A Two-Path Multibehavior Model of User Interaction

Abstract

Personalized recommendation is an important part of e-commerce platforms. In recommendation systems, a neural network is used to enhance collaborative filtering to accurately capture user preferences, so as to obtain better recommendation performance. Traditional recommendation methods focus on the results of a single user behavior, ignoring the modeling of multiple interaction behaviors of users, such as click, add to cart and purchase. Although many studies have also focused on multibehavior modeling, two important challenges remain: (1) Since the multiple behaviors of the time-evolving trends of context information are ignored, it is still a challenge to identify the multimodal relationships of behaviors; (2) surveillance signals are still sparse. In order to solve these problem, this paper proposes a two-path multibehavior model of user interaction (TP_MB). First, a two-path learning strategy is introduced to maximize the multiple-interaction information of users and items learned by the two paths, which effectively enhances the robustness of the model. Second, a multibehavior dependent encoder is designed. Contextual information is obtained through behavior dependencies in the interaction of different users. In addition, three contrastive learning methods are designed, which not only obtain additional auxiliary supervision signals, but also alleviate the problem of sparse supervision signals. Extensive experiments on two real datasets demonstrate that our method outperforms state-of-the-art multibehavior recommendation methods.

1. Introduction

With the rapid development of the Internet, recommendation systems have also emerged [1]. As the number of users grows dramatically, e-commerce platforms continue to offer a wide variety of products to meet the needs of an ever-increasing number of users, and this is where recommendation systems play a key role to help e-commerce platforms solve this problem. Recommendation systems aim to recommend items to the user, who may be interested, even if he or she does not know his or her preferences. To achieve this, the recommendation system needs a large amount of user data for analysis, which can be product information, user personal information, user interaction behavior, etc. Effective modeling of user information provides more satisfactory services to users. Nowadays, recommendation systems have been widely used in various e-commerce platforms [1]. Among a variety of existing recommendation methods, collaborative filtering is used to learn interactions between users and items and find users and items with similar interactions [2]. Personalized recommendations capture user interests by modeling users’ information. With the continuous development of deep learning, many methods have improved collaborative filtering, modeling more complex user–item interactions. For example, NCF [3] and DMF [4,5,6] enabled collaborative filtering to have the ability to learn the nonlinear interaction of users by referring to MLP. It reduced the sparse dimensionality user representations to dense representations by a multilayer encoder [7,8]. In recent years, since neural networks have received increasing attention. User–item interactions were modeled by neural networks, and general user interests were extracted in a focused manner [9,10,11]. Sequential recommendation methods based on user-interactive transformer calculations have achieved great success in recent years. However, these recommendation methods typically addressed a single-behavior type of user interaction. In real-world applications, users’ nonpurchasing behavior, such as click and add-to-cart behaviors, can help capture user interests [3]. Compared with models that model a single behavior, methods of modeling multiple behaviors have achieved great success in recent years. LightGCN was used in GHCF to model user behaviors according to the behavior type of user–item interaction [3]. LightGCN was used in conveying information about various behaviors of users to represent users [1]. Despite the great success of multibehavior recommendation models, these models ignore the relationships that exist between users’ interaction behaviors, and the actual purchase behavior data of users are extremely sparse.

Research strategies have been proposed to model multiple behaviors to characterize specific types of behaviors and to enhance the representation of target behaviors [12,13]. For example, semantics of user–item interactions were extracted through graph neural network-based messaging [12]. Although these approaches were effective, there were still two problems: (1) the multimodal relationship between multiple behaviors was not emphasized, and the model is unable to obtain collaborative signals from the relevant data resulting in low performance; (2) sufficient user interaction data are required when training user data. However, the target behavior data of users is extremely sparse. Therefore, the direct integration of the user’s target behavior can lead to low performance of the model due to the sparse supervised signal.

Based on the above challenges, in order to model multiple types of behavior pattern dependencies, we propose a two-path multibehavior model of user interaction (TP_MB). Here is an introduction to two paths: Compared to a single path in an end-to-end way, two paths can greatly improve the performance of the model. Specifically, they learn behavior dependence by combining specific types of behavior representations, according to the timeline of user–item interactions. Self-supervised learning could be effectively applied to limited labeled data such as natural language and image data, [13,14,15], and self-supervised learning is considered for use in our model. Thus, inter-two-path multibehavior self-supervised learning endows the TP_MB framework to solve the data sparsity problem. That is, each type of user–item interaction is parameterized into a separate embedded space to learn the dependency representation of the user’s personalized behavior type. That is, a self-supervised learning paradigm between paths is used to enhance data supervision signals. The contributions of this paper are as follows:

• In order to distinguish the ability of different users’ behavior perception preferences, we propose a two-path multibehavior model framework of user interaction (TP_MB). The strategy of the multibehavior interaction sequence path according to the timeline of the interaction and the multibehavior interaction graph path based on attention is proposed.
• To make full use of the auxiliary behavior information, we propose two-path modeling. This focuses on the dependencies between multiple behaviors obtained through attention mechanisms within each of the two paths. It emphasizes the necessity of modeling the dependency relationship between different behaviors of users.
• In order to capture the commonality of multiple behaviors of users, we design three contrastive learning methods. This not only enhances the representation results of two paths, but also enables the model to obtain more auxiliary supervision signals in the self-supervised learning within paths and between paths. It effectively alleviates the problem of sparse supervisory signals.
• We conduct extensive experiments on two real-world user behavior datasets. Experiments show that the recommendation performance of TP_MB outperforms many current popular baseline models.

