Collaborative filtering recommendation method based on spectrogram neural network

Abstract

The invention relates to the technical field of machine learning, in particular to a collaborative filtering recommendation method based on a spectrogram neural network. The method comprises the following steps: generating a graph embedded signal corresponding to a user-item interaction graph by using a spectrum GNN based on the user-item interaction graph, and specifically comprises the following steps: scaling an original filtering function by using a frequency signal scaling function based on the original filtering function of the spectrum GNN to generate a first filtering function; respectively using a monomial basis to approximate the first filtering function to train and generate a low-frequency filtering function and a high-frequency filtering function; and based on the user-item interaction diagram, respectively using a low-frequency filtering function and a high-frequency filtering function to generate a low-frequency diagram embedded signal and a high-frequency diagram embedded signal corresponding to the user-item interaction diagram. According to the collaborative filtering recommendation method based on the spectrogram neural network, the characteristics of the user item interaction diagram can be fully reserved, and homogenization of recommendation results is avoided.

Description

Technical Field

[0001] This application relates to the field of machine learning technology, and particularly to a collaborative filtering recommendation method based on spectral graph neural network. Background Art

[0002] Graph Neural Network (GNN) has been widely used in the field of user-item recommendation due to its powerful graph structure modeling ability.

[0003] In the field of user-item recommendation, it usually relies on matrix factorization or shallow embedding methods, which makes it difficult to effectively capture the complex interaction relationships between users and items. However, using GNN to aggregate neighborhood information through message passing mechanism can generate higher-quality node embeddings and significantly improve the recommendation performance.

[0004] Among them, in the field of user-item recommendation, using spectral GNN that deeply analyzes the essential characteristics of user-item interaction data from the perspective of spectral theory has better recommendation performance than using traditional GNN.

[0005] Spectral domain GNN performs eigenvalue decomposition on the graph Laplacian matrix, designs filtering functions in the frequency domain, directly manipulates the eigenvalues of different frequencies, and then makes recommendations.

[0006] However, most of the spectral domain GNNs used in the prior art tend to adopt low-pass filtering functions, only focusing on the influence of low-frequency eigenvalues on recommendations and ignoring the influence of high-frequency signals. This often leads to homogenization of recommendation results, making it difficult to meet the diverse needs of users. At the same time, it is unable to adaptively adjust the waveform according to the user-item data distribution, resulting in poor recommendation effects in complex scenarios (such as long-tail recommendation, cold start). Summary of the Invention

[0007] In order to solve the deficiencies of the prior art, the purpose of this application is to provide a collaborative filtering recommendation method based on spectral graph neural network, which can fully retain the characteristics of the user-item interaction graph and avoid homogenization of recommendation results.

[0008] To achieve the above purpose, this application provides a collaborative filtering recommendation method based on spectral graph neural network, including: Based on the user-item interaction graph, use spectral GNN to generate the graph embedding signal corresponding to the user-item interaction graph, and the graph embedding signal includes a low-frequency graph embedding signal and a high-frequency graph embedding signal; Perform spatial flipping on the high-frequency graph embedding signal; Based on the low-frequency graph embedding signal and the spatially flipped high-frequency graph embedding signal respectively, make recommendation predictions, and train to generate a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model; Use the low-frequency collaborative filtering recommendation model or the high-frequency collaborative filtering recommendation model to predict the next interaction item of the user; Among them, the specific steps of using spectral GNN to generate the graph embedding signal corresponding to the user-item interaction graph based on the user-item interaction graph include:

[0009] Based on the original filtering function of spectral GNN, use the frequency signal scaling function to scale the original filtering function to generate the first filtering function. The specific steps are as follows: ; ; Among them, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-item interaction graph, is the original filtering function, is the frequency signal scaling function, is the first filtering function, , and are scaling parameters, , is used to control the steepness of the waveform. When , it is used to extract low-frequency signals; when , it is used to extract high-frequency signals; is used to control the position of the waveform; is used to scale the size of the extracted waveform; Use the monomial basis to approximate the first filtering function to train and generate the low-frequency filtering function and the high-frequency filtering function respectively; Based on the user-item interaction graph, use the low-frequency filtering function and the high-frequency filtering function to generate the low-frequency graph embedding signal and the high-frequency graph embedding signal corresponding to the user-item interaction graph respectively.

