Personalized recommendation method based on spectral domain graph convolution

Abstract

The method comprises the following steps: 1, preprocessing data; 2, performing 0-1 normalization on discrete attributes and continuous attributes to obtain initial representations of users and articles, and then training embedding of the users and the articles through a full connection layer; 3, extracting a low-frequency signal, and performing information aggregation on the embedding in the step 2 by using spectral domain graph convolution to obtain final embedding representation; and step 4, obtaining a recommendation result. According to the method, the interaction information of the existing user and the article can be better utilized, the deep association between the potential interest of the user and the article feature is mined, the data sparsity problem is relieved, and the precision of the recommendation task is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of recommendation methods of recommendation systems, and specifically relates to a personalized recommendation method based on spectral domain graph convolution. Background Art

[0002] Recommender systems are a technology that recommends items that users may be interested in based on their behavior and preferences. Depending on the industry, they can be identified in various forms, such as product recommendations on online e-commerce sites such as Amazon and Taobao, or playlist generators for video and music services. With the development of the Internet and big data technologies, recommendation systems have become a key technology for various platforms to improve user experience and business efficiency. Existing recommendation methods, such as those based on collaborative filtering and deep learning, still have certain limitations in data sparsity, cold start problems, and the comprehensiveness of feature learning, making it difficult to effectively mine the deep relationship between users and items. Therefore, how to combine user behavior data and item features to improve the accuracy of recommendation tasks through more efficient algorithms has become a hot topic and difficulty in current research.

[0003] Recommendation systems can be divided into neighborhood-based methods and representation learning-based methods from the perspective of whether representation learning is used. Neighborhood-based methods directly recommend items to users that are similar to historical items they have interacted with. In a sense, they represent users' preferences by directly using their historical interaction items. Neighborhood-based methods have achieved great success in practical applications due to their simplicity, efficiency, and effectiveness. However, with the explosive growth of information, neighborhood-based methods have performed poorly in the face of complex and massive information. Representation learning-based methods attempt to encode users and items as continuous vectors in a shared space, making them directly comparable. Representation-based models have attracted attention since the Netflix Grand Prize competition proved that matrix factorization models are superior to classic neighborhood recommendation methods.

[0004] Graph convolution-based recommendation methods are a type of representation learning-based approach that considers information in recommendation systems from a graph perspective. Although graph-based collaborative filtering models are becoming increasingly popular in recommendation systems, they still face some challenges that current technologies have not effectively addressed. One of the main issues is data noise, which is caused by a variety of factors, such as over-recommendation of popular items causing users to click on irrelevant items. Directly aggregating all the information in the user-item interaction graph may lead to inaccuracies in user representation, while multi-hop embedding propagation may aggravate the noise problem. Therefore, how to alleviate the noise problem is an urgent problem to be solved. Summary of the invention

[0005] The purpose of the present invention is to provide a personalized recommendation method based on spectral domain graph convolution, which can alleviate the data sparsity problem and improve the accuracy of recommendation tasks.

[0006] The technical solution adopted by the present invention is a personalized recommendation method based on spectral domain graph convolution, which is specifically implemented in the following steps:

[0007] Step 1, data preprocessing;

[0008] Step 2: Convert discrete attributes to 0-1 and normalize continuous attributes to obtain the initial representation of users and items, and then train the embedding of users and items through the fully connected layer;

[0009] Step 3: extract low-frequency signals and use spectral domain graph convolution to aggregate the information of the embedding in step 2 to obtain the final embedding representation;

[0010] Step 4: Get the recommendation results.

[0011] The present invention is also characterized in that:

[0012] In step 1, user behavior data and item attributes are extracted from the original data source, and invalid data is eliminated, including abnormal users and duplicate registered users, as well as abnormal behaviors such as a large number of meaningless clicks in a short period of time. For missing values ​​in the data, similar users or items are used to fill them. All user behaviors and item attributes must be normalized and converted into a standardized format.

[0013] Step 1 is implemented as follows:

[0014] Step 1.1: Extract user behavior data from system logs or databases, including user clicks, browsing, favorites, and purchase operations, and obtain relevant attribute information of items. Combined with timestamps and context data, construct a record of user-item interactions.