2. Related Work

2.1. Self-Supervised Representation Learning

The purpose of self-supervised learning is to learn useful representations by maximizing the mutual information between the inputs and outputs of the encoder [16]. In visual representation learning, multiple graphs were generated by multiple data augmentation to maximize the mutual information of these graphical features [17]. Figure characterization was based on self-supervised learning to extract figure features [18]. In sequence recommendations, self-supervised signals were obtained by feature masks. With sparse data on the session, the mask generated sparse self-supervised signals, and therefore was applicable to sequence behavior recommendation [19]. On graph-based data, self-supervised learning could provide great advantages [15,20]. The self-supervised learning paradigm captured graph structures and semantic features using the inner dependencies between node attributes and graph structures in the graph [20]. Self-supervised learning dynamically learned relationships of sessions in graph structures [15]. For the problems of dispersion of sequence recommendations, correlation between items and skewness of length distribution, two information enhancement operators were designed to extract high-quality graphs to solve the above problems [21]. For the data sparsity problem existing on the knowledge graph, the performance of the model was effectively improved by treating multilevel graphs as entity and relationship graphs [22]. Even though the advantages of self-supervised learning are huge, it is less applied to multiple interactions of fine-grained users.

2.2. General Recommendation

A collaborative filtering algorithm was used as a recommendation system to predict similar users based on the interests of similar users, and to recommend interested projects to them [2]. Factorization was one of the most popular methods among collaborative filtering methods, which mapped user interactions to a representation space. The Hadamard product of the user–item feature vector was used to represent user preferences [4]. The other methods aimed to differ from the collaborative filtering method and had the same goals as the results of this method. For example, user preferences were predicted by using neural collaborative filtering [3] through MLPS. Researchers effectively used users’ interests and location to provide recommendations to users [23]. They recommended items that might be interesting for users through both online and offline methods based on multiple sales strategies [24], modeled potential user relationships based on user social information from multiple sources [25], and leveraged information from multiple sources to build users’ multiperspective preferences and provided recommendations to them [26].

2.3. Multibehavior Recommendation System

In recent years, various studies have been proposed to deal with multiple user interactions [12,19]. Specifically, MBGCN effectively transmitted heterogeneous behavior information and obtained user characteristics due to the effectiveness of graph neural network [12]. MGNN-SPred proposed to learn global item–item relationships by GNN, and integrated target embedding and current session through a gating mechanism [19]. Finding similar nodes for attributes of nodes and edges in the graph enhanced the interpretation [27]. A collective matrix decomposition model was designed to improve prediction accuracy by sharing parameters in multiple relational domains [28]. By modeling the interests of individual users, better signals of thematic interests could be obtained and thematic predictions could be made for different types of behaviors [29]. Since multiple user behaviors can help to obtain the user’s intention, even though the above studies have been very successful, better model performance cannot be obtained due to the problem of sparse user interaction data.

3. Problem Formulation

User multibehavior interaction items are used as input, and the dependencies between different behaviors are analyzed from a fine-grained perspective by considering the interaction between different behaviors, given $\mathbf{U}=\left\{{\mathbf{u}}_{\mathbf{1}},{\mathbf{u}}_{\mathbf{2}},\dots ,{\mathbf{u}}_{\mathbf{s}}\right\}$ represents the set of users, $\mathbf{I}=\left\{{\mathbf{i}}_{\mathbf{1}},{\mathbf{i}}_{\mathbf{2}},\dots ,{\mathbf{i}}_{\mathbf{t}}\right\}$ represents the set of items and $\mathbf{B}=\left\{{\mathbf{b}}_{\mathbf{1}},{\mathbf{b}}_{\mathbf{2}},...,{\mathbf{b}}_{\mathbf{k}}\right\}$ represents different types of user–item interactions according to the timeline. User interaction behaviors include click, shopping cart, favorite and purchase.

3.1. Methods

In order to distinguish different user behavior perception preferences, we propose a two-path multibehavior of user interaction model (TP_MB), and the model framework is shown in Figure 1. The model consists of a multibehavior interaction sequence path, a multibehavior interaction graph path and path–path self-supervised learning. Each path consists of three parts: (1) multibehavior initial embedding; (2) multibehavior interaction dependencies; (3) a multibehavior self-supervised learning paradigm for paths. The sequence path for capturing individual user characteristics is based on the BERT approach to model user behavior sequences according to the timeline. The graph path models all users to form a user–item behavior graph, where the behavior graph contains extracted behavior subgraphs by behavior categories, and the behavior graph contains all user characteristics. Individual user features in the sequence path are not sufficient to provide enough data for the model, while all user features in the graph path can be effectively modeled as user features. Therefore, sequence and graph paths can complement each other and effectively help to extract users’ feature information. First, embeddings are learned by TP_MB that contains user behavior features through a two-path framework, which are multibehavior interactive sequence path and multibehavior interaction graph path, where ‘pv’ means click, ‘buy’ means purchase, ‘cart’ means shopping cart and ‘fav’ means favorite. Then, the multibehavior dependencies between the auxiliary behavior (click, add to cart) and the target behavior (purchase) are captured in the calculation of user multibehavior, including the calculation of the behavior of the sequence path and the calculation of the behavior of the graph path. Finally, the consistency of user interests is maximized by contrast learning between the multibehavior graph path and the multibehavior sequential path, which predicts items that users will interact with through certain behaviors.

