Graph neural network recommendation system based on layer adaptive spectral domain graph learning

Abstract

The invention relates to a graph neural network recommendation system based on layer adaptive spectral domain graph learning, which is used for solving the problems of over-smoothing and heterogeneity of inputting a commodity incidence relation graph structure when an existing graph neural network method constructs a deep network in an existing recommendation system. Therefore, the effect of a graph recommendation model on related tasks is reduced, and particularly, the long-distance association between commodities is difficult to mine. According to the scheme, the graph spectrum and node feature smoothness is jointly optimized on the recommendation system graph neural network, and the commodity graph structure is adaptively learned and corrected while the over-smoothness is relieved, so that the construction of a deeper graph neural network is supported, and the commodity feature description capability of a recommendation model and the commodity recommendation accuracy are improved.

Description

Technical Field

[0001] This disclosure relates to data processing and information recommendation, and in particular to a graph neural network recommendation system based on layer adaptive spectral domain graph learning. Background Technology

[0002] Graph Neural Networks (GNNs) are important tools for processing graph-structured data, widely used in relational modeling tasks with good results. In typical personalized recommendation scenarios, a graph of relationships between products can be constructed from user behavior logs on the platform. Nodes correspond to recommended products, and edges are generated from user events such as clicks, favorites, adding to cart, and purchases, carrying attributes such as event type, occurrence time, and interaction intensity. By iteratively aggregating and propagating node features on this graph, GNNs help to uncover the relationships between products and users' potential interests, thereby improving the recommendation model's ability to characterize product relevance and user preferences.

[0003] Existing GNNs (such as GCN and GraphSAGE) can achieve good results in recommender systems, but they can suffer from "oversmoothing" when multiple layers are stacked. Specifically, as the number of network layers increases, the features of different nodes tend to be similar or oversmoothed, eventually converging into an informationless subspace. This results in insufficient discrimination of product features and ultimately a significant decrease in the discriminative ability of the model in recommender tasks.

[0004] To alleviate these problems, existing methods have proposed techniques such as residual connections and normalization. However, these methods typically use fixed graph structures, while the relationship graphs in recommendation scenarios are often automatically generated from logs, resulting in noise and bias: for example, accidental click edges caused by accidental touches, selection bias edges introduced by exposure mechanisms, and weakly related edges introduced by session co-occurrence. When the input graph contains many connections inconsistent with true preferences, information from irrelevant neighbors will be mixed in during node feature aggregation, limiting the model's performance. Although some existing methods consider both smoothing and graph structure optimization, these methods use heuristic graph structure adjustments and lack explicit optimization of the graph spectrum, which is theoretically key to controlling the convergence rate of oversmoothing, resulting in suboptimal performance. The most relevant existing methods use explicit optimization of the graph spectrum, but their graph structure optimization is separated from the GNN training process, failing to achieve collaborative optimization of graph structure and node features, thus limiting the improvement in model performance. Summary of the Invention

[0005] To address the aforementioned issues, this disclosure proposes a graph neural network recommendation system based on Layer-Adaptive Spectral Graph Learning (LAG). This framework jointly optimizes the graph spectrum and node feature smoothness on the product relationship graph. While mitigating oversmoothing, it adaptively learns and corrects the relationship graph structure, thereby supporting the construction of deeper graph neural networks and improving the recommendation model's ability to characterize product features. Simultaneously, by introducing a class-wise prototype-based graph construction method, the computational complexity of relationship graph construction is reduced, which is beneficial for scalability in large-scale recommendation systems and maintains the model's generalization performance even when supervision signals are sparse (e.g., click / purchase samples are relatively scarce). By transforming the optimization of the graph spectrum into a regularization loss based on the class prototype, the discriminative power of node features is effectively improved, further mitigating the oversmoothing problem.