[0010] Furthermore, the original filtering function includes any one of the monomial basis filter function and the polynomial basis filter function.

[0011] Furthermore, the specific steps of using the monomial basis to approximate the first filtering function to train and generate the low-frequency filtering function and the high-frequency filtering function respectively are as follows: ; ; Among them, is the low-frequency filtering function, is the trainable i-th weight parameter, n represents the number of layers of the polynomial basis, is the low-frequency filtering training loss function, Eigenvalues after eigenvalue decomposition of the adjacency matrix for the user-project interaction graph.

[0012] Further, the specific steps of respectively using the monomial basis to approximate the first filtering function to train and generate the low-frequency filtering function and the high-frequency filtering function also adopt the following formula: ; ; Wherein, is the high-frequency filtering function, is the trainable i-th weight parameter, n represents the number of layers of the polynomial basis, is the high-frequency filtering training loss function, are the eigenvalues after eigenvalue decomposition of the adjacency matrix for the user-project interaction graph.

[0013] Further, the specific steps of generating the low-frequency graph embedding signal and the high-frequency graph embedding signal corresponding to the user-project interaction graph by respectively using the low-frequency filtering function and the high-frequency filtering function are as follows: ; ; Wherein, is the normalized adjacency matrix of the user-project interaction graph is the eigenvector of is the normalized adjacency matrix after eigenvalue decomposition, represents the normalized adjacency matrix, represents the embedding signal of users and projects at the 0th layer, represents the low-frequency graph embedding signal, represents the high-frequency graph embedding signal, is the high-frequency filtering function, is the low-frequency filtering function, is the weight parameter of the low-frequency filtering function, is the weight parameter of the high-frequency filtering function, and n represents the number of layers of the polynomial basis.

[0014] Further, the specific steps of spatially flipping the high-frequency graph embedding signal are as follows: ; is the high-frequency graph embedding signal before spatial flipping, is the high-frequency graph embedding signal after spatial flipping.

[0015] Further, the specific steps of performing recommendation prediction based on the graph embedding signal of the low frequency and the graph embedding signal of the high frequency after spatial flipping, and training to generate a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are represented by the following formulas: ; where , is the low-frequency embedding representation of user , is the low-frequency embedding representation of item , is the graph embedding signal of the low frequency, is the predicted interest score of user in item .

[0016] Further, the specific steps of performing recommendation prediction based on the graph embedding signal of the low frequency and the graph embedding signal of the high frequency after spatial flipping, and training to generate a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are represented by the following formulas: ; where , is the high-frequency embedding representation of user , is the high-frequency embedding representation of item , is the graph embedding signal of the high frequency before spatial flipping, is the graph embedding signal of the high frequency after spatial flipping, is the predicted interest score of user in item .

[0017] To achieve the above object, the electronic device provided by the present application includes: a processor; a memory storing one or more computer program instructions to be run on the processor; wherein, when the processor runs the computer instructions, it executes the collaborative filtering recommendation method based on the spectral graph neural network as described above.

[0018] To achieve the above object, the computer-readable storage medium provided by the present application stores computer instructions, and when the computer instructions are run by a processor, it executes the steps of the collaborative filtering recommendation method based on the spectral graph neural network as described above.

[0019] A collaborative filtering recommendation method based on spectral graph neural network in this application extracts high-frequency graph embedding signals and low-frequency graph embedding signals from user-item interaction graph data respectively, fully utilizes the features of the user-item interaction graph, and improves the recommendation performance.

