A collaborative filtering recommendation method based on spectral graph neural network

Abstract

The present application relates to the field of machine learning technology, and in particular to a collaborative filtering recommendation method based on spectral graph neural networks. The method comprises: based on a user-item interaction graph, using a spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph, and the specific steps include: based on the original filter function of the spectral GNN, using a frequency signal scaling function to scale the original filter function to generate a first filter function; using a monomial basis to approximate the first filter function to train and generate a low-frequency filter function and a high-frequency filter function; based on the user-item interaction graph, using a low-frequency filter function and a high-frequency filter function to generate a low-frequency graph embedding signal and a high-frequency graph embedding signal corresponding to the user-item interaction graph. The collaborative filtering recommendation method based on a spectral graph neural network of the present application can fully retain the characteristics of the user-item interaction graph and avoid the homogenization of the recommendation results.

Description

Technical Field

[0001] The present application relates to the field of machine learning technology, and in particular 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 capabilities.

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

[0004] Among them, in the field of user-item recommendation, the use of spectral GNN, which 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 eigendecomposition on the graph Laplacian matrix, designs a filter function in the frequency domain, directly manipulates the eigenvalues ​​of different frequencies, and then makes recommendations.

[0006] However, the spectral domain GNNs used in existing technologies mostly tend to adopt low-pass filtering functions, focusing only on the impact of low-frequency eigenvalues ​​on recommendations and ignoring the influence of high-frequency signals. This often leads to homogenized recommendation results and makes it difficult to meet the diverse needs of users. At the same time, it is also 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 recommendations and cold starts). Summary of the Invention

[0007] In order to address the deficiencies in 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 the homogenization of recommendation results.

[0008] To achieve the above objectives, the present application provides a collaborative filtering recommendation method based on spectral graph neural network, comprising:

[0009] Based on the user-item interaction graph, using spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph, wherein the graph embedding signal includes a low-frequency graph embedding signal and a high-frequency graph embedding signal;

[0010] Performing spatial flipping on the high-frequency image embedding signal;

[0011] Performing recommendation prediction based on the low-frequency graph embedding signal and the high-frequency graph embedding signal after spatial flipping, respectively, and training and generating a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model;

[0012] Using the low-frequency collaborative filtering recommendation model or the high-frequency collaborative filtering recommendation model, predicting the user's next interactive item;

[0013] The specific steps of using spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph based on the user-item interaction graph include:

[0014] Based on the original filter function of the spectral GNN, the frequency signal scaling function is used to scale the original filter function to generate a first filter function. The specific steps are as follows:

[0015] ;

[0016] ;

[0017] in, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-item interaction graph, is the original filter function, is the frequency signal scaling function, is the first filter function, 、 and is the scaling parameter, , Used to control the steepness of the waveform. When , it is used to extract low-frequency signals; when When , it is used to extract high-frequency signals; Used to control the position of the waveform; Used to scale the size of the extracted waveform;

[0018] Respectively using a monomial basis to approximate the first filter function to train and generate a low-frequency filter function and a high-frequency filter function;

[0019] Based on the user-item interaction graph, a low-frequency graph embedding signal and a high-frequency graph embedding signal corresponding to the user-item interaction graph are generated using a low-frequency filtering function and a high-frequency filtering function respectively.

[0020] Furthermore, the original filter function includes any one of a monomial-based filter function and a polynomial-based filter function.

[0021] Furthermore, the specific steps of respectively using a monomial basis to approximate the first filter function to train and generate a low-frequency filter function and a high-frequency filter function are as follows:

[0022] ;

[0023] ;

[0024] in, is the low-frequency filter function, is the trainable i-th weight parameter, n represents the number of layers of the polynomial basis, is the low-frequency filter training loss function, Eigenvalues ​​of the adjacency matrix of the user-item interaction graph after eigenvalue decomposition.