[0006] To achieve the above objectives, a graph neural network recommendation system based on layer adaptive spectral domain graph learning is proposed. The system includes an input module, a product recommendation module, and an output module. The input module is configured to be based on a product feature matrix. Obtain the initial latent space feature representation The product recommendation module is configured to represent the initial latent space features. The input is a graph neural network formed by stacking L LAG modules. Each LAG module undergoes sequential processing including constructing a class prototype graph and layer adaptive feature aggregation. The resulting aggregated features are used as input to the next LAG module. Product recommendations are made based on the output of the last LAG module. The process of constructing the class prototype graph includes: calculating the product category... k The average value of the product characteristics is used as the prototype vector for that category. : , For the first The category is a collection of labeled products. For the first i The initial vector of product features for each product; The transformation matrix is ​​composed of prototype vectors. , For the number of categories; use the transformation matrix. Product characteristics of the upper layer Perform linear transformation Projecting product features onto K A sparse similarity adjacency matrix is ​​obtained by retaining only the edges present in the original input graph in a 3D space. ;right Symmetric normalization is performed to obtain the normalized Laplace matrix. and the corresponding graph propagation matrix , For the number of floors, = 1, 2, ..., L. The layer adaptive feature aggregation process includes: based on the initial latent space feature representation... Current graph propagation matrix Layer adaptive smoothing weights and initial state Perform T iterations of feature aggregation The aggregation feature of the Tth time As the first Output characteristics of each LAG module .

[0007] To achieve the above objectives, this disclosure also proposes a computer-readable storage medium storing a computer program that can be loaded by a processor and executed as a system proposed in this disclosure.

[0008] Based on the aforementioned graph neural network recommendation system based on layer adaptive spectral domain graph learning, a corresponding graph neural network recommendation method based on layer adaptive spectral domain graph learning can be derived, the steps of which include: based on the product feature matrix Obtain the initial latent space feature representation ; Represent the initial latent space features The input is a graph neural network formed by stacking L LAG modules. Each LAG module undergoes sequential processing including constructing a class prototype graph and layer adaptive feature aggregation. The resulting aggregated features are used as input to the next LAG module. Product recommendations are made based on the output of the last LAG module. The process of constructing the class prototype graph includes: calculating the product category... k The average value of the product characteristics is used as the prototype vector for that category. : , For the first The category is a collection of labeled products. For the first i The initial vector of product features for each product; The transformation matrix is ​​composed of prototype vectors. , For the number of categories; use the transformation matrix. Product characteristics of the upper layer Perform linear transformation Projecting product features onto K A sparse similarity adjacency matrix is ​​obtained by retaining only the edges present in the original input graph in a 3D space. ;right Symmetric normalization is performed to obtain the normalized Laplace matrix. and the corresponding graph propagation matrix , For the number of floors, = 1, 2, ..., L; The layer adaptive feature aggregation process includes: based on the initial latent space feature representation Current graph propagation matrix Layer adaptive smoothing weights and initial state Perform T iterations of feature aggregation The aggregation feature of the Tth time As the first Output characteristics of each LAG module .

[0009] The beneficial technical effects of this disclosure are as follows: (1) The product recommendation system proposed in this disclosure uses a graph neural network based on layer adaptive spectral domain graph learning, which can effectively alleviate oversmoothing and support deeper networks to enhance recommendation modeling capabilities. (2) Through inter-layer graph structure adaptive learning, inaccurate connections in the input product relationship graph can be suppressed or corrected, thereby reducing the interference of noise edges in the feature aggregation process and improving the accuracy of recommended products. (3) It can handle the learning and reasoning of large-scale products, and has high recommendation effectiveness and real-time performance. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a schematic diagram of the network architecture of a graph neural network recommendation system based on layer adaptive spectral domain graph learning. Detailed Implementation

[0012] In recommender systems, existing graph neural network (GNN) methods generally face problems of "oversmoothing" and heterogeneity in the input relational graph structure when constructing deep networks. This leads to a decline in the performance of graph recommendation models on relevant tasks, especially when it comes to mining long-distance relationships between products. The heterogeneity of the graph structure refers to the diversity of the types, attributes, structures, or relationships of nodes and edges in the graph, rather than a single homogeneous structure.