3.2. Multibehavior Interaction Sequence Path

3.2.1. Multibehavior Interaction Sequence Embedding

The embedding layer of the behavior context sequence path is designed in order to make the behavior interaction context as the input of the sequence path. The multibehavior interaction sequence (MB interaction sequence) is used as the input to the sequence path. Joint embedding of the individual user, item information and corresponding interaction behavior context information can be obtained to form multibehavior interaction sequence embedding. Given ${\mathbf{u}}_{\mathbf{q}}\in \mathbf{U}$, we set each element in the sequence of user interaction according to the timeline as a triple ${\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{x}}}^{{\mathbf{b}}_{\mathbf{k}}}=\left\{({\mathbf{u}}_{\mathbf{q}},{\mathbf{b}}_{\mathbf{k}},{\mathbf{i}}_{\mathbf{x}})|{\mathbf{u}}_{\mathbf{q}}\in \mathbf{U},{\mathbf{b}}_{\mathbf{k}}\in \mathbf{B},{\mathbf{i}}_{\mathbf{x}}\in \mathbf{I}\right\}$, which indicates that user $\mathbf{q}$ interacts with item $\mathbf{x}$ and corresponds to the $\mathbf{k}$-th behavior. The multibehavior sequence of a user contains the interaction information of a single user. Thus, the multibehavior interaction sequence of the user is mapped to the initial embedding matrix ${\mathbf{S}}_{{\mathbf{u}}_{\mathbf{q}}}=[\left({\mathbf{u}}_{\mathbf{q}},{\mathbf{b}}_{\mathbf{1}},{\mathbf{i}}_{\mathbf{x}}\right),\left({\mathbf{u}}_{\mathbf{q}},{\mathbf{b}}_{\mathbf{2}},{\mathbf{i}}_{\mathbf{x}}\right),\dots ,\left({\mathbf{u}}_{\mathbf{q}},{\mathbf{b}}_{\mathbf{k}},{\mathbf{i}}_{\mathbf{x}}\right)]$, as shown in Figure 2.

3.2.2. Multibehavior Interaction Sequence-Dependent Encoder

In order to better extract user preferences and simulate the dependence between different types of behaviors, we use the attention mechanism in user behavior interaction to obtain the commonality of individual behaviors and the relationships of different behaviors. Considering the relationships between different behaviors of users, these relationships will help e-commerce platforms to combine the relationships of behaviors to more accurately recommend items to users, and this attention can capture which behavior has a greater relationship with the purchase behavior, hence the name “multibehavior attention”. The relationships between multiple user behaviors are used to model the fine-grained interaction between users and items, as shown in Figure 2. We propose a multibehavior interaction sequence-dependent encoder (MBS dependency encoder), which is an implicit or explicit user interest in items that users interact with by using them within behaviors and between behaviors. Different behaviors of users differently contribute to items that users may be interested in. Therefore, the MBS dependency encoder captures different relationships using user behaviors with attention, which is shown as attention fusion in Figure 2, based on the self-attention mechanism capturing fine-grained relationships between auxiliary behaviors and target behaviors, modeling multibehavior dependencies. Multiple behaviors put into attention can make behaviors no longer independent, and form a feature vector about the purchase behavior (attention fusion). Specifically, ${\mathbf{S}}_{{\mathbf{u}}_{\mathbf{q}}}$ is a sequence of historical interactions of each user. The input of attention is an auxiliary behavior feature vector ${\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{\mathbf{k}}}\in {\mathbf{R}}^{\mathbf{n}\ast \mathbf{d}}$ and the target behavior feature vector ${\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{{\mathbf{k}}^{{}^{\prime }}}}$ of the same user, $\mathbf{k}\in [\mathbf{1},\mathbf{2},\dots ,\mathbf{K}]$, where ${\mathbf{i}}_{\mathbf{1}}$ represents the first item $\mathbf{i}$ in the item set $\mathbf{I}$. The feature vector ${\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{\mathbf{k}}}$ is an element in the sequence ${\mathbf{S}}_{{\mathbf{u}}_{\mathbf{q}}}$. In addition, we calculate the weight matrix of each auxiliary behavior feature vector ${\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{\mathbf{k}}}$ and target behavior feature vector ${\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{{\mathbf{k}}^{{}^{\prime }}}}$, which is to understand the relationships between behaviors from users’ historical behaviors:

$${\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\mathbf{s}}=\frac{{\left({\mathbf{W}}^{\mathbf{Q}}\times {{\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{\mathbf{k}}}}^{\mathbf{T}}\right)}^{\mathbf{T}}\left({\mathbf{W}}^{\mathbf{K}}\times {{\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{{\mathbf{k}}^{{}^{\prime }}}}}^{\mathbf{T}}\right)}{{\sum }_{\mathbf{k}=\mathbf{1}}^{\mathbf{K}}{\left({\mathbf{W}}^{\mathbf{Q}}\times {{\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{\mathbf{k}}}}^{\mathbf{T}}\right)}^{\mathbf{T}}\left({\mathbf{W}}^{\mathbf{K}}\times {{\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{{\mathbf{k}}^{{}^{\prime }}}}}^{\mathbf{T}}\right)}$$

(1)

$${\alpha }_{\mathbf{k}}^{\mathbf{s}}=dropout\left(softmax\left({\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\mathbf{s}}\right)\right)$$

(2)

$${\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k},{\mathbf{k}}^{\prime }}}={\alpha }_{\mathbf{k}}^{\mathbf{s}}\times {\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{W}}^{\mathbf{V}}$$

