641

4.6. Classification performance evaluation of NIPT-CDR (RQ5)

This paper adopts the F1-Score as an essential metric to evaluate the model's classification performance. The F1-Score is calculated using the following formula: (13) $\text{F1-Score }=\frac{2\times \mathrm{Precision}\times \mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}$(13) The F1-Score combines Precision and Recall to provide a comprehensive evaluation metric. It measures the balance between these two metrics by computing their harmonic mean. A higher F1-Score indicates that the model performs well in Precision and Recall, demonstrating its ability to provide accurate and comprehensive recommendations.

We compare the NIPT-CDR model with six CDR models in scenario 1, where the source domain is Movie, and the target domain is Music. The experimental results, presented as bar charts in Figure 8, clearly demonstrate that our proposed NIPT-CDR model outperforms the other CDR models in terms of the F1-Score metric. This proves that our NIPT-CDR model can provide users with more accurate and comprehensive item recommendations.

Figure 8. F1-score experimental results graph.

4.7. Model applicability study

In the literature (Zang et al., 2022), researchers have defined the concept of domain. For example, the book and movie domains in the Amazon dataset are categorised as item-level domains. On the other hand, the romance and horror movies in the Movielens-25M datasets are attribute-level domains. To assess the applicability of our proposed model across different cross-domain datasets, we compare the NIPT-CDR model with the EMCDR and PTUPCDR models on the Movielens-25M dataset. We selected two pairs of unrelated movie types from Movielens-25M to construct cross-domain scenarios. The statistics are shown in Table 7.

Table 7. Statistics of different cross-domain scenarios on the Movielens-25M dataset.

Dataset		Item		User			Inter
Source	Target	Source	Target	Source	Target	Overlap	Source	Target
Adventure	Crime	3186	4483	80,829	80,242	39,935	2,775,635	1,969,286
Action	Thriller	4097	5345	80,006	79,596	39,346	2,084,853	1,742,554

Figure 9 shows the experimental results. In these two cross-domain scenarios, our proposed NIPT-CDR model exhibits superior performance compared to the common mapping-based model EMCDR and the personalised mapping-based model PTUPCDR. These results demonstrate the applicability of our model on different cross-domain datasets.

Figure 9. Comparison results on the Movielens-25M dataset. In (a), we employ the MAE metric to evaluate the model's performance, and in (b), the metric is RMSE.

5. Conclusion

This paper presents the NIPT-CDR model, which can capture users' transferable preferences more comprehensively and enhance recommendation accuracy in the target domain. Unlike previous methods that only utilise users' historical interaction information to learn personalised mapping functions, NIPT-CDR also explores interaction information about users' neighbours through the intra-domain item supplementing module. After that, the attention network and meta-network are utilised to build personalised bridges. In this way, each user's personalised preference features can be transferred across domains. The experiments indicate that NIPT-CDR outperforms other approaches in three cross-domain scenarios. The proposed model can provide more accurate and personalised recommendation services for cold-start users, thereby improving user satisfaction and business benefits in fields such as e-commerce.

In real life, only a limited number of users interact across multiple domains. As part of our future research, we intend to investigate the NIPT-CDR model to handle more complex cross-domain scenarios that involve non-overlapping users between the two domains.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [Grant No. 62076006] and in part by the University Key Scientific Research Project of Anhui Province [Grant No. 2022AH050821].