[0013] Specifically: 1) Oversmoothing makes deep node features indistinguishable, leading to convergence of product features and weakening discriminative ability. 2) Fixed graph structures cannot correct inaccurate connections in the input relationship graph. In recommendation scenarios, the relationships between products are usually constructed from user clicks, favorites, add-to-cart, and purchase log events, which are easily affected by accidental touches, forming noisy or weakly correlated edges. These connections introduce irrelevant information during feature aggregation, affecting the final recommendation results. 3) Existing methods for mitigating oversmoothing fail to unify oversmoothing suppression with graph spectrum optimization in modeling, or the graph structure adjustment strategy is not globally optimal, resulting in limited model performance improvement in recommendation scenarios, especially in deep network settings. These problems make the performance of deep GNNs in recommendation systems still less than ideal, and it is difficult to achieve stable gains with increasing layers.

[0014] This proposal suggests a Layer Adaptive Spectral Domain Graph Learning (LAG-GNN) framework for a graph neural network recommendation system. By jointly optimizing the graph structure and node features, it simultaneously addresses the issues of oversmoothing and heterogeneity in the association graph. This framework enables the support of deep GNNs in recommendation systems, enhancing the ability to represent product relationships and thus improving recommendation performance.

[0015] The core of this scheme is as follows: First, starting from the spectral analysis of graph convolutional networks, a graph spectral regularization term is derived and its computation in the spatial domain is implemented to explicitly alleviate oversmoothing. Second, the graph spectral regularization term is jointly optimized with node feature smoothness, enabling the model to adaptively adjust the connection strength in the relationship graph while learning product representations, thereby reducing the interference of noisy edges on aggregation. The optimization solution is then mapped to an end-to-end trainable deep graph neural network through algorithmic expansion, improving the recommendation system's ability to model and predict long-distance product associations. Third, a graph construction method based on class prototypes is proposed to reduce the computational complexity of graph structure learning, improve scalability in large-scale recommendation systems, and achieve efficient and robust graph structure optimization. The algorithm expansion maps each step of the iterative optimization algorithm to a layer of a neural network, thus transforming the optimization algorithm into a trainable deep network. The class prototype is the average vector of all sample features in a category, used to represent the center of that category.

[0016] The graph spectrum is the set of eigenvalues ​​of the matrix corresponding to the graph. The graph spectrum regularization term is a constraint added to the machine learning loss function, designed to utilize prior knowledge of the graph's topology to guide the learned graph signals (e.g., node features, labels, representation vectors) to be "smooth" or conform to certain desired spectral characteristics. Its core idea is that if two nodes are connected (or similar) in the graph, then their corresponding signal values ​​should also be similar. This spectral domain graph learning method utilizes the spectral decomposition (eigenvalues, eigenvectors) of the graph's Laplacian matrix to learn features in the graph's "frequency domain" based on the graph's topology and node features.

[0017] The LAG-GNN network disclosed herein is composed of It is composed of stacked LAG modules, such as Figure 1 As shown, each LAG module performs an alternating optimization of graph structure and features. Each LAG module contains two core steps: class prototype graph construction and layer adaptive feature aggregation.

[0018] In the class prototype graph construction step, the prototype of each category is calculated using the labeled node features, and a feature transformation matrix is ​​initialized to map the node features to a low-dimensional space. Based on this, the similarity between nodes is calculated, thereby obtaining a graph structure for relationship modeling. In recommender system applications, the above graph structure can be used to characterize the strength of association between products to support subsequent representation learning and prediction.

[0019] In the layer-adaptive feature aggregation step, node features are aggregated based on the current graph structure, and then the initial latent space features of the node features are weighted and fused with the node features. These are layer adaptive parameters used to control the smoothing intensity. This step is achieved by solving the expanded form of the node feature optimization problem, involving multiple graph convolution iterations.

[0020] The training loss for the entire network combines the standard cross-entropy loss for node classification tasks with prototype regularization loss based on graph spectrum regularization. The latter optimizes the graph spectrum by constraining the correlation between prototypes, further enhancing the model's robustness to oversmoothing. Oversmoothing refers to the phenomenon in graph neural networks where node features tend to become similar as the number of network layers increases, leading to a decrease in the model's discriminative ability. The graph spectrum is the set of eigenvalues ​​of the graph Laplacian matrix.

[0021] The following provides a clear and complete description of how the technical solution of this case is implemented. Obviously, the described implementation methods are only a part of the implementation methods of this case, and not all of them. Based on the implementation methods in this case, all other implementation methods obtained by those skilled in the art without inventive effort are within the scope of protection of this application.