(3)

where ${\mathbf{W}}^{\mathbf{Q}},{\mathbf{W}}^{\mathbf{K}},{\mathbf{W}}^{\mathbf{V}}\in {\mathbf{R}}^{\mathbf{d}\ast \mathbf{n}}$ are the weight matrix of learnable behavior vectors. ${\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\mathbf{s}}\in {\mathbf{R}}^{\mathbf{n}\ast \mathbf{n}}$ represents an relationship matrix between the auxiliary behavior $\mathbf{k}$ and the target behavior ${\mathbf{k}}^{\prime }$. This relationship matrix represents the relationship between the auxiliary and target behaviors. ${\alpha }_{\mathbf{k}}^{\mathbf{s}}$ represents the attention score. ${\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\mathbf{s}}$ represents calculation by softmax function in order to find auxiliary behavior that is closer to the target behavior. To prevent overfitting problems, we use dropout method to obtain ${\alpha }_{\mathbf{k}}^{\mathbf{s}}$. The sequence ${\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k},{\mathbf{k}}^{\prime }}}$ contains the closer relationship between the auxiliary behavior and the target behavior, which is obtained by multiplying the attention score ${\alpha }_{\mathbf{k}}^{\mathbf{s}}$ with the behavior feature vector ${\mathbf{s}}_{{\mathbf{u}}_{\mathbf{q}},{\mathbf{i}}_{\mathbf{1}}}^{{\mathbf{b}}_{\mathbf{k}}}$.

3.2.3. Multibehavior Interaction Sequence Modeling

The history of multiple user interactions in the real world contains a wealth of information. Past studies have modeled user interactions chronologically to predict the next item that a user will interact with. However, due to the existence of many external uncertain factors, it is impossible for users to interact according to the strict sequence of interactive behaviors. The aimless clicking of items by users can be considered as an internal threat, where these excessive and useless clicks are present as noise for the model. External threats include network lag or network updates, such as users not being able to interact with a particular item due to network lag. TP_MB enables a multibehavior attention fusion to extract different user behavior characteristics, which captures personalized user interests by modeling the underlying relationships of different types of behavior. We develop an attention fusion to extract different user behavior features. Inspired by BERT4Rec [30] in terms of text, we introduce a semantic encoder of behavior to capture personalized user interests:

$${\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k},{\mathbf{k}}^{\prime }}}=GELU({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k},{\mathbf{k}}^{\prime }}}\times \mathbf{W}+\mathbf{b})$$

(4)

where we use Gaussian error linear element (GELU) activation function. $\mathbf{W}$ represents the weight matrix of the GELU activation function; $\mathbf{b}$ means bias. ${\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k},{\mathbf{k}}^{\prime }}}$ represents the user partial long-term interest captured by $\mathbf{k}$ behaviors in the user long-term history. Softmax, as the activation function of output, normalizes the results of the concatenation of various behavior sequences:

$${\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}}=softmax({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k},{\mathbf{k}}^{\prime }}}\left|\right|{\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}+\mathbf{1},{\mathbf{k}}^{\prime }}}\left|\right|\dots \left|\right|{\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}+\mathbf{n},{\mathbf{k}}^{\prime }}})$$

(5)

For different users, users have different behavior interaction sequences according to the timeline of user–item interactions leading to different encoding results. The timeline enables TP_MB to better predict purchase intent.

3.2.4. Multibehavior Interaction Sequence Self-Supervised Learning

In TP_MB, it is our goal to capture the commonality of multiple behaviors of the same user and the differences of multiple behaviors of different users. Inspired by EHCF, users’ multibehavior relationships reflect their implicit intentions [2]. Self-supervised learning is a kind of contrast learning in machine learning. Therefore, we design intrapath self-supervised learning of multibehavior interaction sequences to enhance supervision signals of multiple behavior data through self-supervised learning. Specifically, we regard the different behaviors of the same user as positive sample pairs $\left\{\left({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}},{\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}+\mathbf{1}}}\right)|\mathbf{q}\in \mathbf{U}\right\}$, and the different behaviors of different users as negative sample pairs $\left\{\left({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}},{\mathbf{s}}_{\mathbf{p}}^{{\mathbf{b}}_{\mathbf{k}+\mathbf{1}}}\right)|\mathbf{q},\mathbf{p}\in \mathbf{U},\mathbf{q}\ne \mathbf{p}\right\}$. We define the TP_MB objective function according to InfoNCE:

$$L_{SCL}=\sum _{\mathbf{q}\in \mathbf{U}}-log\left(\frac{exp\left(({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}+\mathbf{1}}})\right)}{exp\left(({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}+\mathbf{1}}})\right)+exp\left(({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{s}}_{\mathbf{p}}^{{\mathbf{b}}_{\mathbf{k}+\mathbf{1}}})\right)}\right)$$

(6)