[0015] Step 1.2: Remove invalid users including robot accounts and repeatedly registered accounts, as well as a large number of meaningless clicks and extremely repeated operations in a short period of time. At the same time, for missing user or item attributes in the data, fill them in with similar users or items;

[0016] Step 1.3: Based on the cleaned user behavior data, a user-item bipartite graph is constructed. The user nodes and item nodes are connected through interactive behaviors. Whether there is an edge between the user and the item is assigned a 0-1 value based on whether there is a click, purchase, or collection. If there is the above operation, it is considered that the user and the item have interacted and the value is 1, otherwise it is 0. The adjacency matrix of the bipartite graph can be obtained, denoted as matrix A, and a normalized Laplace matrix is ​​constructed based on the adjacency matrix. The calculation formula is:

[0017]

[0018] Where D is the degree matrix of A, is the normalized Laplacian matrix;

[0019] Step 1.4: Construct positive and negative samples. Select the items that the target user actually clicks or collects as positive samples, and use random sampling to generate negative samples from non-interactive objects.

[0020] The encoding embedding in step 2 is implemented in the following steps:

[0021] Step 2.1: One-Hot encode the discrete attributes. For each discrete attribute, convert it into a One-Hot encoding.

[0022] Step 2.2: Normalize continuous attributes. To avoid attributes with large values ​​dominating the model, these attributes need to be normalized. Normalization scales the attribute values ​​to a specific range.

[0023] Step 2.3: Use an embedding layer to map the normalized values ​​of discrete and continuous attributes into low-dimensional embedding vectors of fixed dimension to generate the final feature representation of users and items.

[0024] In step 3, the Lanczos algorithm is used to efficiently decompose the normalized Laplacian matrix, extract low-frequency signals, and retain the first 128 eigenvalues ​​and corresponding eigenvectors. These low-frequency features help capture the potential relationship between users and items. The spectral domain graph convolution is used to aggregate the information of the embedding in step 2 to obtain the final embedding representation.

[0025] Step 3 is implemented as follows:

[0026] Step 3.1: Decompose the Laplace matrix using the Lanczos algorithm, efficiently calculate its eigenvalues ​​and eigenvectors, and select the first 128 eigenvalues ​​and corresponding eigenvectors representing the low-frequency signal. The eigendecomposition calculation formula is as follows:

[0027] L=PΛP T (2)

[0028] Where P is the eigenvector matrix, which is composed of a set of normalized orthogonal bases. The eigenvector matrix defines the frequency domain, (Λ=diag([λ1,...,λ 128 ]) is a diagonal eigenvalue matrix, all eigenvalues ​​are arranged in ascending order, and the eigenvalues ​​define the frequency of the corresponding eigenvector, thereby effectively retaining the low-frequency information of the graph;

[0029] Step 3.2: From the convolution theorem, we know that the graph convolution in the spectral domain can be calculated by decomposing the eigenvalues ​​and eigenvectors. That is, the eigendecomposition matrix is ​​directly multiplied by the embedding of users and items to obtain the result of the spectral domain graph convolution. The spectral domain graph convolution can be expressed as:

[0030] Z=PΛP T E (3)

[0031] Among them, Z is the embedding vector after spectral domain graph convolution, and E is the initial embedding vector.

[0032] In step 4, the similarity between the user and the item is calculated, and based on the calculated similarity value, the top 20 items with the highest similarity are recommended to the user.

[0033] Step 4 is implemented according to the following steps:

[0034] Step 4.1: Recommend the top 20 items with the highest similarity to the user by calculating the cosine similarity between the user and the item. The similarity calculation formula is:

[0035]

[0036] Among them, e i represents the embedding of user i, e j represents the embedding of item j;

[0037] Step 4.2: The training process is optimized using the standard BPR loss function, and the calculation formula is as follows

[0038]

[0039] in, and Represents user u i and interactive itemsu j and uninteracted items u k The cosine similarity score of .

[0040] The beneficial effects of the present invention are

[0041] 1) The personalized recommendation method based on spectral domain graph convolution of the present invention maps the interaction information between users and items to the frequency domain through the spectral domain graph convolution method, and uses the feature decomposition in the frequency domain to extract low-frequency signals, capturing the global patterns hidden in the interaction data, and can deeply explore the deep correlation between users' potential interests and item features. It not only improves the understanding of user behavior, but also can more accurately match user needs, significantly improve the accuracy of recommendation tasks, and meet the personalized needs of users in different scenarios;

[0042] 2) To address the data sparsity problem that is common in recommendation systems, this paper transforms sparse interaction data into structured graph data by constructing a user-item bipartite graph and a normalized Laplace matrix, and combines the positive and negative sample pair generation mechanism to enhance the robustness of the model to sparse data. Even when there are few user behavior records or a limited number of item interactions, it can still efficiently capture potential associations in the data and improve the accuracy of recommendations;

