Multi-article binding recommendation method based on graph contrast learning

Abstract

The invention discloses a multi-article binding recommendation method based on graph contrast learning, and relates to the technical field of e-commerce application. According to the method, through heterogeneous binding relation modeling, a user-article-binding ternary interaction graph is constructed, direct preference of a user to an article and indirect association of binding driving are jointly learned, and the problem of relation splitting caused by multi-graph splitting in AMCBR and MGCRL is solved; according to the method, light-weight projection head optimization is carried out, double-layer linear projection is adopted to replace a traditional multi-layer perceptron (MLP), the over-smoothing risk is reduced while the contrast characterization distinction degree is enhanced, and the redundancy problem caused by fusion or knowledge modules in MultiCBR and KEMB-Rec is solved; the method introduces a multi-objective loss function, combines main task recommendation loss, cross-view comparison loss and binding comparison loss, and collaboratively optimizes local and global embedding representation, is more comprehensive than EBRec single view loss, and effectively alleviates sparsity and over-smoothing problems.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of e-commerce applications, and particularly relates to a multi-item bundling recommendation method based on graph contrast learning. BACKGROUND

[0002] In recent years, with the rapid development of e-commerce platforms and content services, recommendation systems have become a core component of many enterprises. However, in the multi-item bundling recommendation scenario, traditional recommendation methods face three key challenges: (1) amplification of sparsity: the sparsity of user interaction with single items is further exacerbated in the bundling scenario due to the explosion of combination dimensions; (2) difficulty in capturing dynamic preferences: users' preferences for bundling are prone to change rapidly with the scene, and static modeling is difficult to adapt; (3) difficulty in modeling synergistic effects: in the multi-item association, the synergistic gain of items within the bundle needs more detailed structural representation.

[0003] To address the above challenges, researchers have explored graph structures and contrast learning. Early work focused on the "user-item binary interaction" scenario, and the core idea was to construct positive and negative sample pairs and enhance the representation distinction through contrast loss. For example, SimGCL uses simple graph structures to sample positive and negative samples, verifying the potential of contrast learning in alleviating sparsity, but relying on manually designed samples and not addressing the sampling efficiency problem under large-scale data; subsequent research attempts to optimize the loss function, such as improving the InfoNCE variant to break through the "binary interaction" framework, but still difficult to adapt to the complex relationships of bundling recommendations.

[0004] With the development of graph neural networks (GNN), graph contrast learning (GCL) provides a new approach to modeling high-order associations. GCL abstracts user-item relationships into graph structures, combining GNN propagation and contrast learning to more efficiently mine implicit associations. Typical examples include LightGCN, which simplifies graph convolution and focuses on binary interactions, verifying the benefits of graph structures for recommendations; however, such methods only model "user-item" binary relationships, ignoring the key node "bundle", which results in the inability to fully capture multi-item synergistic effects.

[0005] Further combing existing research can find that although GCL provides a new idea for high-order association modeling, there are still deficiencies in the targeted design for bundle recommendation. On the one hand, existing GCL methods mostly focus on the "single item recommendation" scenario and fail to fully consider the ternary interaction relationship of "user-item-bundle" in the bundle scenario. In CrossCBR, it is pointed out that existing models mostly process user-bundle graph and user-item-bundle graph independently, and fail to fully exploit the collaborative association between the two, which is easy to lead to recommendation bias; Similarly, related research also emphasizes that existing methods only model the bundle-item membership relationship, and it is difficult to capture the high-order association of bundle-user-item. In the multi-graph modeling method specially designed for the bundle scenario, AMCBR captures the ternary interaction by constructing preference graph, collaborative neighborhood graph and item-level preference hypergraph, but its adaptive aggregation module relies on node similarity and popularity weighting, which is easy to be disturbed by noise in sparse scenarios, and the multi-graph contrastive learning only focuses on the cooperation between graphs, and does not deeply exploit the internal association mechanism of "user-item-bundle"; MultiCBR extends user-bundle, user-item, and bundle-item three views, although it covers more relationship types, but the "early fusion" strategy directly weights and combines the multi-view embedding, which may dilute the unique semantics of different views, especially when the bundle-item association is sparse, which is easy to lead to ambiguous representation; MGCRL further splits the interaction relationship into indirect UB hypergraph, UB interaction graph and other multi-views, but its two-level contrastive learning needs to optimize the intra-view and inter-view loss respectively, which leads to the increase of model complexity, and it does not design a special modeling mechanism for the collaborative effect of bundle internal items.

[0006] On the other hand, complex network structure is easy to cause over-smoothing problem, and traditional multi-layer perception (MLP) projection head increases the computational cost. Deep GCN may lead to convergence of node embedding during propagation, especially in bundle recommendation, the personalized preference of users for different bundles may be over-smoothed and blurred; At the same time, the traditional MLP projection head is low in computational efficiency in large-scale bundle scenarios, and a more lightweight design scheme is urgently needed. This problem is particularly evident in item-level representation enhancement methods, such as EBRec, which supplements the bundle-item relationship through B-U-I high-order association, but relies too much on pseudo-interaction data generated by pre-trained models, which may introduce bias in data distribution deviation scenarios, and its representation of bundles still stays at the item aggregation level, without modeling the global features of bundles as independent units; KEMB-Rec models multiple behavior patterns through hypergraph, but its core focuses on the difference and commonality of behavior sequences, without specially designing a collaborative effect modeling module for the bundle scenario, and the additional semantic information introduced by the knowledge graph increases the redundancy of the model, reducing the efficiency in large-scale bundle recommendation.

[0007] These limitations make it difficult for existing GCL methods to adapt to the dual demands of precision and efficiency of bundle recommendation. SUMMARY

[0008] The application aims to provide a multi-item bundled recommendation method based on graph contrastive learning to solve the technical problems proposed in the background art.

[0009] To achieve the above-mentioned purpose, the application provides the following technical scheme: a multi-item bundled recommendation method based on graph contrastive learning, at least comprising the following steps:

[0010] S1: First, local-global double-path embedding is performed, that is, the original graph generates local and global embeddings through GCN and SVD respectively to generate dynamic bundled representation without predefining bundled packages. The local-global double-path embedding process includes local embedding path (GCN), global embedding path (SVD), and generation and representation of virtual bundles.