3.3. Multibehavior Interaction Graph Path

3.3.1. Multibehavior Interaction Graph Embedding

In general, using a single piece of information of the user, one cannot obtain enough available information. Users have multiple behaviors, including click, shopping cart, favorite and purchase. In addition, for the user’s purchase behavior, other behaviors have great value in helping TP_MB extract user interest. Therefore, we set the purchase behavior as the target behavior, and other behaviors as auxiliary behaviors. Learning user interests with the help of auxiliary behaviors is to predict user intent in purchasing behavior. TP_MB builds a user–item graph of different interaction behaviors through all items that users interact with in different behaviors. Multibehavior interaction graph (MB interaction graph) contains all information about user interactions. First, we define $\mathbf{G}=(\mathbf{V},\mathbf{E})$: $\mathbf{V}$ means that the node set includes user set $\mathbf{u}\in \mathbf{U}$ and item set $\mathbf{i}\in \mathbf{I}$, namely $(\mathbf{U},\mathbf{I})\in \mathbf{V}$. $\mathbf{E}$ represents different interaction behaviors between user nodes and item nodes. Furthermore, the embedding of a multibehavior graph is composed of multiple behavior subgraph embeddings, so our behavior subgraph embedding can be expressed as ${\mathbf{G}}_{\mathbf{b}}=({\mathbf{V}}_{\mathbf{b}},{\mathbf{E}}_{\mathbf{b}})$. For example, the behavior subgraph composed of the items clicked by the user, ${\mathbf{G}}_{\mathbf{click}}=\left({\mathbf{V}}_{\mathbf{click}},{\mathbf{E}}_{\mathbf{click}}\right)$,${\mathbf{G}}_{\mathbf{click}}$ represents the graph representation where the user interacts with items by clicking. ${\mathbf{V}}_{\mathbf{click}}$ represents the user and item node connected with the click behavior, and ${\mathbf{E}}_{\mathbf{click}}$ represents the user’s click behavior.

3.3.2. Multibehavior Interaction Graph Dependency Encoder

We design a multibehavior interaction graph information aggregation. Research results on graph convolution showed that general research focused on node characterization of simple undirected graphs [31]. The above work ignored edges between nodes that also had multiple properties, such as behavior. Inspired by graph neural network processing user multirelational data GHCF [3], we propose a multibehavior interaction graph path, and use neural networks to obtain the global representation of user interaction, as shown in Figure 3. Specifically, it first focuses on the node representation of the learning graph. For each behavior subgraph, it is embedded into the adjacency matrix ${\mathbf{A}}_{\mathbf{k}}$, which is composed of the matrix ${\mathbf{R}}_{\mathbf{k}}$. ${\mathbf{L}}_{\mathbf{k}}$ is the normalized Laplacian matrix of k behavior, composed of the degree matrix of $\mathbf{k}$ behavior ${\mathbf{D}}_{\mathbf{k}}^{-\frac{\mathbf{1}}{\mathbf{2}}}$, and identity matrix of $\mathbf{k}$ behavior ${\mathbf{I}}_{\mathbf{k}}$. For the multibehavior interaction graph of users, GCN can be used to better obtain the global representation of all users. We follow LightGCN:

$${\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}}^{(\mathbf{l}+\mathbf{1})}=sigmoid({\mathbf{L}}_{\mathbf{k}}\times {\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}}^{\left(\mathbf{l}\right)}\times {\mathbf{W}}_{\mathbf{k}})$$

(7)

where ${\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}}^{\left(\mathbf{l}\right)}$ is the node feature matrix of layer l of nodes in the figure, and ${\mathbf{W}}_{\mathbf{k}}$ is the transformation matrix of behavior graph information transfer. $Sigmoid$ is the activation function. GCN has a total of $\mathbf{L}$ layers, and $\mathbf{l}$ represents the order of neighbors we obtain. By obtaining the features of nodes with $\mathbf{k}$ behaviors in the graph, we design a multibehavior interaction graph attention encoder (MBG dependency encoder), which is shown as graph-inner attention in Figure 3. The encoder constructs with the graph node representation under different behaviors. The influence score of the corresponding auxiliary behavior graph with respect to the target behavior graph can be obtained. Therefore, we introduce a multibehavior interaction graph attention encoder, auxiliary behavior graph ${\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}}$ and target behavior graph ${\mathbf{x}}_{{\mathbf{b}}_{{\mathbf{k}}^{\prime }}}$ as input:

$${\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{{}^{\prime }}}^{\mathbf{g}}=\frac{{({\mathbf{W}}^{\mathbf{Q}}\times {\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}})}^T({\mathbf{W}}^{\mathbf{K}}\times {\mathbf{x}}_{{\mathbf{b}}_{{\mathbf{k}}^{{}^{\prime }}}})}{{\sum }_{{\mathbf{k}=\mathbf{1}}^{\mathbf{K}}}{({\mathbf{W}}^{\mathbf{Q}}\times {\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}})}^T({\mathbf{W}}^{\mathbf{K}}\times {\mathbf{x}}_{{\mathbf{b}}_{{\mathbf{k}}^{{}^{\prime }}}})}$$

(8)

$${\alpha }_{\mathbf{k}}^{\mathbf{g}}=dropout\left(softmax\left({\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\mathbf{g}}\right)\right)$$

(9)

$${\mathbf{X}}_{{\mathbf{b}}_{\mathbf{k}}}={\alpha }_{\mathbf{k}}^{\mathbf{g}}\times {\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{W}}^{\mathbf{V}}$$

(10)

where ${\mathbf{W}}^{\mathbf{Q}}\in {\mathbf{R}}^{\mathbf{d}\ast \mathbf{n}}$,${\mathbf{W}}^{\mathbf{K}}\in {\mathbf{R}}^{\mathbf{d}\ast \mathbf{n}}$,${\mathbf{W}}^{\mathbf{V}}\in {\mathbf{R}}^{\mathbf{d}\ast \mathbf{n}}$ is the weight matrix of the learnable behavior matrix. ${\alpha }_{\mathbf{k}}^{\mathbf{g}}$ is the attention score, which is regarded as the weight added to the auxiliary behavior ${\mathbf{x}}_{{\mathbf{b}}_{\mathbf{k}}}$. ${\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\mathbf{g}}$ is calculated in the same way as we mentioned in Section 2.2. By taking the relationship matrix ${\mathbf{A}}_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\mathbf{g}}$ as the input, it is obtained by multiclassification. ${\mathbf{X}}_{{\mathbf{b}}_{\mathbf{k}}}$ is the auxiliary behavior feature matrix of the target behavior as the final output of the MBG dependency encoder.