[0043] 3) The present invention uses the Lanczos algorithm to efficiently decompose the Laplace matrix, retaining only the most representative low-frequency features, significantly reducing the computational complexity. In addition, the model is optimized by introducing the BPR loss function, and the similarity relationship between users and items is adjusted in a targeted manner during the training process to improve the ranking effect of the recommendation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the process of the personalized recommendation method based on spectral domain graph convolution of the present invention;

[0045] Figure 2 It is a schematic diagram of the structure of spectral domain graph convolution in the personalized recommendation method based on spectral domain graph convolution of the present invention. DETAILED DESCRIPTION

[0046] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Example 1

[0048] The present invention provides a personalized recommendation method based on spectral domain graph convolution, such as Figure 1 As shown, the specific implementation steps are as follows:

[0049] Step 1, data preprocessing, preprocessing of data sources, the purpose is to clean the raw data and provide high-quality input data for subsequent operations;

[0050] Step 2, encoding and embedding, is to encode, embed and map the features of users and items to ensure that these features can be effectively used in the subsequent recommendation model training, thereby improving the accuracy and efficiency of personalized recommendations. Specifically, step 2 is divided into three main steps, covering discrete attribute processing, continuous attribute normalization and embedding representation generation, to ensure that the model can efficiently and accurately learn user preferences and item features;

[0051] Step 3: extract low-frequency signals and use spectral domain graph convolution to aggregate the information of the embedding in step 2 to obtain the final embedding representation;

[0052] Step 4: Calculate the similarity between the user and the item, and recommend the top 20 items with the highest similarity to the user based on the calculated similarity value.

[0053] Example 2

[0054] A personalized recommendation method based on spectral domain graph convolution, in which in step 1, user behavior data and item attributes are extracted from the original data source, and invalid data is eliminated, including removing abnormal users and duplicate registered users, and processing abnormal behaviors of a large number of meaningless clicks in a short period of time. For missing values ​​in the data, similar users or items are used to fill them. All user behaviors and item attributes must be normalized and converted into a standardized format.

[0055] Step 1 is implemented as follows:

[0056] Step 1.1: Extract user behavior data from system logs or databases, including user clicks, browsing, favorites, and purchase operations. At the same time, obtain relevant attribute information of items, such as category, brand, price, description, tags, etc., and combine timestamps and context data to build a record of user-item interactions.

[0057] Step 1.2: Remove invalid users including robot accounts and repeatedly registered accounts, as well as a large number of meaningless clicks and extremely repeated operations in a short period of time; at the same time, for missing user or item attributes in the data, use similar users or items to fill them;

[0058] Step 1.3: Based on the cleaned user behavior data, a user-item bipartite graph is constructed. The user nodes and item nodes are connected through interactive behaviors. Whether there is an edge between the user and the item is assigned a 0-1 value based on whether there are clicks, purchases, favorites, and other operations. If there are the above operations, it is considered that the user and the item have interacted and the value is 1, otherwise it is 0. The adjacency matrix of the bipartite graph can be obtained, denoted as matrix A, and a normalized Laplace matrix is ​​constructed based on the adjacency matrix. The calculation formula is:

[0059]

[0060] Where D is the degree matrix of A, is the normalized Laplacian matrix;

[0061] Step 1.4: Construct positive and negative samples. Select the items that the target user actually clicks or collects as positive samples, and use random sampling to generate negative samples from non-interactive objects.

[0062] First, data extraction and preliminary integration: extract user behavior data from system logs or databases, including user clicks, browsing, collections, purchases, and other operations. These behavior data can reflect the interaction between users and items. In addition, it is necessary to collect relevant attribute information of items, such as category, brand, price, description, tags, etc., and combine timestamps and context data to build a complete record of interactions between users and items. This process ensures that the data used not only reflects user preferences, but also provides an in-depth understanding of the characteristics of items and the interaction environment.

[0063] Secondly, data cleaning and exception handling: After data collection, data cleaning is performed to remove invalid users. Invalid users include robot accounts, repeatedly registered accounts, and user behaviors that perform a large number of meaningless clicks and extremely repetitive operations in a short period of time, which often interfere with subsequent analysis results. At the same time, for missing user or item attributes in the data, the features of similar users or similar items are used to fill in, thereby ensuring the integrity of the data and avoiding the reduction in the accuracy of the recommendation system due to missing values.