[0011] S2: Then, joint embedding fusion is performed, that is, multi-view features are integrated to construct a unified representation of user-item pairs.

[0012] S3: Finally, contrastive learning optimization is performed to enhance the robustness of the model through cross-view contrastive loss.

[0013] Further, in the local embedding path, the user set and the item set form a bipartite graph .

[0014] To capture the structural relationship between nodes, first, a normalized adjacency matrix is constructed, and its elements are defined as:

[0015]

[0016] wherein, represents the interaction behavior of user and item ; and represent the neighbor set of user and item , respectively.

[0017] The local embedding path adopts a graph convolutional network (GCN) to aggregate multi-order neighborhood information through a hierarchical propagation mechanism. The update formula of the representation of the nodes in the first layer is:

[0018]

[0019] wherein, is the node embedding matrix in the first layer; is a learnable parameter; the negative slope of the LeakyReLU activation function is fixed at 0.5; and the output of the activation function is passed through After layer propagation, get local embedding , which retains the direct interaction pattern and local community structure between users and items as the output of view Figure 1 .

[0020] Further, the global embedding path mines the potential low-rank structure of the interaction matrix based on singular value decomposition (SVD);

[0021] First, perform truncated singular value decomposition on the adjacency matrix A:

[0022]

[0023] where, ,are left and right singular vectors respectively, is a singular value diagonal matrix; Use singular vectors to construct SVD enhanced graph

[0024] , generate global embedding by message passing . .Capture the global low-rank structure of user-item interaction as the output of view (view2). Figure 2

[0025] Further, the virtual bundling mechanism captures the collaborative effect among multiple items by dynamically constructing joint representations of user-item pairs;

[0026] The positive sample virtual bundling represents the joint representation of the user and his real interaction item, which is defined as:

[0027]

[0028] where, represents the joint embedding of the user, represents the joint embedding of the item , represents the vector splicing operation, represents the projection operation. Further, after obtaining view

[0029] and view Figure 1 , combine implicit weighted fusion and explicit contrast projection of the two views; Figure 2

[0030] The S2 includes at least the following steps:

[0031] S2.1: Perform embedding generation and fusion;

[0032] The multi-layer graph convolution is propagated to generate a hierarchical local representation, and then the multi-order neighbor information is aggregated as a local embedding path through cross-layer summation. A global semantic representation is generated by SVD decomposition to generate a global embedding. Finally, feature fusion is performed, and the user and items The local and global embeddings are concatenated (Concat) to generate a joint representation of the user and item :

[0033]

[0034]

[0035] wherein, represents the local embedding of the user ; represents the global embedding of the user ; represents the local embedding of the item ; represents the global embedding of the item ; represents a concatenation fusion operation;

[0036] S2.2: Positive and negative sample construction;

[0037] A virtual bundled representation is dynamically generated using the joint embedding, and the positive sample is bundled as follows:

[0038]

[0039] wherein the item is the real interaction target of the user , and is referred to as a positive sample item;

[0040] The negative sample is the joint representation of the user and the corresponding negative item :

[0041]

[0042] The negative sample is an item other than the positive sample of the user in the current batch;

[0043] S2.3: Projection head mapping and embedding alignment;

[0044] The joint semantic space of the user-item is implicitly aligned by nonlinear projection, and the concatenated dimensional vector is reduced to dimensional

[0045]

[0046] The projection head is a two-layer fully connected network containing the ReLU activation function. and These are the projection matrices for the first and second layers, respectively; the dimensionality reduction preserves the joint semantic information of the user and item while reducing computational complexity.

[0047] Then, L2 normalization is used to normalize the projected embedding.

[0048]

[0049] Implicit contrast alignment is used instead of explicit stitching and blending. Through cross-view contrast loss and collaborative design of the projector head, dynamic complementarity of local (GCN) and global (SVD) embedding is achieved.

[0050] Furthermore, the contrastive learning optimization L achieves global optimization through weighted fusion by designing a collaborative optimization framework that combines the main task loss, contrastive learning loss, and a bundled contrastive loss with a regularization term.

[0051] The main task loss adopts Bayesian personalized ranking loss, which optimizes the user's ranking preference for "positive samples" and "negative samples" to ensure that items and bundles that the user actually interacts with are ranked before uninterrupted items.

[0052]

[0053] in, This represents the sample set for the training batch, including user-positive-negative item triples ( ); The user embedding matrix is ​​generated by fusing local GCN embeddings and global SVD embeddings. For the number of users, For the embedded dimension; The item embedding matrix is ​​generated by merging two views. For the quantity of items; and These represent positive sample items. and negative sample items The embedding vector, where User Items that are actually interacted with These are items in the same batch that the user has not interacted with; Represents the Sigmoid function;

[0054] For each triple, first calculate the user Correct items Predicted score and negative items Predicted score The difference between the two reflects the ranking relationship that positive samples are better than negative samples. By using the logarithmic function and taking the negative, the larger the difference in positive scores, the smaller the loss, thereby forcing the model to learn a ranking pattern that conforms to the user's true preferences.

[0055] The contrastive learning loss is used to address the feature distribution shift caused by the different modeling granularity between "local GCN embedding" and "global SVD embedding". The contrastive learning loss enhances feature consistency by forcibly aligning the dual-view embeddings of the same node through contrastive learning.

[0056]

[0057] in, This represents the embedding matrix generated from the user's global path. The embedding matrix represents the global path generated for an item; Indicates temperature parameter; Indicates the weight of the comparative loss; Indicates other users The local embeddings are used as negative samples in contrastive learning;

[0058] When comparing targets, let the user The global embedding should be as similar as possible to its local embedding. And let the user... Global embedding with other users The local embeddings should be as dissimilar as possible;

[0059] Local embedding excels at capturing fine-grained interactions but is prone to blurring in sparse scenes; global embedding excels at uncovering global patterns but may overlook local details. Contrastive learning loss achieves complementarity between the two through contrastive learning, and global embedding calibrates local embedding in sparse scenes.

[0060] The bundled contrastive loss explicitly models the synergistic effect of item combinations by comparing the joint embedding of "user-positive bundled combinations" and "user-negative bundled combinations", thereby enhancing the model's ability to capture multi-item associations.