3.3.3. Multibehavior Interaction Graph Self-Supervised Learning

As we all know, the sparsity problem of user interaction behavior in the recommendation system is widespread [32]. There is also a unequal data distribution problem among behaviors. For example, users click too many times and make few purchases. Therefore, to alleviate this problem, TP_MB enhances sparse supervised signals using self-supervised learning of multibehavior interaction graphs rather than capturing user interest using a single behavior. Specifically, the output of MBG dependency encoder and the embedding of the graph of the target behavior are taken as input. That is to say, the embedding ${\mathbf{X}}_{\mathbf{k}}$ of the graph of the auxiliary behavior and the embedding ${\mathbf{X}}_{{\mathbf{k}}^{\prime }}$ of the graph of the target behavior are used as input. Contrastive learning is one of the methods in self-supervised learning. Thus, features are learned by constructing positive and negative examples and establishing a contrastive loss. Therefore, intrapath multibehavior interaction graph self-supervised learning is designed to enhance multibehavior data supervision signals through self-supervised learning. Graph self-supervised learning based on InfoNCE can effectively alleviate the unequal data distribution problem of different behaviors among users. In TP_MB, different behavior graph of the same user are regarded as positive sample pairs $\left\{\left({\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}},{\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}+\mathbf{1}}\right)|\mathbf{q}\in \mathbf{U}\right\}$, and different behaviors of different users are regarded as negative sample pairs $\left\{\left({\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}},{\mathbf{X}}_{\mathbf{p}}^{\mathbf{k}+\mathbf{1}}\right)|\mathbf{q},\mathbf{p}\in \mathbf{U},\mathbf{q}\ne \mathbf{p}\right\}$. We maximize mutual information between users by comparing positive and negative sample pairs:

$$L_{GCL}=\sum _{\mathbf{q}\in {\mathbf{U}}^{+},\mathbf{p}\in {\mathbf{U}}^{-}}-log\left(\frac{exp({\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}}\times {\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}+\mathbf{1}})}{exp({\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}}\times {\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}+\mathbf{1}})+exp({\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}}\times {\mathbf{X}}_{\mathbf{p}}^{\mathbf{k}+\mathbf{1}})}\right)$$

(11)

The consistency of two-behavior graph is maximized via the self-supervised loss defined above. And we maximize the difference between different user behaviors to obtain behavior data enhancement.

3.4. Contrast Loss for Two-Path Enhancement

Since the problem of user interaction data sparsity has always existed, even the sequence self-supervision proposed in Section 3.2.4 and the graph self-supervision proposed in Section 3.3.3 can effectively alleviate this problem. However, using only these two self-supervision methods will not perform better than combining the two supervision methods to complement each other. Specifically, multibehavior interactions between different multibehavior paths are based on use InfoNCE loss. We regard the sequence path and graph path of the same user as positive samples, expressed by $\left\{\left({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}},{\mathbf{X}}_{\mathbf{q}}^{{\mathbf{k}}^{\prime }}\right)|\mathbf{q}\in {\mathbf{U}}^{+}\right\}$. The sequence path and graph path of different users are regarded as negative samples expressed by $\left\{\left({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}},{\mathbf{X}}_{\mathbf{p}}^{{\mathbf{k}}^{\prime }}\right)|\mathbf{q}\in {\mathbf{U}}^{+},\mathbf{p}\in {\mathbf{U}}^{-}\right\}$. Self-supervised losses for InfoNCE-based sequences and Graphs $L_{SGCL}$ are as follows:

$$L_{SGCL}=\sum _{\mathbf{q}\in {\mathbf{U}}^{+},\mathbf{p}\in {\mathbf{U}}^{-}}-log\frac{exp(({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}+\mathbf{1}})/\tau )}{exp(({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{X}}_{\mathbf{p}}^{\mathbf{k}+\mathbf{1}})/\tau )+exp(({\mathbf{s}}_{\mathbf{q}}^{{\mathbf{b}}_{\mathbf{k}}}\times {\mathbf{X}}_{\mathbf{q}}^{\mathbf{k}+\mathbf{1}})/\tau )}$$

(12)

$$L_{CL}=\lambda (L_{SCL}+L_{GCL}+L_{SGCL})$$

(13)

$\tau$ is the temperature coefficient that balances the intensity of learning between the two paths. ${\lambda }_1$ is a hyperparameter. $L_{SCL}$ is the sequence self-supervised learning of multibehavior interactions within two paths we mentioned in Section 3.2.4. $L_{GCL}$ is the self-supervised learning of multibehavior interaction graphs within two paths we mentioned in Section 3.3.3. Therefore, we propose the two contrastive learning losses as the supplement. The final loss function list $L_{CL}$ is composed of sequence loss function $L_{SCL}$, graph loss function $L_{GCL}$ and sequence graph loss function $L_{SGCL}$ for each pair of behaviors.