[0064] Then, construct the user-item bipartite graph and normalized Laplace matrix: Based on the cleaned user behavior data, construct the user-item bipartite graph, and the user nodes and item nodes are connected through interaction behavior. Specifically, the connection weight between the user and the item is represented by a 0-1 assignment. If the user has clicked, purchased, or collected an item, it is considered that there is an interaction and the value is 1; if there is no interaction, the value is 0. In this way, an adjacency matrix of the bipartite graph can be obtained, and a normalized Laplace matrix can be constructed based on the adjacency matrix. The Laplace matrix helps the subsequent calculation of the spectral domain graph convolution, so that the model can better capture the relationship between users and items.

[0065] Next, construct positive and negative sample pairs: In order to train the recommendation model, it is necessary to construct positive and negative sample pairs. Positive samples usually select items that the target user actually clicks on or collects, which can reflect the user's interests and preferences; negative samples are obtained by randomly sampling from non-interactive items, that is, selecting items that the user has not interacted with as negative samples. By constructing positive and negative samples, the learning ability of the model can be effectively enhanced, enabling it to distinguish between items that the user is interested in and items that he is not interested in, thereby improving the accuracy and effectiveness of the recommendation system.

[0066] Through these data preprocessing steps, the original, unprocessed user behavior data can be converted into high-quality structured data, providing a solid foundation for subsequent recommendation model training. These steps not only optimize data quality and solve problems such as cold start and data sparsity, but also enable the recommendation system to more accurately capture changes in user interests and improve the personalization and accuracy of recommendation results.

[0067] Example 3

[0068] The personalized recommendation method based on spectral domain graph convolution, in which the encoding embedding in step 2 is implemented according to the following steps:

[0069] Step 2.1: One-Hot Encode Discrete Attributes, such as categories and labels, which usually have a limited range of values. For each discrete attribute, convert it to a One-Hot encoding. For example, if the item has a category attribute, each category can be converted into an independent dimension, where the dimension corresponding to the item belonging to that category is 1, and the dimension of other categories is 0;

[0070] Step 2.2: Normalize continuous attributes, such as price and rating, which usually have an infinite range of values. In order to avoid attributes with large values ​​dominating the model, these attributes need to be normalized. Normalization scales the attribute value to a specific range (such as [0,1]);

[0071] Step 2.3: Use an embedding layer to map the normalized values ​​of discrete and continuous attributes into low-dimensional embedding vectors of fixed dimension to generate the final feature representation of users and items.

[0072] First, the discrete attributes are One-Hot encoded. These discrete attributes (such as the category and label of the item) usually have a limited range of values, but they are crucial to the performance of the recommendation system. One-Hot encoding is a commonly used processing method that converts each discrete attribute into an independent dimension, each dimension corresponds to a possible value, and marks the items belonging to that category as 1, and other categories as 0. Taking the item category as an example, assuming that there are three categories of items: "electronic products", "clothing" and "food", through One-Hot encoding, "electronic products" will be converted to [1,0,0], "clothing" to [0,1,0], and "food" to [0,0,1].

[0073] Next, the continuous attributes (such as the price and rating of an item) are normalized. Continuous attributes usually have a large range of values, which can cause some attributes to have too much influence on the model, thus affecting the learning effect of the model. Therefore, in order to prevent attributes with large values ​​from dominating the training of the model, the normalization method is used to map the values ​​of these attributes to a uniform range (such as [0,1]). Through normalization, the model can learn all features more fairly and prevent a certain feature from having a disproportionate impact on model training.

[0074] The discrete and continuous attributes after One-Hot encoding and normalization are input into the embedding layer for mapping to generate a low-dimensional dense vector representation. The embedding vector contains the processing results of the discrete and continuous attributes, and these embedding vectors will serve as the input of the subsequent fully connected layer. The present invention adopts a 5-layer fully connected neural network, aiming to further optimize the embedded representation of users and items through layer-by-layer mapping and nonlinear transformation. The ReLU (Rectified Linear Unit) activation function is used between each layer. Through the step-by-step calculation of the 5-layer fully connected neural network, it is possible to deeply learn the feature representation of users and items.

[0075] Example 4

[0076] A personalized recommendation method based on spectral domain graph convolution, in which in step 3, the Lanczos algorithm is used to efficiently decompose the normalized Laplacian matrix, extract low-frequency signals, retain the first 128 eigenvalues ​​and corresponding eigenvectors, these low-frequency features help capture the potential relationship between users and items, and use spectral domain graph convolution to aggregate the information of the embedding in step 2 to obtain the final embedding representation. The size of the eigenvalue determines the frequency distribution of the corresponding eigenvector in the frequency domain. Low-frequency eigenvalues ​​usually carry the global information of the graph, thereby retaining the main structure and low-frequency information of the graph.