[0020] A collaborative filtering recommendation method based on spectral graph neural network in this application can dynamically adjust the waveform of the original filtering function by setting a frequency scaling function that can adjust the waveform steepness, position, and size of low-frequency and high-frequency signals. While maintaining continuity, it adjusts the smoothness of the eigenvalue of the user-item interaction graph, facilitating more fully utilizing the features of the user-item interaction graph to accurately extract graph embedding signals of different frequencies of the user-item interaction graph, and achieving better recommendation effects in self-supervised scenarios.

[0021] A collaborative filtering recommendation method based on spectral graph neural network in this application uses spatial flipping to enhance the expressive ability of graph embedding, fully retains the features of user-item interaction data, thereby avoiding the homogenization of recommendation results and improving the recommendation accuracy.

[0022] Other features and advantages of this application will be described in the subsequent specification, and partly become obvious from the specification, or are understood by implementing this application. Brief Description of the Drawings

[0023] The drawings are used to provide further understanding of this application, and constitute a part of the specification. Together with the embodiments of this application, they are used to explain this application and do not constitute a limitation to this application. In the drawings: Figure 1 It is a schematic flow chart of the collaborative filtering recommendation method based on spectral graph neural network of this application; Figure 2 It is a schematic flow chart of generating graph embedding signals; Figure 3 It is a schematic content diagram of the data set in Embodiment 1 of this application; Figure 4 It is a schematic diagram of the recommendation performance of each recommendation model; Figure 5 It is a schematic diagram of the best parameters of the model for different data sets. Detailed Embodiments

[0024] Embodiments of the present application will be described in more detail below with reference to the accompanying drawings. Although some embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. On the contrary, these embodiments are provided to more thoroughly and completely understand the present application. It should be understood that the drawings and embodiments of the present application are only for exemplary purposes and are not used to limit the protection scope of the present application.

[0025] It should be understood that the various steps recited in the method embodiments of the present application can be executed in a different order and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present application is not limited in this regard.

[0026] The term "including" and its variants used herein are open-ended, that is, "including but not limited to". The term "based on" is "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". The relevant definitions of other terms will be given in the following description.

[0027] It should be noted that the modifiers "a" and "multiple" mentioned in the present application are illustrative rather than restrictive. Those skilled in the art should understand that unless clearly specified otherwise in the context, it should be understood as "one or more". "Multiple" should be understood as two or more.

[0028] Spectral Graph Neural Network is a type of deep learning model based on Spectral Graph Theory, aiming to efficiently model graph-structured data through frequency-domain analysis.

[0029] Its core idea is to map graph data to the frequency-domain space, and use Graph Fourier Transform (GFT) and filter design to capture the low-frequency and high-frequency features of the user interaction graph, thereby solving tasks such as node classification, link prediction, and graph classification.

[0030] Exemplarily, given a user-item interaction graph , let and be the node set and edge set of this graph. The user set is denoted as , the item set is denoted as , and the node set is denoted as . The interaction matrix between users and items is , where, if the th user and the If there is an interaction between items, then the adjacency matrix can be represented as follows:

[0031] Spectral GNN performs graph convolution in the spectral domain of the Laplacian matrix. The normalized Laplacian matrix can be defined as , where represents the normalized adjacency matrix, represents the degree matrix of the graph. Its eigenvalues and corresponding eigenvectors are obtained through eigenvalue decomposition, , where is the eigenvector, is the corresponding eigenvalue, The eigenvalue range of

[0032] signal The graph Fourier transform of can be defined as: , and the inverse transform is .

[0033] This transform enables operations to be formulated, such as filtering in the spectral domain. The filtering operation on the signal can be defined as:

[0034] f() is the filtering function. It is difficult to directly calculate because the eigenvalue decomposition of a large Laplacian matrix is very time-consuming. Therefore, spectral GNN often uses some polynomials to approximate :

[0035] where are usually learnable or fixed scalars, usually uses various forms of polynomial bases, refers to a series of eigenvalues in the range of [-1, 1] obtained through eigenvalue decomposition of the adjacency matrix . When the eigenvalue is close to -1, it exhibits high-frequency characteristics, and when the eigenvalue is close to 1, it exhibits low-frequency characteristics.