[0061]

[0062] in, Indicates user bonded with Joint embedding projection, Indicates user negative binding Joint embedding projection, This indicates the weight of the bundled comparison loss.

[0063] The regularization term is used to prevent model overfitting, and the regularization term is introduced to constrain all learnable parameters, which is defined as:

[0064]

[0065] Wherein, , is the user and item embedding matrix, is all the weight and bias parameters of the projection head;

[0066] The main task loss, the contrastive learning loss, the bundled contrastive loss and the regularization term constitute the total loss function for optimization, to realize the comprehensive improvement of the ranking accuracy, the feature consistency, the bundled cooperativeness and the parameter robustness in the multi-item bundled recommendation scene;

[0067] Firstly, the four losses are mean-standard deviation standardized; , , ,

[0068] Subsequently, the multi-objective loss function is converted into a single-objective optimization problem:

[0069]

[0070] Wherein, represent the contribution proportion of each loss in the total loss, and the setting can realize the equivalent weight optimization of the four optimization objectives, and ensure the balanced consideration of each expected performance index in the model training process.

[0071] The application proposes a multi-item bundled recommendation method based on graph contrastive learning, that is, a BundleGCL model is built to jointly learn the direct preference of users to items and the indirect association driven by bundling by constructing a user-item-virtual bundle architecture, and a lightweight double-layer projection head is designed to optimize feature alignment; at the same time, a multi-objective loss function is constructed by combining the main task recommendation loss, the contrastive loss under cross-view and the bundled contrastive loss, so as to achieve the purpose of cooperative optimization of local and global embedding representation; experiments on cross-domain datasets (Yelp, Tmall, Ml10m) show that the proposed algorithm BundleGCL comprehensively surpasses existing benchmark models in recommendation performance, and exhibits more significant advantages in data sparse scenarios, effectively verifying the technical breakthrough of the model in capturing dynamic user preferences and item collaborative relationships; through systematic ablation experiments, the dual contribution of the heterogeneous bundle modeling mechanism and the lightweight projection head design is further revealed.

[0072] Compared with the prior art, the application has the beneficial effects that:

[0073] ​1. The present application models the isomorphic binding relationship, constructs a user-item-binding ternary interaction graph, and jointly learns the direct preference of the user for the item and the indirect association driven by the binding, thereby overcoming the relationship fragmentation problem caused by multi-graph splitting in AMCBR and MGCRL.

[0074] 2. The present application optimizes the lightweight projection head, adopts double-layer linear projection to replace the traditional multi-layer perception machine (MLP), enhances the contrast of the representation and reduces the risk of over-smoothing, and solves the redundancy problem caused by the fusion or knowledge module in MultiCBR and KEMB-Rec.

[0075] 3. The present application introduces a multi-objective loss function, combines the main task recommendation loss, cross-view contrast loss and binding contrast loss, and cooperatively optimizes the local and global embedding representation, which is more comprehensive than the single view loss of EBRec, and effectively alleviates the sparsity and over-smoothing problem. BRIEF DESCRIPTION OF DRAWINGS

[0076] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used for the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0077] Figure 1 It is a schematic diagram of the whole application;

[0078] Figure 2 It is a performance performance diagram of the projection head of the present application with different number of layers under the binding subset with different scales;

[0079] Figure 3 It is a performance diagram of different temperature coefficients of the present application;

[0080] Figure 4 It is a parameter of the present application, which affects the performance of the present application;

[0081] Figure 5 It is a sensitivity analysis diagram of the model parameters of the present application. DETAILED DESCRIPTION

[0082] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments.

[0083] The BundleGCL method provided by the application combines local graph convolution (GCN) and global low-rank decomposition (SVD) through a multi-view graph contrast learning framework, designs a bundling method based on parameter sharing and contrast loss, and effectively improves the robustness of a recommendation system. In model implementation, the GCN branch generates local embedding by aggregating neighborhood nodes to capture the fine-grained topology structure of user-item interaction, and the SVD branch decomposes the interaction matrix from a global perspective to mine potential low-rank statistical rules. The two branches are coupled through a shared embedding matrix, and a cross-view contrast loss function is introduced to align the local and global embedding spaces and avoid semantic deviation caused by decoupling of the two paths. This bundling mechanism enables the model to dynamically balance local details and global patterns in both sparse and dense data scenarios.

[0084] Specifically as follows:

[0085] Referring to Figure 1 , a multi-item bundling recommendation method based on graph contrast learning at least includes the following steps:

[0086] S1: First, local-global dual-path embedding is performed, that is, the original graph generates local and global embedding through GCN and SVD respectively to generate dynamic bundling representation without predefining a bundling package. The local-global dual-path embedding process includes local embedding path (GCN), global embedding path (SVD), and generation and representation of virtual bundling.

[0087] S2: Then, joint embedding fusion is performed, that is, multi-view features are integrated to construct a unified representation of user-item pairs.

[0088] S3: Finally, contrast learning optimization is performed to enhance the robustness of the model through a cross-view contrast loss.

[0089] In the local embedding path, the user set and the item set constitute a bipartite graph .

[0090] To capture the structural relationship between nodes, first, a normalized adjacency matrix is constructed, and the element is defined as:

[0091]

[0092] wherein, represents the interaction behavior of the user and the item . and represent the neighbor set of the user and the item respectively.

[0093] The local embedding path adopts a graph convolutional network (GCN) to aggregate multi-order neighborhood information through a hierarchical propagation mechanism, and the first-order neighborhood information is aggregated by the first-layer node embedding matrix The representation update formula of the first-layer node is:

[0094]

[0095] wherein, is the first-layer node embedding matrix; is a learnable parameter; the negative slope of the LeakyReLU activation function is fixed at 0.5; and the output of the first-layer propagation is the local embedding . After the second-layer propagation, the global embedding is obtained, which retains the direct interaction pattern and local community structure between users and items and is taken as the output of view1. Figure 1

[0096] The global embedding path is based on singular value decomposition (SVD) to mine the potential low-rank structure of the interaction matrix;

[0097] First, the adjacency matrix A is subjected to truncated singular value decomposition:

[0098]

[0099] wherein, , are the left singular vector and the right singular vector, respectively, is a singular value diagonal matrix;

[0100] The SVD-enhanced graph is constructed using the singular vectors, and the global embedding is generated through message passing. The global low-rank structure of the user-item interaction is captured as the output of view2. Figure 2

[0101] The local embedding can effectively capture the micro-level interaction pattern through the iterative aggregation mechanism of the neighborhood nodes, but its representation ability for sparse long-tail nodes is relatively sensitive; while the global embedding extracts potential features based on matrix decomposition techniques and has the ability to infer missing interaction relationships, but it may ignore the subtle features of local structures in the learning process. The representation characteristics of the two are complementary, which provides a theoretical basis for realizing local-global semantic collaboration in the subsequent multi-view contrastive learning framework.