[0077] Example 5

[0078] The personalized recommendation method based on spectral domain graph convolution, wherein step 3 is implemented in the following steps:

[0079] Step 3.1: Decompose the Laplace matrix using the Lanczos algorithm, efficiently calculate its eigenvalues ​​and eigenvectors, and select the first 128 eigenvalues ​​and corresponding eigenvectors representing the low-frequency signal. The eigendecomposition calculation formula is as follows:

[0080] L=PΛP T (2)

[0081] Where P is the eigenvector matrix, which is composed of a set of normalized orthogonal bases. The eigenvector matrix defines the frequency domain, (Λ=diag([λ1,...,λ 128 ]) is a diagonal eigenvalue matrix, all eigenvalues ​​are arranged in ascending order, and the eigenvalues ​​define the frequency of the corresponding eigenvector, thereby effectively retaining the low-frequency information of the graph;

[0082] Step 3.2: From the convolution theorem, we know that the graph convolution in the spectral domain can be calculated by decomposing the eigenvalues ​​and eigenvectors. That is, the eigendecomposition matrix is ​​directly multiplied by the embedding of users and items to obtain the result of the spectral domain graph convolution. The spectral domain graph convolution can be expressed as:

[0083] Z=PΛP TE (3)

[0084] Among them, Z is the embedding vector after spectral domain graph convolution, E is the initial embedding vector, and the specific structure is as follows Figure 2 As shown in Figure 2. By performing spectral domain graph convolution on these embedding vectors, we can better combine the structural information of the graph with the characteristics of users and items, thereby generating more accurate and meaningful final embedding representations. These final embedding representations will be used for subsequent recommendation calculations or similarity matching.

[0085] Example 6

[0086] A personalized recommendation method based on spectral domain graph convolution, wherein step 4 includes two parts, namely, personalized recommendation by calculating cosine similarity and model optimization using BPR loss function.

[0087] Step 4.1: Recommend the top 20 items with the highest similarity to the user by calculating the cosine similarity between the user and the item. The similarity calculation formula is:

[0088]

[0089] Among them, e i represents the embedding of user i, e j Represents the embedding of item j. The cosine similarity calculates the angle between two vectors in the vector space. The value range is [-1,1][-1,1]. The closer the value is to 1, the higher the similarity. Based on the calculated similarity, we can recommend the top 20 items with the highest similarity to the user. These items are usually the most compatible with the user's interests and needs.

[0090] Step 4.2: In order to further improve the performance of the model, the standard BPR (Bayesian Personalized Ranking) loss function is used for optimization during the training process. The training process uses the standard BPR loss function for optimization. The calculation formula is as follows

[0091]

[0092] in, and Represents user u i and interactive itemsu j and uninteracted items u kThe cosine similarity score is used to map the predicted value to the range [-1,1], which is used to measure the priority of one item relative to another. The core idea of ​​this loss function is that the goal of the optimization model is to make the items that the user has actually interacted with have a higher score or similarity than the items that have not been interacted with, thereby improving the accuracy of the recommendation. By minimizing this loss function, the model can gradually learn the true preference relationship between users and items, and ultimately provide users with personalized and accurate recommendations.

[0093] The personalized recommendation method based on spectral domain graph convolution in the present invention can better utilize the interaction information of existing users and items, explore the deep correlation between users' potential interests and item features, alleviate the data sparsity problem, and improve the accuracy of recommendation tasks.

Claims

1. A personalized recommendation method based on spectral domain graph convolution, characterized in that: Please follow the steps below to implement: Step 1, data preprocessing; Step 2: Convert discrete attributes to 0-1 and normalize continuous attributes to obtain the initial representation of users and items, and then train the embedding of users and items through the fully connected layer; Step 3: extract low-frequency signals and use spectral domain graph convolution to aggregate the information of the embedding in step 2 to obtain the final embedding representation; Step 4: Get the recommendation results.

2. The personalized recommendation method based on spectral domain graph convolution according to claim 1, characterized in that: In step 1, user behavior data and item attributes are extracted from the original data source, and invalid data is eliminated, including removing abnormal users and duplicate registered users, and processing abnormal behaviors of a large number of meaningless clicks in a short period of time. For missing values ​​in the data, similar users or items are used to fill them. All user behaviors and item attributes must be normalized and converted into a standardized format.