[0036] Example 1 An embodiment of the present application provides a collaborative filtering recommendation method based on a spectral graph neural network. The following will refer to Figures 1-4 to describe in detail the collaborative filtering recommendation method based on the spectral graph neural network of the present application.

[0037] Step S101: Based on the user-item interaction graph, use spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph; Exemplarily, for a user-item interaction graph , and are the node set and edge set of the graph. We represent the user set as , the item set is represented as , the node set is represented as . The interaction matrix between users and items is , where, for the -th user and the -th item having an interaction, then . Then the adjacency matrix of the user-item interaction graph can be represented as follows:

[0038] Spectral GNN performs graph convolution in the spectral domain of the Laplacian matrix. The normalized Laplacian matrix can be defined as , where represents the normalized adjacency matrix of the user-item interaction graph, represents the degree matrix of the user-item interaction graph. Its eigenvalues and the corresponding eigenvectors are obtained through eigenvalue decomposition, , where is the eigenvector, is the corresponding eigenvalue, and the eigenvalue range of is [0, 2].

[0039] Referring to Figure 2 , based on the user-item interaction graph, the specific steps of using spectral GNN to generate the graph embedding signal corresponding to the user-item interaction graph include: S201: Based on the original filtering function of spectral GNN, use a frequency signal scaling function to scale the original filtering function to generate a first filtering function; In this embodiment, first, use the Jacobi polynomial basis function as the original filtering function of spectral GNN, and the formula is as follows: .

[0040] Where represents the i-th Jacobi polynomial basis of , is a parameter, is the eigenvalue after eigenvalue decomposition of the normalized adjacency matrix, is the original filtering function.

[0041] In this embodiment, the used Jacobi polynomial basis function is determined by the parameter For the definition, these parameters can be adjusted to adapt to different user-item interaction data characteristics. For example, changing can adjust the shape of the basis function to better fit the attenuation or enhancement characteristics of the user-item interaction data characteristics near the interval endpoints, thereby improving the filtering effect.

[0042] In this embodiment, since it is considered that the waveform of the original filtering function will directly affect the performance of the recommendation model. However, the current original filtering function is still not flexible enough to adjust the waveform. Therefore, in this embodiment, in order to flexibly adjust the waveform of the original filter function, the original filtering function is scaled by using a frequency signal scaling function, and the scaled original filtering function is used as the first filtering function. The specific steps are as follows: ; ; Among them, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-item interaction graph, is the original filtering function, is the frequency signal scaling function, is the first filtering function, , and are scaling parameters, where , is used to control the steepness of the waveform. When , it is used to extract low-frequency signals. When , it is used to extract high-frequency signals. is used to control the position of the waveform, is used to scale the size of the extracted waveform.

[0043] In this embodiment, a frequency signal scaling function composed of the Sigmoid function is used. This frequency signal scaling function can dynamically adjust the waveform of the original filtering function by setting frequency scaling functions for adjusting the steepness, position, and size of the waveform. While maintaining continuity, it adjusts the smoothness of the eigenvalues of the user-item interaction graph, and further makes more full use of the characteristics of the user-item interaction graph in the recommendation scenario to accurately extract the graph embedding signal of the user-item interaction graph, achieving a better recommendation effect in the self-supervised scenario.