[0102] The virtual bundling mechanism captures the collaborative effect among multiple items by dynamically constructing the joint representation of user-item pairs;

[0103] ​​Unlike traditional predefined bundles, virtual bundles have the following characteristics: (1) dynamically generated: without predefining fixed bundle combinations, but building during the training process; (2) implicitly represented: automatically learning bundle semantics through the model, rather than explicitly storing bundle embeddings; (3) contrastively optimized: strengthening the synergistic relationship of items within the bundle through positive and negative sample comparison. The positive sample virtual bundle represents the joint representation of the user and his real interaction items, which is defined as:

[0104]

[0105] where, represents the joint embedding of the user, represents the joint embedding of the item , represents the vector concatenation operation, represents the projection operation;

[0106] The virtual bundle representation will be the basis for the input constructed as positive and negative samples, and its projection process forms a complete closed loop with the contrastive learning process defined in formulas (9)-(10).

[0107] In the bundle recommendation field, traditional methods rely on static predefined combinations, while the proposed method realizes dynamic user-item pair generation; in terms of representation, traditional models use independent bundle ID embeddings, while the proposed method innovatively uses user-item joint representation projection; in the cold start scenario, traditional methods are limited by historical bundle data, while virtual bundles achieve zero-shot adaptation through item feature generalization. The joint representation generated by virtual bundles provides a basis for multi-view embedding fusion, and the next section will detail how to integrate these heterogeneous features into a unified representation space.

[0108] After obtaining the view Figure 1 and view Figure 2 , the two views are combined in an implicit weighted fusion and explicit contrastive projection manner;

[0109] S2 includes at least the following steps:

[0110] S2.1: Perform embedding generation and fusion;

[0111] Generate hierarchical local representations through multi-layer graph convolution propagation, then aggregate multi-order neighbor information as local embedding paths through cross-layer summation, generate global semantic representations using SVD decomposition to generate global embeddings, and finally perform feature fusion to generate user and item Concatenate the local and global embeddings to generate the joint representation of the user ) / item :

[0112]

[0113]

[0114] where, denotes the local embedding of a user ; denotes the global embedding of a user ; denotes the local embedding of an item ; denotes the global embedding of an item ; denotes the concatenation operation;

[0115] S2.2: Positive and negative sample construction;

[0116] The virtual bundle representation is dynamically generated using the joint embedding. The positive sample bundle is as follows:

[0117]

[0118] where the item is the real interaction target of the user , referred to as the positive sample item; in Figure 1 , the user node (red) and the item node (blue) are connected by a solid line.

[0119] The negative sample is the joint representation of the user and its corresponding negative item :

[0120]

[0121] The negative sample is an item other than the positive sample of the user in the current batch; in Figure 1 , the user node and the item node are connected by a dashed line.

[0122] S2.3: Projection head mapping and embedding alignment;

[0123] The joint semantic space of users and items is implicitly aligned by a nonlinear projection, reducing the dimensional vector to dimensional

[0124]

[0125] where the projection head is a two-layer fully connected network with a ReLU activation function, and are the first and second projection matrices, respectively; after dimensionality reduction, the joint semantic information of users and items is preserved, while the computational complexity is reduced;

[0126] Then L2 normalization is used: standardize the projected embeddings:

[0127]

[0128] Implicit contrastive alignment is adopted instead of explicit concatenation fusion. Through the collaborative design of cross-view contrastive loss and projection head, the dynamic complementarity of local (GCN) and global (SVD) embeddings is achieved, and its core advantages are reflected in the following two aspects:

[0129] (1) Adaptive feature interaction

[0130] The projection head, as a nonlinear feature distiller, maps the joint embedding of users and items (local + global) to a low-dimensional contrastive space, and achieves information purification through two-stage operations of linear transformation and ReLU activation.

[0131] Linear transformation: compresses redundant dimensions and forces the model to focus on (align) cross-view common features (such as the core interests of users).

[0132] ReLU activation: introduces nonlinear expression ability, enhances the ability to capture weak signals (such as low-frequency interactions) in sparse data, and suppresses noise (such as accidental clicks).

[0133] (2) Generalization of sparse-dense scenarios

[0134] Sparse data: The nonlinear mapping of the projection head alleviates the feature ambiguity problem caused by the lack of neighborhood information in GCN, and at the same time, the global inference ability of SVD is "distilled" to the local embedding through the contrastive loss.

[0135] Dense data: The dimension reduction operation (2d→d) of the projection layer implicitly realizes feature selection, filters the local noise that GCN may overfit, and preserves the semantic association revealed by SVD.

[0136] Contrastive learning optimizes L Through the collaborative optimization framework of main task loss, contrastive learning loss, bundled contrastive loss, and regularization term, global optimization is achieved through weighted fusion;

[0137] The main task loss adopts Bayesian personalized ranking loss, which optimizes the user's ranking preference for "positive samples" and "negative samples" through the main task loss, ensuring that the items the user actually interacts with are ranked before the bundled items that have not been interacted with;

[0138]

[0139] where, represents the sample set of the training batch, including user-positive item-negative item triplets (u, i, j) ); denotes a user embedding matrix, which is generated by fusing local GCN embedding and global SVD embedding, is the number of users, is the embedding dimension; denotes an item embedding matrix, which is generated by dual-view fusion, is the number of items; and denote embedding vectors of positive sample items and negative sample items respectively, where is the item actually interacted by the user, is the item not interacted by the user in the same batch; denotes a Sigmoid function;

[0140] For each triple, first, the predicted score of the user to the positive item and the predicted score of the user to the negative item are calculated, and the difference between the two reflects the ranking relationship that the positive sample is better than the negative sample. By taking the negative of the logarithmic function, the greater the positive score difference, the smaller the loss, so as to force the model to learn the ranking mode consistent with the user's real preference;