[0022] (a) Input data Input graph structure data, including a set of product nodes. , representing the set of all products on the e-commerce platform, edge set This represents the relationships between products, such as the edges in the Amazon product co-purchase dataset's central graph representing products being purchased simultaneously, and the adjacency matrix. , where represents the similarity between products, and N is the number of products.

[0023] Product Feature Matrix Each row represents an input feature of a product, and F is the total number of input features. These input features can be extracted from the platform's product information and content information. The content information includes, but is not limited to: brand, store, price, new product launch time, title text, and product image content.

[0024] Training set products The label information is used to provide supervision information during training.

[0025] The data mentioned above can come from graph structures in any task scenario, and the method of this invention does not limit the specific business type.

[0026] (II) Data Processing Flow (2.1) Dimensionality reduction of input features For the input product feature matrix Perform a linear transformation to obtain the initial latent space feature representation. :

[0027] in, For a trainable linear transformation weight matrix, This step represents the dimension of the latent features. It is used to perform a unified mapping and dimensionality reduction on the original features, providing a foundation for subsequent graph construction and feature aggregation.

[0028] For example, the linear transformation is implemented using a multilayer perceptron (MLP).

[0029] (2.2) Class prototype diagram construction (the first step for each LAG module) Input: Product feature matrix from the previous layer and training set products Product category labels. It is the field of real numbers. For the number of floors, = 1, 2, ..., L, one LAG module corresponds to one layer. The labels are used for loss calculation during training.

[0030] (2.2.1) Calculate the class prototype vector: for each product category Calculate the average value of the product features of all products labeled as product category k, and use this value as the prototype vector of that product category. : .

[0031] in, For the first The category is a collection of labeled products. Let be the initial feature vector of the i-th item. All The transformation matrix is ​​composed of prototype vectors. The initial value, where This represents the number of categories. The initial product feature vectors of each product constitute .

[0032] (2.2.2) Feature transformation and similarity calculation: using the transformation matrix Perform a linear transformation on the product features of the previous layer: Projecting product features into a low-dimensional space, i.e., a space with dimension 1. This reduces the number of parameters and avoids model overfitting. Then, the similarity between items i and j is calculated as follows: .

[0033] (2.2.3) Graph sparsification: Only retain the edges that exist in the original input graph (i.e., This yields a sparse similarity adjacency matrix. This step uses the original graph topology as a priori, calculating only the weights of the existing edges, thus reducing computational complexity.

[0034] (2.2.4) Graph normalization: for Symmetric normalization is performed to obtain the normalized Laplace matrix. :

[0035] in This is the corresponding degree matrix. The corresponding graph propagation matrix. This is used for subsequent feature aggregation.

[0036] It should be noted that class prototype initialization is optional. Random initialization and training can be used, but using class prototype initialization can improve convergence speed and robustness.

[0037] (2.3) Layer Adaptive Feature Aggregation Input: Initial latent space features Current graph propagation matrix Layer adaptive smoothing weights .

[0038] (2.3.1) Set the initial state (i.e., the product characteristics output by the previous module).

[0039] (2.3.2) Iterative diffusion: Iteratively using the following formula Sub-feature aggregation to approximate the solution of the feature optimization problem:

[0040] in, The LAG module's adaptive smoothing weights control the degree of preservation of initial features and the degree of dependence on graph smoothing, and are learned by the network through the features of the current layer.

[0041] Output: After T iterations, As the output feature of this LAG module This output feature combines the effects of multi-layer graph structure optimization and layer adaptive feature aggregation.

[0042] It is important to note the number of iterations. It can be adjusted according to network depth. It can be used as a lightweight alternative, but may affect accuracy. Smoothing weights. It can be set to a fixed hyperparameter, but through data learning, the layer can be made adaptive and achieve better performance. When smoothing the weights... When setting the hyperparameter to a fixed value, it is preferable to set it to 0.5.

[0043] (2.4) Network Integration and Loss Function (2.4.1) Network layer: Features output by each LAG module It can pass through an optional linear transformation layer and a ReLU activation function before being input into the next LAG module.