[0044] S202: Respectively use monomial bases to approximate the first filtering function to train and generate a low-frequency filtering function and a high-frequency filtering function; In this embodiment, since the eigenvalue decomposition of the large Laplacian matrix is very time-consuming and it is very difficult to directly calculate the first filtering function, for the convenience of calculation, the monomial basis is used to approximate the first filtering function. When using the monomial basis to obtain the graph embedding signal, it has different expressions in different quadrants: In the first quadrant, it behaves as a low-frequency filtering function, Low(I): ; In the fourth quadrant, it behaves as a low-frequency filtering function, Low(IV): ; In the second quadrant, it behaves as a high-frequency filtering function, High(II): ; In the third quadrant, it behaves as a high-frequency filtering function, High(III): 。

[0045] The inventors have found through research that the graph embedding signals in the first and third quadrants can effectively improve the similarity between users and items, while the graph embedding signals in the second and fourth quadrants will inhibit the similarity between users and items. Therefore, the monomial basis is used to approximate the first filtering function for the first and third quadrants respectively to train and generate low-frequency and high-frequency filtering functions, so as to obtain the graph embedding signals in the first and third quadrants.

[0046] The specific steps adopt the following formula: ; ; where, is the low-frequency filtering function, is the trainable i-th weight parameter, n represents the number of layers of the polynomial basis, is the low-frequency filtering training loss function, is the eigenvalue after the eigenvalue decomposition of the adjacency matrix of the user-item interaction graph.

[0047] ; ; where, is the high-frequency filtering function, is the trainable i-th weight parameter, n represents the number of layers of the polynomial basis, is the high-frequency filtering training loss function, is the eigenvalue after the eigenvalue decomposition of the adjacency matrix of the user-item interaction graph.

[0048] S203: Based on the user-item interaction graph, use a low-frequency filtering function and a high-frequency filtering function respectively to generate a low-frequency graph embedding signal and a high-frequency graph embedding signal corresponding to the user-item interaction graph; ; ; wherein, is the normalized adjacency matrix of the user-item interaction graph is the eigenvector of the normalized adjacency matrix after eigenvalue decomposition, represents the normalized adjacency matrix, represents the embedding signals of users and items at the 0th layer, represents the low-frequency graph embedding signal, represents the high-frequency graph embedding signal, is the high-frequency filtering function, is the low-frequency filtering function, is the weight parameter of the low-frequency filtering function, is the weight parameter of the high-frequency filtering function, and n represents the number of layers of the polynomial basis.

[0049] Step S102: Perform a spatial flip on the high-frequency graph embedding signal; Since the graph embedding signal cannot express negative signs when calculating the similarity between nodes, which suppresses some characteristics of the eigenvalues, it is necessary to perform a spatial flip on the high-frequency graph embedding signal in the third quadrant.

[0050] In this embodiment, to perform a spatial flip on the graph embedding signal corresponding to the high-frequency signal, the following formula is used: ; is the high-frequency graph embedding signal before spatial flip, is the high-frequency graph embedding signal after spatial flip.

[0051] Step S103: Perform recommendation prediction respectively based on the low-frequency graph embedding signal and the spatially flipped high-frequency graph embedding signal, and train to generate a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model; In this embodiment, the inner product of the graph embedding representation of the user and the graph embedding representation of the item is used as the predicted interest score of the user for the item; For the low-frequency graph embedding signal, the following formula is used: ; wherein, , is the user The low-frequency embedding representation, for the item The low-frequency embedding representation, is the low-frequency graph embedding signal, is the predicted user 's interest score for the item .

[0052] For the high-frequency graph embedding signal, the following formula is adopted: ; where , is the high-frequency embedding representation of the user , is the high-frequency embedding representation of the item , is the high-frequency graph embedding signal before spatial flipping, is the high-frequency graph embedding signal after spatial flipping, is the predicted user 's interest score for the item .

[0053] In this embodiment, the Bayesian Personalized Ranking (i.e., BPR) is used as the loss function for recommendation prediction, and the formula is as follows: ; where is the neighbor set of user 𝑢, is the user who does not belong to ; The final loss function adopts the following formula: ; where W controls the influence factor of the L2 norm.

[0054] For the low-frequency graph embedding signal and the high-frequency graph embedding signal, a low-frequency collaborative filtering recommendation model (SimGCF(I)) and a high-frequency collaborative filtering recommendation model (SimGCF(III)) are respectively trained and generated.