[0141]

[0142]

[0143] wherein, denotes an embedding matrix of the user generated by global path, denotes an embedding matrix of the item generated by global path, denotes a temperature parameter, denotes a contrastive loss weight, denotes the local embedding of other users as negative samples in contrastive learning,

[0144] When the contrastive target is reached, the global embedding of the user is as similar as possible to the local embedding of the user , and the global embedding of the user is as dissimilar as possible to the local embedding of other users

[0145] ​Local embedding is good at capturing fine-grained interactions but may be blurred in sparse scenarios, while global embedding is good at mining global patterns but may ignore local details, and the contrastive learning loss realizes the complementarity of the two through contrastive learning, and the global embedding calibrates the local embedding in sparse scenarios;

[0146] The traditional contrastive loss only focuses on single node features, and the bundled contrastive loss explicitly models the synergistic effect of item combinations by comparing the joint embeddings of "user-positive bundled combination" and "user-negative bundled combination", thereby enhancing the model's ability to capture multi-item associations;

[0147]

[0148] wherein, represents the joint embedding projection of the user and the positive bundle , represents the joint embedding projection of the user and the negative bundle , represents the bundled contrastive loss weight;

[0149] It is particularly pointed out that the bundled features in the application are modeled through the joint representation of the item features and the user features contained therein, without the need for an independent bundled embedding matrix , which not only simplifies the model but also improves the adaptability to dynamic bundles.

[0150] Compared with the traditional contrastive loss, the core innovation of the bundled contrastive loss lies in: (1) joint embedding modeling: by constructing user-bundle joint features instead of single node features, the association between the two is directly captured; (2) projection head enhancement: double-layer linear projection not only realizes dimension reduction, but also introduces nonlinearity through the introduction of ReLU activation, thereby enhancing the modeling ability for nonlinear synergistic effects; (3) after projection, L2 normalization (see formula 9) is used to standardize the feature scale, thereby ensuring that the similarity calculation focuses on the synergistic pattern rather than the embedding modulus.

[0151] The regularization term is used to prevent model overfitting, and the regularization term is introduced to constrain all learnable parameters, and its definition is:

[0152]

[0153] wherein, , is the user and item embedding matrix, is all the weight and bias parameters of the projection head;

[0154] The main task loss, the contrast learning loss, the bundled contrast loss and the regularization term constitute a total loss function for optimization, to realize the comprehensive improvement of the ranking accuracy, the feature consistency, the bundled cooperativeness and the parameter robustness in the multi-item bundled recommendation scenario.

[0155] Firstly, the four losses are mean-standard deviation standardized; , , , The four losses are mean-standard deviation standardized;

[0156] Then, the multi-objective loss function is converted into a single-objective optimization problem:

[0157]

[0158] Wherein, represents the contribution ratio of each loss in the total loss, is set to 0.25, The equivalent weight optimization of the four optimization objectives can be realized, and the balanced consideration of each expected performance index in the model training process is ensured.

[0159] Based on the above embodiment, the following experimental verification is proposed:

[0160] Experimental data and settings

[0161] The public data sets Yelp, Tmall and Ml10m are used as test verification data sets. The information of the data sets is shown in Table 1.

[0162] Table 1: Basic information of data sets

[0163]

[0164] The experimental environment of the present application is: Python 3.12.3; Pytorch2.3.1+CUDA12.1; the specific experimental parameter settings are shown in Table 2.

[0165] Table 2: Parameter list

[0166]

[0167] Comparative experiment

[0168] In order to verify the generalization ability of the model, experiments are carried out on three public data sets, and Recall@20, Recall@40 and NDCG@20, NDCG@40 are used as evaluation indexes. Recall@K is to measure the proportion of covering the user's real interested items in the top K results in the recommendation list.

[0169]

[0170] Among them,​ represents the set of items that the user actually likes, represents the total number of items that the user actually likes. is the set of top K items recommended by the model, represents the number of items in the recommendation list B that hit the user's actual interest items. NDCG@K is a measure of the ranking quality of the top K results of the recommendation list, emphasizing the position weight of the items that the user is interested in.

[0171]

[0172] wherein, represents the discounted cumulative gain, which is used to measure the actual ranking quality of the top K results of the recommendation list, and is calculated in the following way:

[0173]

[0174] represents the ideal discounted cumulative gain, which is the maximum DCG value under a theoretically perfect ranking, i.e. the DCG value after all items are sorted in descending order of relevance, and is the same as the formula, but the items are sorted in descending order of relevance.

[0175] The results of the BundleGCL proposed in the present application are compared with those of six baseline models, as shown in Table 3.

[0176] Table 3: Performance comparison of BundleGCL and baseline models

[0177]

[0178] From the comparative experiments, it can be found that BundleGCL is significantly better than the baseline model in all indicators (R@20, N@20, R@40, N@40) of Yelp, Tmall and Ml10m data sets, verifying its universality and robustness. However, the effect improvement on different data sets is different. The global-local complementary mechanism of BundleGCL effectively mines implicit interactions, and the model performs significantly better in sparse scenarios. Among them, on the Yelp data set, R@20 is improved by 22.8%, N@20 is improved by 25.2%, R@40 is improved by 19.7%, and N@40 is improved by 22.9%. While on the Tmall data set, R@20 is improved by 56.2%, N@20 is improved by 63.2%, R@40 is improved by 49.1%, and N@40 is improved by 57.1%. Although the improvement is small in dense scenarios, such as Ml10m data set, R@20 is improved by 1.6%, N@20 is improved by 1.8%, R@40 is improved by 0.6%, and N@40 is improved by 0.5%, but it is still stable and leading, indicating that the model can still refine the recommendation granularity through contrast learning when the data is sufficient.