[0025] Furthermore, the specific steps of respectively using a monomial basis to approximate the first filter function to train and generate a low-frequency filter function and a high-frequency filter function also use the following formula:

[0026] ;

[0027] ;

[0028] in, is the high-frequency filter 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, Eigenvalues ​​of the adjacency matrix of the user-item interaction graph after eigenvalue decomposition.

[0029] Furthermore, the specific steps of generating a low-frequency graph embedding signal and a high-frequency graph embedding signal corresponding to the user-item interaction graph using a low-frequency filter function and a high-frequency filter function respectively based on the user-item interaction graph adopt the following formula:

[0030] ;

[0031] ;

[0032] in, is the normalized adjacency matrix of the user-item interaction graph The eigenvector of is the normalized adjacency matrix The eigenvalues ​​after eigenvalue decomposition, represents the normalized adjacency matrix, represents the embedding signals of users and items at layer 0, represents the low-frequency graph embedding signal, represents the high-frequency graph embedding signal, is the high-frequency filter function, is the low-frequency filter function, is the weight parameter of the low-frequency filter function, is the weight parameter of the high-frequency filter function, and n represents the number of layers of the polynomial basis.

[0033] Furthermore, the specific step of performing spatial flipping on the high-frequency image embedding signal adopts the following formula:

[0034] ;

[0035] is the high-frequency image embedding signal before spatial flipping, It is the high-frequency image embedding signal after spatial flipping.

[0036] Furthermore, the specific steps of performing recommendation prediction based on the low-frequency graph embedding signal and the high-frequency graph embedding signal after spatial flipping, and training and generating a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are as follows:

[0037] ;

[0038] in, , For users The low-frequency embedding representation of For the project The low-frequency embedding representation of is the low-frequency graph embedding signal, For predicted users About the project interest score.

[0039] Furthermore, the specific steps of performing recommendation prediction based on the low-frequency graph embedding signal and the high-frequency graph embedding signal after spatial flipping, and training and generating a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are as follows:

[0040] ;

[0041] in, , For users The high-frequency embedding representation of For the project The high-frequency embedding representation of is the high-frequency image embedding signal before spatial flipping, is the high-frequency image embedding signal after spatial flipping, For predicted users About the project interest score.

[0042] To achieve the above-mentioned purpose, the electronic device provided by this application includes:

[0043] processor;

[0044] a memory having stored thereon one or more computer program instructions executed on the processor;

[0045] When the processor runs the computer instructions, it executes the collaborative filtering recommendation method based on spectral graph neural network as described above.

[0046] To achieve the above-mentioned purpose, the computer-readable storage medium provided in the present application stores computer instructions thereon. When the computer instructions are executed by a processor, the steps of the collaborative filtering recommendation method based on spectral graph neural network as described above are executed.

[0047] The present application proposes a collaborative filtering recommendation method based on spectral graph neural network, which extracts high-frequency graph embedding signals and low-frequency graph embedding signals from user-item interaction graph data respectively, fully utilizing the characteristics of the user-item interaction graph and improving the recommendation performance.

[0048] The present application discloses a collaborative filtering recommendation method based on a spectral graph neural network. By setting a frequency scaling function that can adjust the waveform steepness, position and size of low-frequency and high-frequency signals, the waveform of the original filter function can be dynamically adjusted. While maintaining continuity, the smoothness of the eigenvalues ​​of the user-item interaction graph is adjusted, so as to make fuller use of the features of the user-item interaction graph to accurately extract graph embedding signals of different frequencies of the user-item interaction graph, thereby achieving better recommendation effects in self-supervised scenarios.

[0049] The present application proposes a collaborative filtering recommendation method based on spectral graph neural network, which uses spatial flipping to enhance the expressive power of graph embedding, fully retains the characteristics of user-item interaction data, thereby avoiding the homogenization of recommendation results and improving the recommendation accuracy.