[0055] Step S104: Use the low-frequency collaborative filtering recommendation model or the high-frequency collaborative filtering recommendation model to predict the next interaction item of the user; In this method, some user-item interaction datasets are used for the training and prediction of the collaborative filtering recommendation models (SimGCF(III) and SimGCF(I)), refer to Figure 3 , Figure 3 which is the content schematic diagram of the dataset in Embodiment 1 of this application, as shown in Figure 3As shown, the dataset includes four datasets: Gowalla, Amazon - Books, Yelp, and Alibaba - iFashio. Among them, Gowalla is widely used as an interest - point network for evaluating recommendation algorithms. Amazon - Books is a dataset of user rating histories based on an online bookstore. Yelp is a business recommendation dataset where each business is regarded as an item. Alibaba - iFashio includes clicks of iFashion users on products.

[0056] In this embodiment, 80% of the user interaction data is used for training, 10% for validation, and the remaining 10% for testing.

[0057] In this embodiment, Recall@K and NDCG@K are used as evaluation metrics, where K ∈ [10, 20], and the latest recommendation model is selected as our baseline model for performance comparison. Refer to Figure 4 , Figure 4 For the schematic diagram of the recommendation performance of each recommendation model, the SimGCF(I) of this application significantly outperforms models such as JGCF in terms of various performance metrics on the Gowalla and Amazon - Books datasets. And by using spatial flipping to recover high - frequency graph embedding signals, and on this basis, SimGCF(III) that also uses frequency signal scaling also has a significant improvement in performance compared to the current advanced collaborative filtering recommendation models. That is, the performance of SimGCF(I) and SimGCF(III) has both improved compared to the baseline model and the difference between the two is not large. Therefore, when actually selecting a model to predict the next interaction item of users, either the low - frequency collaborative filtering recommendation model SimGCF(I) or the high - frequency collaborative filtering recommendation model SimGCF(III) can be used.

[0058] Exemplarily, refer to Figure 5 , Figure 5 For the schematic diagram of the best parameters of the SimGCF(I) model on different datasets. Figure 5 It shows the best values of parameters such as the Jacobi function parameter a, Jacobi function parameter b, embedding dimension, L2 - norm weight, number of graph convolutional layers n, learning rate of the low - frequency collaborative filtering recommendation model (SimGCF(I)) on different datasets. and other parameters.

[0059] Example 2 In this embodiment, an electronic device is further provided, which includes a processor and a memory. The memory is used to store non-transitory computer-readable instructions. The processor is used to run the non-transitory computer-readable instructions, and when the non-transitory computer-readable instructions are run by the processor, one or more steps of the collaborative filtering recommendation method based on the spectral graph neural network described above can be executed. The memory and the processor can be interconnected through a bus system and / or other forms of connection mechanisms.

[0060] For example, the processor can be a central processing unit (CPU), a digital signal processor (DSP), or other forms of processing units with data processing capabilities and / or program execution capabilities, such as a field programmable gate array (FPGA), etc.; for example, the central processing unit (CPU) can be of the X86 or ARM architecture, etc.

[0061] For example, the memory can include any combination of one or more computer program products, and the computer program products can include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. Volatile memory can include, for example, random access memory (RAM) and / or cache memory, etc. Non-volatile memory can include, for example, read-only memory (ROM), hard disk, erasable programmable read-only memory (EPROM), portable compact disc read-only memory (CD-ROM), USB memory, flash memory, etc. One or more computer program modules can be stored on the computer-readable storage medium, and the processor can run one or more computer program modules to implement various functions of the electronic device. Various application programs and various data, as well as various data used and / or generated by the application programs, can also be stored in the computer-readable storage medium.

[0062] It should be noted that in the embodiments of the present application, the specific functions and technical effects of the electronic device can refer to the description of the collaborative filtering recommendation method based on the spectral graph neural network above, and will not be elaborated here.