3. The personalized recommendation method based on spectral domain graph convolution according to claim 2, characterized in that: The step 1 is specifically implemented according to the following steps: Step 1.1: Extract user behavior data from system logs or databases, including user clicks, browsing, favorites, and purchase operations, and obtain relevant attribute information of items. Combined with timestamps and context data, construct a record of user-item interactions. Step 1.2: Remove invalid users including robot accounts and repeatedly registered accounts, as well as a large number of meaningless clicks and extremely repeated operations in a short period of time. At the same time, for missing user or item attributes in the data, fill them in with similar users or items; Step 1.3: Based on the cleaned user behavior data, a user-item bipartite graph is constructed. The user nodes and item nodes are connected through interactive behaviors. Whether there is an edge between the user and the item is assigned a 0-1 value based on whether there is a click, purchase, or collection. If there is the above operation, it is considered that the user and the item have interacted and the value is 1, otherwise it is 0. The adjacency matrix of the bipartite graph can be obtained, denoted as matrix A, and a normalized Laplace matrix is ​​constructed based on the adjacency matrix. The calculation formula is: Where D is the degree matrix of A, is the normalized Laplacian matrix; Step 1.4: Construct positive and negative samples. Select the items that the target user actually clicks or collects as positive samples, and use random sampling to generate negative samples from non-interactive objects.

4. The personalized recommendation method based on spectral domain graph convolution according to claim 1, characterized in that: The encoding embedding in step 2 is specifically implemented according to the following steps: Step 2.1: One-Hot encode the discrete attributes. For each discrete attribute, convert it into a One-Hot encoding. Step 2.2: Normalize continuous attributes. To avoid attributes with large values ​​dominating the model, these attributes need to be normalized. Normalization scales the attribute values ​​to a specific range. Step 2.3: Use an embedding layer to map the normalized values ​​of discrete and continuous attributes into low-dimensional embedding vectors of fixed dimension to generate the final feature representation of users and items.

5. The personalized recommendation method based on spectral domain graph convolution according to claim 1, characterized in that: In step 3, the Lanczos algorithm is used to efficiently decompose the normalized Laplacian matrix, extract low-frequency signals, and retain the first 128 eigenvalues ​​and corresponding eigenvectors. These low-frequency features help capture the potential relationship between users and items. The spectral domain graph convolution is used to aggregate information on the embedding in step 2 to obtain the final embedding representation.

6. The personalized recommendation method based on spectral domain graph convolution according to claim 5, characterized in that: The step 3 is specifically implemented according to the following steps: Step 3.1: Decompose the Laplace matrix using the Lanczos algorithm, efficiently calculate its eigenvalues ​​and eigenvectors, and select the first 128 eigenvalues ​​and corresponding eigenvectors representing the low-frequency signal. The eigendecomposition calculation formula is as follows: L=PΛP T (2) Where P is the eigenvector matrix, which is composed of a set of normalized orthogonal bases. The eigenvector matrix defines the frequency domain, (Λ=diag([λ1,...,λ 128 ]) is a diagonal eigenvalue matrix, all eigenvalues ​​are arranged in ascending order, and the eigenvalues ​​define the frequency of the corresponding eigenvector, thereby effectively retaining the low-frequency information of the graph; Step 3.2: From the convolution theorem, we know that the graph convolution in the spectral domain can be calculated by decomposing the eigenvalues ​​and eigenvectors. That is, the eigendecomposition matrix is ​​directly multiplied by the embedding of users and items to obtain the result of the spectral domain graph convolution. The spectral domain graph convolution can be expressed as: Z=PΛP T E (3)Where Z is the embedding vector after spectral domain graph convolution, and E is the initial embedding vector.

7. The personalized recommendation method based on spectral domain graph convolution according to claim 1, characterized in that: In step 4, the similarity between the user and the item is calculated, and based on the calculated similarity value, the top 20 items with the highest similarity are recommended to the user.

8. The personalized recommendation method based on spectral domain graph convolution according to claim 7, characterized in that: The step 4 is specifically implemented according to the following steps: Step 4.1: Recommend the top 20 items with the highest similarity to the user by calculating the cosine similarity between the user and the item. The similarity calculation formula is: Among them, e i represents the embedding of user i, e j represents the embedding of item j; Step 4.2: The training process is optimized using the standard BPR loss function, and the calculation formula is as follows in, and Represents user u i and interactive itemsu j and uninteracted items u k The cosine similarity score of .

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