[0050] Other features and advantages of the present application will be set forth in the following description, and in part will be apparent from the description, or may be learned by practicing the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings are used to provide a further understanding of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the present application and do not constitute a limitation of the present application. In the accompanying drawings:

[0052] Figure 1 This is a flowchart of the collaborative filtering recommendation method based on spectral graph neural network of this application;

[0053] Figure 2 A schematic diagram of the process of generating graph embedding signals;

[0054] Figure 3 This is a schematic diagram of the content of the data set of Example 1 of this application;

[0055] Figure 4 Schematic diagram of the recommendation performance of each recommendation model;

[0056] Figure 5 Schematic diagram of the optimal model parameters for different data sets. DETAILED DESCRIPTION

[0057] The following describes embodiments of the present application in more detail with reference to the accompanying drawings. Although certain embodiments of the present application are shown in the accompanying 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 described herein. Instead, these embodiments are provided to provide a more thorough and complete understanding of the present application. It should be understood that the drawings and embodiments of the present application are for illustrative purposes only and are not intended to limit the scope of protection of the present application.

[0058] It should be understood that the various steps described in the method embodiments of the present application can be performed in different orders 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 respect.

[0059] As used herein, the term "including" and its variations are open-ended, i.e., "including but not limited to." The term "based on" means "based, at least in part, on." The term "one embodiment" means "at least one embodiment," the term "another embodiment" means "at least one additional embodiment," and the term "some embodiments" means "at least some embodiments." Other terms are defined in the following description.

[0060] It should be noted that the modifications of "one" and "plurality" mentioned in this application are illustrative rather than restrictive. Those skilled in the art will understand that unless the context clearly indicates otherwise, they should be understood as "one or more." "Plurality" should be understood as two or more.

[0061] Spectral Graph Neural Network (SGN) is a deep learning model based on spectral graph theory, which aims to achieve efficient modeling of graph-structured data through frequency domain analysis.

[0062] The core idea is to map graph data into 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.

[0063] For example, given a user-item interaction graph ,set up and is the set of nodes and edges of the graph. The user set is represented as , the project set is represented as , the node set is represented as The interaction matrix between users and items is , where if users and Items have interactions, then The adjacency matrix can be expressed as follows:

[0064]

[0065] Spectral GNN performs graph convolution in the spectral domain of the Laplacian matrix. The normalized Laplacian matrix can be defined as ,in represents the normalized adjacency matrix, Represents the degree matrix of the graph. Its eigenvalues ​​and corresponding eigenvectors are obtained by eigenvalue decomposition. ,in is the eigenvector, is the corresponding eigenvalue, The eigenvalue range of is [0, 2].

[0066] Signal The graphical Fourier transform of can be defined as: , the inverse transformation is .

[0067] This transform enables operations such as filtering to be formulated in the spectral domain. The filtering operation can be defined as:

[0068]

[0069] f() is the filter function, directly calculated is difficult because the eigenvalue decomposition of large Laplacian matrices is very time-consuming. Therefore, spectral GNNs often use some polynomials to approximate :

[0070]

[0071] in is usually a learnable or fixed scalar, Various forms of polynomial bases are commonly used, It means through the adjacency matrix The eigenvalue decomposition obtains a series of eigenvalues ​​in the range of [-1, 1]. When the eigenvalue is close to -1, it shows high-frequency characteristics, and when the eigenvalue is close to 1, it shows low-frequency characteristics.

[0072] Example 1

[0073] An embodiment of the present application provides a collaborative filtering recommendation method based on spectral graph neural network, which will be referred to below. Figure 1-Figure 4 The collaborative filtering recommendation method based on spectral graph neural network of this application is described in detail.