4. Experiments

We conduct experiments on two public datasets to verify the effectiveness of TP_MB. Our aim is to study the following questions:

• RQ1: Can TP_MB achieve better performance compared to the state-of-the-art model?
• RQ2: In our designed TP_MB, what is the influence of each component on each other?
• RQ3: How do different hyperparameters affect model performance?

4.1. Experimental Results and Analysis

Experiments on two real datasets in the real world demonstrate the effectiveness of our proposed TP_MB and compare it with other baseline models and mainstream models. We evaluated TP_MB using a series of parameterization and ablation studies.

4.2. Datasets

We evaluated the effectiveness of our model on two different types of datasets, as shown in

Table 1. Statistics of experimental dataset.

Dataset	User	Item	Interaction	Interaction Behavior Types
Tmall	27,155	22,014	613,978	{click,add_to_cart,buy}
CIKM2019EComm AI	23,023	25,054	41,526	{click,add_to_cart,buy}

. Tmall is one of the largest e-commerce platforms in China. This dataset contains the following user interaction data: click, add to cart, purchase. We followed the method in [3] for data processing. CIKM2019 EComm AI is the e-commerce data provided by CIKM2019 e-commerce artificial intelligence challenge. Each piece of data consists of a user, an item and an interaction. And a timestamp is appended to the end of each piece of data. Among them, user interaction includes click, add to shopping cart and purchase, and various user interaction behaviors reflect the user’s intention for the item.

4.3. Implementation Details and Environment

We chose pytorch as the deep learning framework. The Adam optimizer was used to optimize the parameters during the training process, and the maximum sequence length was set to 100. The adjustment range of learning rate is $\left\{{0.6e}^{-3},{1e}^{-3},{2e}^{-3},{3e}^{-3}\right\}$. The size of each batch entered from the dataset was 256. The decay rate at each epoch in the training phase is ${0.1e}^{-4}$. The adjustment range of the number of layers for the information transmission of the graph was 1–4. In addition, due to the small number of behavior types, overfitting problems were prone to occur during the experiment. We used dropout in the graph convolutional network to solve this problem. In our evaluation, four evaluation indicators were selected, which are hit rate (Hit), normalized loss cumulative gain (NDCG), mean reciprocal rank (MRR) and area under the metric (AUC). The first three were used to measure the accuracy of our recommendation model. The area under the metric (AUC) is a performance indicator to measure the pros and cons of the learner.

4.4. Baseline

In order to fully verify the validity of TP_MB, we selected three different types of recommendation system models as the baseline models for comparative experiments. These were single-behavior recommendation system methods, sequential recommendation methods and multibehavior recommendation system methods.

Single-behavior recommended Methods:

• LightGCN [32]: A simplified method of traditional GCN. This model removed the feature transformation and nonlinear activation operations of the aggregation layer and propagation layer in the standard GCN, and only consisted of neighborhood aggregation, making it more concise and more suitable for recommendation systems.
• BERT4Rec [30]: This modeled user behavior through self-attention mechanism, and fused project neighbor information for recommendation.

General sequence recommendations:

• Caser [33]: For the most recent projects, graph convolution was embedded in time and space to model the dynamic change of user interest over time.

Multibehavior recommendation methods:

• GHCF [3]: The model encoded the behavior of users interacting with items, and the behavior pattern was embedded into the overall heterogeneous graph as a node when composing the graph. At the same time, LightGCN was used to realize aggregation and propagation between nodes.
• DHSL-GM [34]: Similar users and similar items constituted hypergraphs, respectively. The gated neural network was used to predict less popular items in a more balanced manner. This was the latest use of self-supervised learning to model the representation of users and products on the dual hypergraph. This model is a relatively advanced method at present, and is also the main comparison object of this paper.

4.5. Performance Comparison

We summarize the detailed evaluation results of all methods on Tmall and CIKM2019E datasets in

Table 2. Overall performance comparison of all methods on Tmall dataset.

	Tmall
	NDCG@10	Hit@10	MRR@10	AUC@10
Bert4Rec	0.1985	0.3274	0.1447	0.6583
LightGCN	0.2051	0.3447	0.1503	0.6539
Caser	0.1933	0.3231	0.1522	0.6876
GHCF	0.3754	0.4635	0.3164	0.6873
DHSL_GM	0.3983	0.5126	0.3437	0.6981
TP_MB	0.4393	0.6053	0.4066	0.7505
TP_MB_t	0.4471	0.6241	0.4137	0.7601
Impro[TP_MB]	10.3%	18.1%	8.2%	7.5%
Impro[TP_MB_t]	12.3%	21.8%	20.3%	8.9%

and

Table 3. Overall performance of time-based method compared to all methods on CIKM2019ECommAI dataset.

	CIKM2019E
	NDCG@10	Hit@10	MRR@10	AUC@10
Bert4Rec	0.2264	0.2896	0.1878	0.6686
LightGCN	0.2352	0.2534	0.1811	0.6671
Caser	0.2139	0.2962	0.1790	0.6731
GHCF	0.3244	0.4337	0.2926	0.6866
DHSL_GM	0.3662	0.4537	0.3108	0.6874
TP_MB	0.3970	0.5277	0.3344	0.7273
TP_MB_t	0.4037	0.5394	0.3421	0.7314
Impro [TP_MB]	8.4%	16.3%	7.6%	5.8%
Impro [TP_MB_t]	10.2%	18.8%	9.8%	6.4%

, where TP_MB and TP_MB_t results are compared with baseline as well as state-of-the-art models. The results of TP_MB and TP_MB_t are in bold.