[0044] (2.4.2) Output: The output of the last LAG module is mapped to the category dimension K through a linear transformation layer, and then the product classification prediction result is obtained through the softmax function. For example, predicting user ratings of products during a cold start. For regression or other graph tasks, this can be replaced with a corresponding output mapping function, and this invention does not limit this. The cold start prediction refers to predicting early behavior or preferences for new items (goods, content, etc.) or new systems in the absence of sufficient historical data ("cold" state).

[0045] (2.4.3) Total loss function: Consists of the task's cross-entropy loss and the graph spectrum regularization loss of the class prototype graph:

[0046] in, It is the standard cross-entropy loss. It is a collection of tagged products. It is the prototype regularization loss, defined as ,in yes The normalized version of the line. For goods The predicted vector, For goods The label vector, The preset weight is preferably set to 1. This represents a vector of all 1s with dimension H1.

[0047] This loss, designed to minimize the correlation between prototypes, is derived from the optimization of the graph spectrum and is used to enhance the distinguishability between classes, thereby alleviating the oversmoothing problem. In recommendation scenarios, this enhanced distinguishability helps maintain the discriminative ability of product representations, reduces representation convergence caused by deep propagation, and improves the stability of the recommendation model.

[0048] Based on the above, it can be seen that, compared to existing technologies that only indirectly influence the second largest feature value through heuristic methods such as graph sparsification, resulting in a loose optimization objective and limited effect, this disclosure proposes an explicit graph spectral regularization term (ultimately manifested as prototype regularization loss) that directly optimizes the entire graph spectrum, thereby maximizing the distance between the graph and the oversmoothed subspace. This directly constrains the spectral characteristics of the recommendation graph, thus suppressing the convergence of user / item representations caused by deep propagation. Compared to existing technologies that separate graph learning and feature learning, or combine them but fail to form an inter-layer adaptive mechanism with a clear explanation of the optimization problem, this disclosure maps the joint optimization process of graph and feature learning into an end-to-end trainable neural network module (LAG module) through algorithmic expansion, achieving layer adaptive smoothing intensity. Compared to existing technologies that typically only use task-related loss functions (such as cross-entropy), this disclosure introduces a multi-objective loss function that combines task loss and spectrum-driven prototype regularization loss to jointly supervise model training. Furthermore, this disclosure creatively employs a class prototype-based graph construction method to weight and modify the product relationships constructed using logs without introducing unfounded new edges, thereby achieving efficient, scalable, and sparse-supervised layer adaptive graph structure learning.

[0049] (III) Beneficial Technical Effects From the above, we can conclude that: First, this approach effectively mitigates oversmoothing, supporting deeper networks to enhance recommendation modeling capabilities. Specifically, on multiple datasets, our method maintains a leading or competitive position across different network depths, and its performance does not significantly degrade as the network deepens. This indicates that our method can stably learn node representations within deeper graph propagation ranges, thus being more effective in characterizing multi-hop association information in recommendation scenarios. A comparison with existing results is shown in the table below, with results representing node classification accuracy and the standard deviation after 10 experiments.

[0050] Secondly, this approach is robust to heterogeneous and noisy graph structures. Specifically, through adaptive learning of inter-layer graph structures, this method can suppress or correct inaccurate connections in the input graph, thereby reducing the interference of noisy edges during feature aggregation. It performs particularly well on datasets with high heterogeneity and large graph structure noise, such as Cornell and Texas (see Table 1).

[0051] Table 1

[0052] Third, this scheme is highly scalable and efficient in training. Specifically, in prototype-based graph construction, the computational complexity of graph learning is approximately... It is linearly related to the number of edges, enabling it to adapt to the training and updating process of large-scale data and supporting efficient representation learning and inference on large-scale product sets (such as OGBN-Products).

[0053] Fourth, this scheme combines high performance with spectral interpretability. Specifically, the network design stems from a clear spectral optimization objective, providing theoretical support for its performance improvement and making it easy to understand and improve.