[0074] Step S101: Based on a user-item interaction graph, using a spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph;

[0075] For example, for a user-item interaction graph , and is the set of nodes and edges of the graph. We denote the user set as , the item set is represented as , the node set is represented as The interaction matrix between users and items is , among which, users and Items have interactions, then . Then the adjacency matrix of the user-item interaction graph can be expressed as follows:

[0076]

[0077] Spectral GNN performs graph convolution in the spectral domain of the Laplacian matrix. The normalized Laplacian matrix can be defined as ,in represents the normalized adjacency matrix of the user-item interaction graph, Represents the degree matrix of the user-item interaction graph. Its eigenvalues ​​are obtained by eigenvalue decomposition and the corresponding eigenvectors , ,in is the eigenvector, is the corresponding eigenvalue, The eigenvalue range of is [0, 2].

[0078] See Figure 2 Based on the user-item interaction graph, the specific steps of using the spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph include:

[0079] S201: Based on an original filter function of the spectral GNN, use a frequency signal scaling function to scale the original filter function to generate a first filter function;

[0080] In this embodiment, first, the Jacobi polynomial basis function is used as the original filter function of the spectral GNN, and the formula is as follows:

[0081] .

[0082] in, express The i-order Jacobi polynomial basis of , As parameters, is the eigenvalue after eigenvalue decomposition of the normalized adjacency matrix, is the original filter function.

[0083] In this embodiment, the Jacobi polynomial basis function used is composed of parameters To define, we can adapt these parameters to different user-item interaction data characteristics. For example, changing The shape of the basis function can be adjusted to better fit the attenuation or enhancement characteristics of the user-item interaction data near the endpoints of the interval, thereby improving the filtering effect.

[0084] In this embodiment, considering the original filter function The waveform of will directly affect the performance of the recommendation model. However, the current original filter function Still not flexible enough to adjust Therefore, in this embodiment, in order to flexibly adjust the waveform of the original filter function, the original filter function is scaled by using a frequency signal scaling function, and the scaled original filter function is used as the first filter function. The specific steps are as follows:

[0085] ;

[0086] ;

[0087] in, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-item interaction graph, is the original filter function, is the frequency signal scaling function, is the first filter function, 、 and is the scaling parameter, where , Used to control the steepness of the waveform. When , it is used to extract low-frequency signals. , is used to extract high-frequency signals. is used to control the position of the waveform, Used to scale the size of the extracted waveform.

[0088] In this embodiment, a frequency signal scaling function composed of a Sigmoid function is used. The frequency signal scaling function can dynamically adjust the waveform of the original filter function by setting a frequency scaling function that adjusts the steepness, position and size of the waveform. While maintaining continuity, the smoothness of the eigenvalues ​​of the user-item interaction graph is adjusted, thereby making more full use of the features of the user-item interaction graph in the recommendation scenario to accurately extract the graph embedding signal of the user-item interaction graph, thereby achieving better recommendation effects in self-supervised scenarios.

[0089] S202: using a monomial basis to approximate the first filter function to generate a low-frequency filter function and a high-frequency filter function;

[0090] In this embodiment, since the eigenvalue decomposition of a large Laplacian matrix is ​​very time-consuming and it is very difficult to directly calculate the first filter function, a monomial basis is used to approximate the first filter function for ease of calculation. However, when the monomial basis is used to obtain the graph embedding signal, it has different expressions in different quadrants:

[0091] In the I quadrant, it behaves as a low-frequency filter function, Low(I): ;

[0092] In the IV quadrant, it behaves as a low-frequency filter function, Low(IV): ;

[0093] In the second quadrant, it behaves as a high-frequency filter function, High(II): ;

[0094] In the third quadrant, it behaves as a high-frequency filter function, High(III): .

[0095] The inventors found that the graph embedding signals in the first and third quadrants can effectively enhance the similarity between users and items, while the graph embedding signals in the second and fourth quadrants will suppress the similarity between users and items. Therefore, the inventors used the monomial basis to approximate the first filter function for training to generate low-frequency filter functions and high-frequency filter functions for the first and third quadrants respectively to obtain the graph embedding signals in the first and third quadrants.