[0179] For high sparsity scenarios, the enhancement effect of the heterogeneous bundled relationship modeling proposed by the application supplements the missing interactions in sparse data by constructing indirect user-item associations through bundled nodes. When user-item direct interactions are sparse (such as Tmall sparsity 99.988%), traditional models (such as LightGCN) can only learn user interests through a small number of direct interactions, while BundleGCL uses the co-occurrence relationship of bundled items to infer potential preferences through the indirect path of "user → bundle → item". At the same time, the collaborative effect is amplified, and BundleGCL forces the joint representation of users and bundled items to be aligned through bundled contrast loss, so that the model pays more attention to the collaborative effect of item combinations rather than single sparse interactions. In addition, double linear projection replaces traditional MLP to relieve oversmoothing and enhance feature discrimination in sparse data. Therefore, it performs well in high sparsity scenarios. In low sparsity scenarios, when user-item interactions are sufficient (such as MovieLens sparsity 99.018%), direct interactions can adequately represent user preferences, and the indirect information provided by bundling becomes secondary, so the improvement is limited (Recall@20 only increases by 1.6%). At this time, the model relies more on the main task loss, and the marginal benefit of bundled contrast loss is reduced.

[0180] 4.3 Ablation experiment

[0181] The Yelp dataset is a classic recommendation system public dataset with interaction diversity and real scene generalization. Secondly, the interaction data volume (about 100 million) of Yelp is moderate, which can reflect the potential of the model in large-scale data and avoid the computational overhead of large-scale data sets (such as the millions of interactions of Tmall) when verifying the ablation experiment. The present application selects the Yelp dataset as the ablation experiment verification test set.

[0182] Analysis of the influence of the number of projection head layers on the model

[0183] To further explore the performance of the model under different projection head layers, the present application designs two experiments, (1) direct comparison: based on the complete dataset, covering all user-item interactions, the effects of different layers of projection heads are analyzed. (2) Group experiment: divide the dataset into small (1-10 items), medium (11-30 items), large (31-50 items), and xlarge (51+ items) subsets according to the number of user interactions with items, and focus on the differences in recommendation effects under different complexities.

[0184] To explore and verify the superiority of the double-layer projection head in the model, the present application performs an ablation experiment on the number of projection heads, analyzes the effects of different layers of projection heads, and the experimental results are shown in Table 4.

[0185] Table 4: Performance comparison under different projection heads

[0186]

[0187] According to the experimental results in Table 4, combined with the characteristics of the multi-item bundling recommendation scene, the influence of different layer projection heads on the model effect can be analyzed in depth from the aspects of feature modeling ability and bundling scene adaptability.

[0188] Single-layer projection head

[0189] It performs the weakest on the four indicators, and it performs the weakest among the four evaluation indicators. Its core limitation is that linear mapping cannot adapt to the nonlinear collaborative relationship in the bundling scene. In bundling recommendation, the user's preference for item combinations is not a simple superposition of single-item preferences, but contains complex nonlinear patterns such as complementarity and scene relevance. Single-layer linear transformation can only achieve linear alignment of features, and it is difficult to capture the above high-order collaborative signals, resulting in the semantic association between global SVD embedding and local GCN embedding being fragmented, especially in sparse interaction scenarios, which can exacerbate representation ambiguity due to insufficient effective signal extraction.

[0190] Double-layer projection head

[0191] The performance is significantly better than other structures, and its advantage comes from the precise modeling of nonlinear synergy in the bundling scene. The first layer of linear transformation realizes the basic alignment of global and local features, focusing on the commonality across views; the second layer uses ReLU and other nonlinear activation functions to effectively capture the nonlinear synergy effect between items within the bundle, while suppressing noise signals in sparse interactions; the balance between parameter size and expression ability is formed in the two-layer structure, which avoids the insufficient modeling ability of single-layer and introduces redundant parameters, and can accurately aggregate the multi-scale information required by bundling while maintaining the feature discrimination.

[0192] Three-layer projection head

[0193] The performance is slightly lower than that of the double-layer, and the problem lies in the mismatch between the over-deep structure and the distribution of bundling features:

[0194] The redundant parameters introduced by the three-layer network are prone to overfitting the noise patterns in the bundling interaction (such as accidentally co-occurring item combinations), which destroys the compactness of the feature space in contrast learning - that is, the embedding distance of similar bundles is enlarged, while the discrimination of different bundles is reduced. In addition, in the sparse data scene of bundle recommendation, an over-deep network will amplify sample bias, leading to a decline in the model's generalization ability for new bundles or long-tail bundles.

[0195] From the results in Table 4, the advantage of the double-layer projection head is not simply a moderate number of layers, but its structural characteristics precisely match the core needs of bundle recommendation: through nonlinear transformation, it captures the high-order features required by multi-item synergy, avoids overfitting of sparse signals by over-deep networks, and achieves an optimal balance between nonlinear synergy modeling capability and model generalization efficiency in the complex feature space of user-item-bundle ternary interaction, verifying its exclusive adaptability to the bundling scene.

[0196] To more intuitively show the performance differences of different projection head layers under different subsets of bundles, a comparison bar chart is drawn to explore the performance of different projection heads under small, medium, large, and xlarge scale bundle subsets. The results are as follows Figure 2 ;

[0197] Combining experimental results and chart analysis, the impact of different layer projection heads on model effectiveness can be analyzed from two aspects: feature modeling capability and adaptability to the bundling scene. The above content indicates that the double-layer projection head can precisely capture the nonlinear synergy effect within the bundle through "linear alignment + nonlinear activation", while avoiding the redundant parameters of over-deep networks.

[0198] In the scenarios with high complexity of collaborative relationships such as medium, large, xlarge, etc., the advantages of the double-layer projection head are very significant, the linear alignment guarantees the association of basic features, the non-linear activation excavates the structure design of high-order collaboration, and the theoretical assumption of accurately capturing non-linear collaboration and maintaining the simplicity of the model is completely consistent.

[0199] Exploring the influence of the projection head module and the bundling module on the model

[0200] The present application improves the model effect by heterogeneous virtual bundling relationship modeling and lightweight double-layer projection head design, but in order to explore the effect of the two in the model alone, an ablation experiment is performed, which mainly includes three aspects, one is the bundleGCL model with double-layer projection head and bundling proposed in the present application, two is the lack of projection head module, and three is the lack of bundling relationship modeling, and the results are shown in Table 5.

[0201] Table 5: Influence of bundling strategy and projection head design on experimental effect

[0202]

[0203] (1) Importance of projection head structure

[0204] Performance degradation: after removing the projection head, all indicators decrease by 11.8%-13.7%, indicating that the projection head has important significance in the model.

[0205] Mechanism of action: the projection head maps the global SVD embedding and the local GCN embedding to a unified space through nonlinear mapping, enhancing the semantic consistency of contrastive learning.