[0054] The above implementation utilizes LAG-GNN to deeply mine the relationships between products on e-commerce platforms, accurately identifying potential product associations and user interest groups. Even if the original product relationship graph contains noise or missing data, LAG-GNN can effectively correct the graph structure through layer adaptive graph learning, improving the accuracy of product recommendations. This method can be widely applied to tasks such as precision marketing, personalized recommendations, and intelligent search, helping e-commerce platforms provide users with more relevant product recommendations, improving conversion rates and user satisfaction.

[0055] However, this solution can also be used on social network platforms. By using LAG-GNN to deeply mine the interaction graph between users, it can accurately identify user interest communities or potential connections. Even if the original social relationship graph has a lot of noise or missing data, it can still obtain robust node classification results through layer adaptive graph learning, which can be used for precision marketing or content recommendation.

[0056] In addition, this solution can also be used in intelligent recommendation systems, financial risk control models, knowledge graph reasoning systems, and intelligent transportation network analysis.

[0057] This invention can be a system, method, and / or computer program product.

[0058] For example, a graph neural network recommendation system based on layer adaptive spectral domain graph learning includes an input module, a product recommendation module, and an output module; the input module is configured to be based on a product feature matrix. Obtain the initial latent space feature representation The product recommendation module is configured to represent the initial latent space features. The input is a graph neural network formed by stacking L LAG modules. Each LAG module sequentially undergoes processing including constructing a class prototype graph and layer adaptive feature aggregation. The resulting aggregated features are used as input to the next LAG module, and product recommendations are made based on the output of the last LAG module. The process of constructing the class prototype graph includes: calculating the average value of product features belonging to product category k, which serves as the prototype vector for that category. : , For the first The category is a collection of labeled products. Let be the initial vector of the product features of the i-th product; The transformation matrix is ​​composed of prototype vectors. , For the number of categories; use the transformation matrix. Product characteristics of the upper layer Perform linear transformation The product features are projected into a K-dimensional space; only the edges present in the original input graph are retained, resulting in a sparse similarity adjacency matrix. ;right Symmetric normalization is performed to obtain the normalized Laplace matrix. and the corresponding graph propagation matrix , l For the number of floors, l= 1, 2, ..., L; The layer adaptive feature aggregation process includes: based on the initial latent space feature representation Current graph propagation matrix Layer adaptive smoothing weights and initial state Perform T iterations of feature aggregation The aggregation feature of the Tth time As the first l Output characteristics of each LAG module .

[0059] For example, a graph neural network recommendation method based on layer adaptive spectral domain graph learning includes the following steps: based on the product feature matrix Obtain the initial latent space feature representation ; Represent the initial latent space features The input is a graph neural network formed by stacking L LAG modules. Each LAG module sequentially undergoes processing including constructing a class prototype graph and layer adaptive feature aggregation. The resulting aggregated features are used as input to the next LAG module, and product recommendations are made based on the output of the last LAG module. The process of constructing the class prototype graph includes: calculating the average value of product features belonging to product category k, which serves as the prototype vector for that category. : , For the first The category is a collection of labeled products. Let be the initial vector of the product features of the i-th product; The transformation matrix is ​​composed of prototype vectors. , For the number of categories; use the transformation matrix. Product characteristics of the upper layer Perform linear transformation The product features are projected into a K-dimensional space; only the edges present in the original input graph are retained, resulting in a sparse similarity adjacency matrix. ;right Symmetric normalization is performed to obtain the normalized Laplace matrix. and the corresponding graph propagation matrix , l For the number of floors, l= 1, 2, ..., L; The layer adaptive feature aggregation process includes: based on the initial latent space feature representation Current graph propagation matrix Layer adaptive smoothing weights and initial state Perform T iterations of feature aggregation The aggregation feature of the Tth time As the first l Output characteristics of each LAG module .

[0060] Computer program products may include computer-readable storage media on which computer-readable program instructions are loaded to enable a processor to implement various aspects of the present invention. A computer-readable storage medium may be a tangible device capable of holding and storing instructions for use by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combinations thereof. The computer-readable storage medium as used herein is not to be construed as a transient signal itself, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0061] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0062] The computer program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, Python, etc., and conventional procedural programming languages ​​such as "C" or similar languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions. This electronic circuitry can execute the computer-readable program instructions to implement various aspects of the invention.