[0096] The specific steps are as follows:

[0097] ;

[0098] ;

[0099] in, is the low-frequency filter function, is the trainable i-th weight parameter, n represents the number of layers of the polynomial basis, is the low-frequency filter training loss function, Eigenvalues ​​of the adjacency matrix of the user-item interaction graph after eigenvalue decomposition.

[0100] ;

[0101] ;

[0102] in, is the high-frequency filter 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, Eigenvalues ​​of the adjacency matrix of the user-item interaction graph after eigenvalue decomposition.

[0103] S203: Based on the user-item interaction graph, using a low-frequency filter function and a high-frequency filter function to generate a low-frequency graph embedding signal and a high-frequency graph embedding signal corresponding to the user-item interaction graph respectively;

[0104] ;

[0105] ;

[0106] in, is the normalized adjacency matrix of the user-item interaction graph The eigenvector of is the normalized adjacency matrix The eigenvalues ​​after eigenvalue decomposition, represents the normalized adjacency matrix, represents the embedding signals of users and items at layer 0, represents the low-frequency graph embedding signal, represents the high-frequency graph embedding signal, is the high-frequency filter function, is the low-frequency filter function, is the weight parameter of the low-frequency filter function, is the weight parameter of the high-frequency filter function, and n represents the number of layers of the polynomial basis.

[0107] Step S102: performing spatial flipping on the high-frequency image embedding signal;

[0108] Since the graph embedding signal cannot express a negative sign when calculating the similarity between nodes, which suppresses some characteristics of the eigenvalue, it is necessary to perform spatial flipping on the high-frequency graph embedding signal in the third quadrant.

[0109] In this embodiment, the image embedding signal corresponding to the high-frequency signal is spatially flipped using the following formula:

[0110] ;

[0111] is the high-frequency image embedding signal before spatial flipping, It is the high-frequency image embedding signal after spatial flipping.

[0112] Step S103: performing recommendation prediction based on the low-frequency graph embedding signal and the high-frequency graph embedding signal after spatial flipping, and training and generating a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model;

[0113] 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 user interest score for the item;

[0114] For low-frequency graph embedding signals, the following formula is used:

[0115] ;

[0116] in, , For users The low-frequency embedding representation of For the project The low-frequency embedding representation of is the low-frequency graph embedding signal, For predicted users About the project interest score.

[0117] For high-frequency graph embedding signals, the following formula is used:

[0118] ;

[0119] in, , For users The high-frequency embedding representation of For the project The high-frequency embedding representation of is the high-frequency image embedding signal before spatial flipping, is the high-frequency image embedding signal after spatial flipping, For predicted users About the project interest score.

[0120] In this embodiment, the Bayesian Personalization Rating (BPR) is used as the loss function for recommendation prediction, and the formula is as follows:

[0121] ;

[0122] in, is the neighbor set of user 𝑢, For those who do not belong users;

[0123] The final loss function uses the following formula:

[0124] ;

[0125] Among them, W controls The influence factor of the L2 norm.

[0126] For low-frequency graph embedding signals and high-frequency graph embedding signals, a low-frequency collaborative filtering recommendation model (SimGCF(I)) and a high-frequency collaborative filtering recommendation model (SimGCF(III)) are trained and generated respectively.

[0127] Step S104: using the low-frequency collaborative filtering recommendation model or the high-frequency collaborative filtering recommendation model to predict the user's next interactive item;

[0128] In this approach, some user-item interaction datasets are used for training and prediction of collaborative filtering recommendation models (SimGCF(III) and SimGCF(I)), see Figure 3 , Figure 3 This is a schematic diagram of the content of the data set of Example 1 of this application, such as Figure 3 As shown in the figure, the datasets include Gowalla, Amazon-Books, Yelp, and Alibaba-iFashio. Gowalla is widely used as a point-of-interest network for evaluating recommendation algorithms. Amazon-Books is a historical user rating dataset based on an online bookstore. Yelp is a business recommendation dataset where each business is considered an item. Alibaba-iFashio includes clicks on products by iFashion users.