[0206] (2) Necessity of bundling recommendation mechanism

[0207] Performance degradation: after removing the bundling recommendation, the indicators decrease by 14.9%-16.0%, indicating that the importance of the bundling recommendation in the model is superior to that of the projection head structure.

[0208] Mechanism of action: the bundling recommendation realizes the complementarity of long-term preferences and real-time behaviors by jointly optimizing the global-local dual path. When only relying on a single path (such as only global SVD or local GCN), the model cannot balance multi-scale user interests, resulting in simultaneous decrease in recommendation coverage and ranking accuracy.

[0209] 4.4 Influence of parameters in BundleGCL

[0210] 4.4.1 Influence of temperature coefficient on model performance

[0211] The temperature coefficient, as a core parameter in the recommendation system, directly affects the confidence distribution of the model on user interest and the diversity of the recommendation results, so it is necessary to discuss the performance of the model under different temperature coefficients. The following is the comparative study of the performance of the model under different temperature coefficients by the present application, such as Figure 3 .

[0212] It can be found from the figure that when the value of is 0.2, the model reaches the performance peak - R@20 and N@20 respectively rise to 0.0974 and 0.0837, which is about 11% higher than 0.0878 and 0.0752 when =1. At this time, the recommendation system can accurately lock the user's short-term interest (the top 20 items with the highest click rate) and maintain moderate exploratory.

[0213] Parameter and sensitivity analysis

[0214] Heterogeneous virtual bundling relationship modeling is the key innovation of the present application, and the bundling contrast loss is also the key loss function of the experiment. By adjusting the different bundling contrast loss weight values, the performance of the model under different values can be found, and the sensitivity and stability of the model are verified. The experimental results are as follows Figure 4 .

[0215] Figure 5 The stable performance of the model under different contrast loss weights is shown. Each evaluation index presents convergence characteristics within the parameter range (0.1-0.5), and the maximum value of Recall@20 is 0.0978 and remains stable within the error range of ±0.0025, verifying the strong robustness of the model to parameter changes. Figure 5 The parameter sensitivity ranking of

[0216] Although the current ablation experiment focuses on the Yelp dataset, the model has verified the universality of the model in the complete experiment of Tmall and Ml10m. Through the ablation experiment, it is proved that the combination of the projection head structure and the bundling recommendation mechanism forms the algorithm characteristics of "feature alignment and multi-path cooperation", both of which play an important role in the model.

[0217] In the recommendation system, data sparsity has a significant impact on recommendation performance: in the sparse scenario, traditional GCN is prone to over-smoothing due to the dilution of neighborhood information, while SVD is unstable due to noise interference in low-rank decomposition; in the dense scenario, GCN may over-rely on local structure and ignore cross-community interests, while SVD is dominated by high-frequency interactions and suppresses long-tail features. The joint embedding fusion mechanism proposed in the present application has a significant advantage in sparse data by adaptively weighting and integrating double-path features. Specifically, GCN supplements the missing local interactions through multi-hop neighbor aggregation, and SVD infers potential interests using global statistics, which complement each other: GCN alleviates the noise sensitivity problem of SVD in sparse data, and SVD makes up for the lack of long-range association capture of GCN. Experiments show that on the Yelp and Tmall datasets with strong sparsity, the joint embedding makes the evaluation index Recall@20 of the Yelp dataset increase from 0.0793 to 0.0974, with an increase of more than 22%, and the evaluation index of the Tmall dataset is from 0.0528 to 0.0825, with an increase of more than 56%. This breakthrough effect is due to the double regularization of the contrastive learning framework - it not only enhances the embedding discriminability through cross-view contrast, but also forces the model to extract cross-view common features through parameter sharing, so that a high-discriminative user-item unified representation can still be constructed when data is scarce.

[0218] In summary:

[0219] In the present application, the deficiencies of traditional graph contrastive learning and traditional bundling methods in recommendation systems are discussed, and a contrastive learning model BundleGCL is proposed, which combines a virtual bundling recommendation mechanism and a projection head structure. By constructing a user-item-virtual bundle architecture, a virtual bundle node is introduced as an intermediary for high-order relationships, establishing a dual-channel modeling mechanism for user direct preferences and indirect associations. The lightweight double-layer projection head mechanism ensures feature alignment accuracy while overcoming the representation oversmoothing problem caused by traditional multi-layer perceptron. In addition, the multi-objective joint optimization strategy proposed in this paper achieves collaborative training of main task recommendation, cross-view contrast, and bundle relationship learning, forming a dynamic complementarity of local fine-grained and global statistical features. Experimental results show that BundleGCL significantly outperforms baseline models in the Yelp and Tmall high-sparse dataset scenarios, with a 22.8% improvement in Recall@20 on Yelp and a 56.2% improvement in NDCG@20 on Tmall, verifying the universality and robustness of the method.

[0220] It will be apparent to those skilled in the art that the application is not limited to the details of the above-exemplified embodiments and that the present application can be implemented in other particular forms without departing from the spirit or essential characteristics of the present application. The embodiments should therefore be considered in all respects as illustrative and not restrictive, the scope of the application being indicated by the appended claims rather than by the above description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. No reference signs in the claims should be considered as limiting the scope of the claims with respect to the figures of the patent document.

Claims

1. A multi-item bundled recommendation method based on graph contrastive learning, characterized in that: At least the following steps are included: S1: First, local-global dual-path embedding is performed, that is, the original graph generates local and global embeddings through GCN and SVD respectively, generating dynamic bundled representations without pre-defining bundles. The local-global dual-path embedding process includes the generation and representation of local embedding paths, global embedding paths and virtual bundles. S2: Then perform joint embedding fusion, that is, integrate multi-view features to build a unified representation of user-item pairs; S3: Finally, comparative learning optimization is performed to enhance the robustness of the model by comparing loss across views.