[0063] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0064] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0065] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions that execute on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0066] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions. It will be well known to those skilled in the art that implementation in hardware, implementation in software, and implementation using a combination of software and hardware are equivalent.

[0067] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein. The scope of the invention is defined by the appended claims.

Claims

1. A graph neural network recommendation system based on layer adaptive spectral domain graph learning, characterized in that: The system includes an input module, a product recommendation module, and an output module; The input module is configured to be based on the product feature matrix. Obtain the initial latent space feature representation ; The product recommendation module is configured to represent the initial latent space features. The input is a graph neural network formed by stacking L LAG modules. Each LAG module is processed sequentially, including building a class prototype graph and layer adaptive feature aggregation. The aggregated features are used as the input of the next LAG module. Product recommendation is performed based on the output of the last LAG module. The steps for constructing the prototype diagram include: calculating the categories belonging to the product category. k The average value of the product characteristics is used as the prototype vector for that category. : , For the first The category is a collection of labeled products. For the first i The initial vector of product features for each product; The transformation matrix is ​​composed of prototype vectors. , For the number of categories; use the transformation matrix. Product characteristics of the upper layer Perform linear transformation Projecting product features onto K A sparse similarity adjacency matrix is ​​obtained by retaining only the edges present in the original input graph in a 3D space. ;right Symmetric normalization is performed to obtain the normalized Laplace matrix. and the corresponding graph propagation matrix , For the number of floors, = 1,2,…,L; The layer adaptive feature aggregation process includes the following steps: based on the initial latent space feature representation Current graph propagation matrix Layer adaptive smoothing weights and initial state Perform T iterations of feature aggregation The aggregation feature of the Tth time As the first Output characteristics of each LAG module .

2. The system according to claim 1, characterized in that, The input module is implemented using a multilayer perceptron.

3. The system according to claim 1, characterized in that, Normalized Laplace matrix ,in This is the corresponding degree matrix.

4. The system according to claim 1, characterized in that, The total training loss of a graph neural network formed by stacking L LAG modules. Cross-entropy loss of the task Graph spectrum regularization loss of class prototype graph constitute: in, It is a collection of tagged products. For goods The predicted vector, For goods The label vector, As weight; , yes The line-normalized version, The dimension is H A vector of type 1 with all elements being 1.

5. The system according to claim 1, characterized in that, The product features include vectors extracted from brand, store, price, new product launch time, title text, and product image content.

6. The system according to claim 1, characterized in that, Output features After passing through a linear transformation layer and the ReLU activation function, it is input into the next LAG module.

7. A computer-readable storage medium, characterized in that: The system contains a computer program that can be loaded by a processor and executed as described in any one of claims 1 to 6.

8. A graph neural network recommendation method based on layer adaptive spectral domain graph learning, characterized in that the steps are as follows: include: Based on product feature matrix Obtain the initial latent space feature representation ; Representing the initial latent space features The input is a graph neural network formed by stacking L LAG modules. Each LAG module is processed sequentially, including building a class prototype graph and layer adaptive feature aggregation. The aggregated features are used as the input of the next LAG module. Product recommendation is performed based on the output of the last LAG module. The process of constructing the prototype diagram includes: calculating the categories of goods. k The average value of the product characteristics is used as the prototype vector for that category. : , For the first The category is a collection of labeled products. For the first i The initial vector of product features for each product; The transformation matrix is ​​composed of prototype vectors. , For the number of categories; use the transformation matrix. Product characteristics of the upper layer Perform linear transformation Projecting product features onto K A sparse similarity adjacency matrix is ​​obtained by retaining only the edges present in the original input graph in a 3D space. ;right Symmetric normalization is performed to obtain the normalized Laplace matrix. and the corresponding graph propagation matrix , For the number of floors, = 1,2,…,L; The layer adaptive feature aggregation process includes the following steps: based on the initial latent space feature representation Current graph propagation matrix Layer adaptive smoothing weights and initial state Perform T iterations of feature aggregation The aggregation feature of the Tth time As the first Output characteristics of each LAG module .

9. The method according to claim 8, characterized in that, The initial latent space feature representation is obtained by analyzing the product feature matrix. It is obtained by performing a linear transformation.

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