The main observations are three main reasons for why TP_MB outperforms other baselines on two datasets:

(1) Multibehavior recommendation methods (such as GHCF and DHSL-GM) perform better than single-behavior recommendation methods (such as LightGCN, BERT4Rec, Caser). This demonstrates the effectiveness of modeling user preferences by exploring multibehavior information.

(2) The improvement of TP_MB is due to the exploration of multibehavior dependencies that are ignored by existing methods. This suggests that modeling different behavior dependencies can make the model better. It is verified that our two-path comparison method gives the model the ability to deal with behavior dependencies. Unlike the graph-based self-supervised method GHCF, the two-path self-supervised learning paradigm included in TP_MB incorporates auxiliary self-supervised signals from different types of behavior dimensions. The direction of parameter optimization is provided for the model.

(3) These models do not extract the interactions between multiple behaviors, except for DHSL_GM, which is a dual-hypergraph convolution model. And our model outperforms DHSL_GM because our two path is in the form of sequence path and graph path contrast, and the possibility of overfitting is less than that of DHSL_GM. The superiority of our model can be demonstrated compared to these baseline models. As shown in Figure 4a,b, TP_MB and TP_MB_t outperforms the other models both on the Tmall and CIKM datasets. In addition, TP_MB outperforms TP_MB for connection time, indicating that time has great potential in terms of improving model performance.

In addition, TP_MB_t outperforms TP_MB compared to the baseline and the state-of-the-art research methods when utilizing timestamps. This is because the sequence data contain sequential time that can prove that the TP_MB captures dependency of the behavior correctly. Thus, for TP_MB_t, effectively using timestamps can help to improve model performance.

4.6. Ablation Study

We performed ablation studies on the model to justify the key components. The analysis details are summarized as follows. In particular, we describe the model variables in the experiment:

• Removing path attention w/o-Att: Different modal relationships between multiple behaviors are not captured using attention in the two paths.
• Removing two-path self-supervision w/o-DCL: No two-path contrastive learning strategy is used to supplement sparse data.

Table 4. Ablation study.

Data	Tmall		CIKM2019E
Metric	Hit@10	NDCG@10	Hit@10	NDCG@10
w/o-Att	0.3431	0.1863	0.2581	0.1264
w/o-DCL	0.3108	0.1773	0.3630	0.1973
TP_MB	0.6053	0.4393	0.5277	0.3970
TP_MB_t	0.6241	0.4471	0.5394	0.4037

and Figure 5b show the results of TP_MB ablation study. We summarize the following findings:

(1) TP_MB compared with w/o-Att, combining interdependencies between different types of interactions on all items can greatly improve performance. This demonstrates the legitimacy of our self-attention structures for learning explicit paired relationships between different types of behavior.

(2) The effect of TP_MB after the removal of two path self-supervision (w/o-DCL) decreased significantly, thus illustrating the importance of considering dense data across multiple behavior types when analyzing user preferences.

(3) Compared to TP_MB, TP_MB_t uses timestamps and obtains better results. This is sufficient to prove that TP_MB_t captures more information and helps improve the performance of the model.

4.7. Loss Weight Analysis

In Figure 5a, it can be seen that as the loss weight increases from 0.1–0.5, the performance increases and then decreases when TP_MB_t is the TP_MB connection timestamp. The best performance in Tmall and CIKM2019ECommAI is $\lambda$ = 0.2, and the best $\lambda$ differs for different datasets. The reason is that the sparsity is different for different datasets.

4.8. Hyperparameter Analysis

In this section of the experiment, we investigate the effects of different hyperparameter settings in our designed TP_MB and TP_MB_t framework. The experimental results are shown in Figure 6a,b. We study the effect of one hyperparameter at a time and keep the other parameters at their default settings.

$\beta$ hyperparameter: This controls the importance of the self-supervised learning task and the recommendation task between paths in TP_MB. When the value of $\beta$ is low, the model pays less attention to the recommendation task. The model cannot obtain enough supervisory signals from the training data to update the parameters. With the increase in $\beta$, the performance of the model also improves. When $\beta$ = 0.3, the performance is the best. When $\beta$ is larger than a certain value ($\beta$ = 0.4), the performance of the model decreases slightly in both datasets.

Embedding dimension d. When the embedding dimension is 256 on the Tmall dataset, the dimension on the CIKM dataset is 128, The model has good performance, as shown in Figure 6b. When the embedding dimension is set too high, it will cause the tensor dimension to be too large. While further increasing the amount of calculation, it will also lead to nondiscriminative characterization results. So, the embedding dimension is also crucial. Experimental results show that this model can improve learning performance in a higher dimension. This shows that the model is capable of learning from user–item multiple interactions.

On the other hand, it can be found that the addition of timestamps to TP_MB improves the results of NDCG@10 without changing the hyperparameters and dimensions in Figure 7a,b, which is more evidence of the effectiveness of using time.

5. Conclusions

In this paper, we propose a two-path multibehavior model of user interaction (TP_MB). TP_MB utilizes a multibehavior dependency encoder to extract dependencies between multiple behaviors. To enhance the performance of the model, we use three self-supervised learning methods to obtain more supervised signals, which can effectively alleviate the data sparsity problem and improve the prediction performance. The experimental results show that our model can achieve significant improvements over the state-of-the-art model on two public datasets. However, our study only studies short-term behavior, and does not consider users’ long-term interests. In the future, we plan to study combination both long-term and short-term interests of users and effectively use temporal data to better model user intent.