2. The multi-item bundling recommendation method based on graph contrastive learning according to claim 1, characterized in that: The user set in the local embedding path With items collection Composition of a two-part diagram ; To capture the structural relationships between nodes, a normalized adjacency matrix is ​​first constructed. Its elements are defined as: ； in, Indicates user and items Interactive behavior; and Representing users respectively and items The set of neighbors; The local embedding path employs a graph convolutional network, aggregating multi-order neighborhood information through a hierarchical propagation mechanism. The formula for updating the representation of a layer node is: ； in, For the first Layer node embedding matrix; These are learnable parameters; the negative slope of the LeakyReLU activation function is fixed at 0.5; after... After layer propagation, local embedding is obtained. The direct interaction pattern between users and items and the local community structure are preserved as the output of View 1.

3. The multi-item bundling recommendation method based on graph contrastive learning according to claim 2, characterized in that: The global embedding path is based on singular value decomposition to mine the potential low-rank structure of the interaction matrix; First, perform truncated singular value decomposition on the adjacency matrix A: ； in, , These are the left singular vector and the right singular vector, respectively. It is a singular value diagonal matrix; Constructing SVD Enhanced Graphs using Singular Vectors Generate global embeddings through message passing . Capture the global low-rank structure of user-item interactions as the output of view 2.

4. The multi-item bundling recommendation method based on graph contrastive learning according to claim 3, characterized in that: The virtual bundling mechanism captures the synergistic effect between multiple items by dynamically constructing a joint representation of user-item pairs; Positive sample virtual bundling represents the joint representation of a user and the items they interact with in real life, and is defined as follows: ； in, Indicates the joint embedding of users, Represents items joint embedding, This represents a vector concatenation operation. This indicates a projection operation.

5. The multi-item bundling recommendation method based on graph contrastive learning according to claim 4, characterized in that: The method combines implicit weighted fusion and explicit contrast projection after obtaining View 1 and View 2. S2 includes at least the following steps: S2.1: Perform embedding generation and fusion; Multi-layer graph convolution propagation generates hierarchical local representations. Then, multi-level neighbor information is aggregated through cross-layer summation as a local embedding path. SVD decomposition is used to generate global semantic representations and global embeddings. Finally, feature fusion is performed for the user. and items By concatenating local and global embeddings, a user ( ) / thing( The joint representation of ) ； ； in, Indicates user Local embedding; Indicates user Global embedding; For items Local embedding; For items Global embedding; This indicates a splicing and merging operation; S2.2: Construction of positive and negative samples; Virtual bundled representations are dynamically generated using joint embeddings. Positive sample bundles are as follows: ； Among the items User The actual interactive targets are called positive sample items; Negative samples are users Its corresponding negative items The joint representation of: ； negative samples This is the current batch excluding users Other items besides the positive sample; S2.3: Projection head mapping and embedding alignment; By implicitly aligning the user-item joint semantic space through nonlinear projection, the stitched... Dimensionality reduction of dimensional vectors to dimension ； The projection head is a two-layer fully connected network containing the ReLU activation function. and These are the projection matrices for the first and second layers, respectively; the dimensionality reduction preserves the joint semantic information of the user and item while reducing computational complexity. Then, L2 normalization is used to normalize the projected embedding. ； Implicit contrast alignment is used instead of explicit stitching and blending. Through cross-view contrast loss and collaborative design of the projector head, dynamic complementarity of local (GCN) and global (SVD) embedding is achieved.

6. The multi-item bundling recommendation method based on graph contrastive learning according to claim 5, characterized in that: The contrastive learning optimization L achieves global optimization through weighted fusion by designing a collaborative optimization framework that combines the main task loss, contrastive learning loss, and a bundled contrastive loss with a regularization term. The main task loss adopts Bayesian personalized ranking loss, which optimizes the user's ranking preference for "positive samples" and "negative samples" to ensure that items and bundles that the user actually interacts with are ranked before uninterrupted items. ； in, This represents the sample set for the training batch, including user-positive-negative item triples ( ); The user embedding matrix is ​​generated by fusing local GCN embeddings and global SVD embeddings. For the number of users, For the embedded dimension; The item embedding matrix is ​​generated by merging two views. For the quantity of items; and These represent positive sample items. and negative sample items The embedding vector, where User Items that are actually interacted with These are items in the same batch that the user has not interacted with; Represents the Sigmoid function; For each triple, first calculate the user Correct items Predicted score and negative items Predicted score The difference between the two reflects the ranking relationship that positive samples are better than negative samples. By using the logarithmic function and taking the negative, the larger the difference in positive scores, the smaller the loss, thereby forcing the model to learn a ranking pattern that conforms to the user's true preferences. The contrastive learning loss is used to address the feature distribution shift caused by the different modeling granularity between "local GCN embedding" and "global SVD embedding". The contrastive learning loss enhances feature consistency by forcibly aligning the dual-view embeddings of the same node through contrastive learning. ； in, This represents the embedding matrix generated from the user's global path. The embedding matrix represents the global path generated for an item; Indicates temperature parameter; Indicates the weight of the comparative loss; Indicates other users The local embeddings are used as negative samples in contrastive learning; When comparing targets, let the user The global embedding should be as similar as possible to its local embedding. And let the user... Global embedding with other users The local embeddings should be as dissimilar as possible; Local embedding excels at capturing fine-grained interactions but is prone to blurring in sparse scenes; global embedding excels at uncovering global patterns but may overlook local details. Contrastive learning loss achieves complementarity between the two through contrastive learning, and global embedding calibrates local embedding in sparse scenes. The bundled contrastive loss explicitly models the synergistic effect of item combinations by comparing the joint embedding of "user-positive bundled combinations" and "user-negative bundled combinations", thereby enhancing the model's ability to capture multi-item associations. ； in, Indicates user bonded with Joint embedding projection, Indicates user negative binding Joint embedding projection, Indicates the weighted comparison loss; The regularization term is used to prevent the model from overfitting. It is introduced to constrain all learnable parameters and is defined as follows: ； in, , Embed matrices for users and items. For all weights and bias parameters of the projection head; The main task loss, contrastive learning loss, bundled contrastive loss, and regularization term constitute the total loss function for optimization, which aims to comprehensively improve the ranking accuracy, feature consistency, bundled synergy, and parameter robustness in multi-item bundled recommendation scenarios. First of all , , , The four losses were standardized using the mean-standard deviation method. The multi-objective loss function is then transformed into a single-objective optimization problem: ； in, Representing the percentage contribution of each type of loss to the total loss, set It can achieve equivalent weight optimization of four optimization objectives, ensuring a balanced consideration of various expected performance indicators during model training.

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