[0063] Embodiment 3 In this embodiment, a computer-readable storage medium is further provided, and the storage medium is used to store non-transitory computer-readable instructions. For example, when the non-transitory computer-readable instructions are executed by a computer, one or more steps of the collaborative filtering recommendation method based on the spectral graph neural network described above can be executed.

[0064] For example, the storage medium can be applied to the above-mentioned electronic device. For example, the storage medium can be the memory in the electronic device of Embodiment 2. For example, the relevant description of the storage medium can refer to the corresponding description of the memory in the electronic device of Embodiment 2, and will not be elaborated here.

[0065] It should be noted that the above storage medium (computer-readable medium) of the present application can be a computer-readable signal medium, a non-transitory computer-readable storage medium, or any combination of the two. A non-transitory computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the non-transitory computer-readable storage medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0066] In the present application, a non-transitory computer-readable storage medium can be any tangible medium that contains or stores a program, which can be used by or in conjunction with an instruction execution system, apparatus, or device. And in the present application, a computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium can also be any computer-readable medium other than a non-transitory computer-readable storage medium, and this computer-readable signal medium can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium can be transmitted using any appropriate medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination of the above.

[0067] The above computer-readable medium can be included in the above electronic device; or it can exist separately and not be assembled into the electronic device.

[0068] The computer program code for performing the operations of the present application can be written in one or more programming languages or combinations thereof. The above programming languages include but are not limited to object-oriented programming languages such as Java, Smalltalk, C++, and also include conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server.

[0069] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a part of code that contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as combinations of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0070] The units involved in the embodiments described in this application can be implemented in software or in hardware. Among them, the name of the unit does not constitute a limitation to the unit itself in some cases.

[0071] The functions described above can be at least partially performed by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that can be used include: Field Programmable Gate Arrays (FPGAs), Application Specific Integrated Circuits (ASICs), Application Specific Standard Products (ASSPs), Systems on Chip (SOCs), Complex Programmable Logic Devices (CPLDs), etc.

[0072] The above description is only for some embodiments of the present application and an explanation of the technical principles applied. Those skilled in the art should understand that the scope of disclosure involved in the present application is not limited to the technical solutions formed by the specific combination of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosure concept. For example, technical solutions formed by mutually replacing the above features with (but not limited to) technical features having similar functions disclosed in the present application.

[0073] In addition, although the operations are depicted in a particular order, this should not be construed as requiring that the operations be performed in the particular order shown or in sequential order. In certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the foregoing description, these should not be construed as limitations on the scope of the present application. Certain features that are described in the context of separate embodiments may also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment may also be implemented separately or in any suitable subcombination in multiple embodiments.

[0074] Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are merely example forms of implementing the claims.

Claims

1. A collaborative filtering recommendation method based on spectral graph neural network, comprising: Based on the user-item interaction graph, use spectral GNN to generate graph embedding signals corresponding to the user-item interaction graph, where the graph embedding signals include low-frequency graph embedding signals and high-frequency graph embedding signals; Perform spatial flipping on the high-frequency graph embedding signals; Based on the low-frequency graph embedding signals and the spatially flipped high-frequency graph embedding signals respectively, perform recommendation prediction and train to generate a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model; Use the low-frequency collaborative filtering recommendation model or the high-frequency collaborative filtering recommendation model to predict the next interaction item of the user; Among them, the specific steps of using spectral GNN to generate graph embedding signals corresponding to the user-item interaction graph based on the user-item interaction graph include: Based on the original filtering function of spectral GNN, use a frequency signal scaling function to scale the original filtering function to generate a first filtering function. The specific steps are as follows: ； ； Among them, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-project interaction diagram, is the original filtering function, is the frequency signal scaling function, is the first filtering function, 、 and are scaling parameters, , is used to control the steepness of the waveform. When , it is used to extract low-frequency signals; when , it is used to extract high-frequency signals; is used to control the position of the waveform; is used to scale the size of the extracted waveform; Use monomial basis to approximate the first filtering function respectively to train and generate a low-frequency filtering function and a high-frequency filtering function; Based on the user-item interaction graph, use the low-frequency filtering function and the high-frequency filtering function respectively to generate low-frequency graph embedding signals and high-frequency graph embedding signals corresponding to the user-item interaction graph.

2. The collaborative filtering recommendation method based on the spectral graph neural network according to claim 1, characterized in that, The original filtering function includes any one of a monomial basis filter function and a polynomial basis filter function.

3. The collaborative filtering recommendation method based on the spectral graph neural network according to claim 1, wherein The specific steps of using monomial basis to approximate the first filtering function respectively to train and generate a low-frequency filtering function and a high-frequency filtering function are as follows: ； ； Among them, is a low-frequency filtering function, is the $i$-th trainable weight parameter, and $n$ represents the number of layers of the polynomial basis. is the low-frequency filtering training loss function, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-item interaction graph.

4. The collaborative filtering recommendation method based on the spectral graph neural network according to claim 1, wherein The specific steps of using monomial basis to approximate the first filtering function respectively to train and generate a low-frequency filtering function and a high-frequency filtering function also adopt the following formula: ； ； Among them, is a high-pass filtering function, is the $i$-th trainable weight parameter, and $n$ represents the number of layers of the polynomial basis, is the high-pass filtering training loss function, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-item interaction graph.

5. The collaborative filtering recommendation method based on the spectral graph neural network according to claim 1, wherein The specific steps of using the low-frequency filtering function and the high-frequency filtering function respectively to generate low-frequency graph embedding signals and high-frequency graph embedding signals corresponding to the user-item interaction graph based on the user-item interaction graph are as follows: ； ； Among them, is the normalized adjacency matrix of the user-project interaction graph is the eigenvector of which is the normalized adjacency matrix after eigenvalue decomposition, represents the normalized adjacency matrix, represents the embedding signals of users and projects at the 0th layer, represents the low-frequency graph embedding signal, represents the high-frequency graph embedding signal, is the high-frequency filtering function, is the low-frequency filtering function, is the weight parameter of the low-frequency filtering function, is the weight parameter of the high-frequency filtering function, and n represents the number of layers of the polynomial basis.

6. The collaborative filtering recommendation method based on the spectral graph neural network according to claim 4, characterized in that, The specific steps of performing spatial flipping on the high-frequency graph embedding signals are as follows: ； is the high-frequency graph embedding signal before spatial flipping, is the high-frequency graph embedding signal after spatial flipping.

7. The collaborative filtering recommendation method based on a spectral graph neural network according to claim 6, wherein The specific steps of performing recommendation prediction based on the low-frequency graph embedding signals and the spatially flipped high-frequency graph embedding signals respectively and training to generate a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are as follows: ； Among them, , is the low-frequency embedding representation of the user , is the low-frequency embedding representation of the item , is the low-frequency graph embedding signal is the predicted interest score of the user for the item .

8. The collaborative filtering recommendation method based on the spectral graph neural network according to claim 6, characterized in that, The specific steps of performing recommendation prediction based on the low-frequency graph embedding signals and the spatially flipped high-frequency graph embedding signals respectively and training to generate a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are as follows: ； Among them, , is the high-frequency embedding representation of the user , is the high-frequency embedding representation of the project , is the high-frequency graph embedding signal before spatial flipping, is the high-frequency graph embedding signal after spatial flipping, is the predicted interest score of the user for the project .

9. An electronic device, characterized in that, Including: A processor; A memory storing one or more computer program instructions running on the processor; Among them, when the processor runs the computer program instructions, it executes the collaborative filtering recommendation method based on spectral graph neural network according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, Stored thereon are computer instructions, which when run by a processor, execute the steps of the collaborative filtering recommendation method based on spectral graph neural network according to any one of claims 1-8.

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