[0129] In this embodiment, 80% of the user interaction data is used for training, 10% of the data is used for validation, and the remaining 10% is used for testing.

[0130] In this implementation, 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. Figure 4 , Figure 4 The figure shows the recommendation performance of each recommendation model. The performance indicators of SimGCF(I) of this application on the Gowalla and Amazon-Books datasets are significantly better than those of models such as JGCF. SimGCF(III), which uses spatial inversion to restore high-frequency graph embedding signals and also uses frequency signal scaling on this basis, has also achieved significant improvements in performance compared to the current advanced collaborative filtering recommendation models. That is, the performance of SimGCF(I) and SimGCF(III) are both improved compared to the baseline model, and the difference between the two is not much. Therefore, when actually selecting a model to predict the user's next interactive item, either the low-frequency collaborative filtering recommendation model SimGCF(I) or the high-frequency collaborative filtering recommendation model SimGCF(III) can be used.

[0131] For example, see Figure 5 , Figure 5 Schematic diagram of the optimal model parameters of SimGCF(I) on different data sets. Figure 5 The Jacobi function parameter a, Jacobi function parameter b, embedding dimension, L2 norm weight, number of graph convolution layers n, learning rate, and The optimal values ​​of other parameters.

[0132] Example 2

[0133] This embodiment also provides an electronic device comprising a processor and a memory. The memory is configured to store non-transitory computer-readable instructions. The processor is configured to execute the non-transitory computer-readable instructions. When the processor executes the non-transitory computer-readable instructions, the processor can perform one or more steps of the collaborative filtering recommendation method based on a spectral graph neural network described above. The memory and the processor can be interconnected via a bus system and / or other connection mechanisms.

[0134] 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); for example, the central processing unit (CPU) can be an X86 or ARM architecture, etc.

[0135] For example, the memory may include any combination of one or more computer program products, and the computer program product may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and / or cache memory. Non-volatile memory may include, for example, read-only memory (ROM), a hard disk, an erasable programmable read-only memory (EPROM), a portable compact disk read-only memory (CD-ROM), a USB memory, a flash memory, etc. One or more computer program modules may be stored on the computer-readable storage medium, and the processor may execute one or more computer program modules to implement various functions of the electronic device. Various applications and various data, as well as various data used and / or generated by the application, may also be stored in the computer-readable storage medium.

[0136] It should be noted that in the embodiments of the present application, the specific functions and technical effects of the electronic device can be referred to the above description of the collaborative filtering recommendation method based on spectral graph neural network, which will not be repeated here.

[0137] Example 3

[0138] This embodiment further provides a computer-readable storage medium for storing 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 spectral graph neural network described above may be performed.

[0139] 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 Example 2. For example, the relevant description of the storage medium can refer to the corresponding description of the memory in the electronic device of Example 2, and will not be repeated here.

[0140] It should be noted that the storage medium (computer-readable medium) mentioned above in the present application may be a computer-readable signal medium or a non-transitory computer-readable storage medium or any combination of the above two. The non-transitory computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of non-transitory computer-readable storage media may 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.

[0141] In this application, a non-transitory computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. This propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a non-transitory computer-readable storage medium that 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 the computer-readable medium may 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.

[0142] The computer-readable medium may be included in the electronic device, or may exist independently without being incorporated into the electronic device.

[0143] Computer program code for carrying out the operations of the present application may be written in one or more programming languages, or a combination thereof, including, but not limited to, object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may execute entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on the remote computer or server.

[0144] The flow charts and block diagrams in the accompanying drawings illustrate the possible architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present application. In this regard, each box in the flow chart or block diagram can represent a module, program segment or a part of code, and the module, program segment or a part of code includes one or more executable instructions for realizing the prescribed logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented using a dedicated hardware-based system that performs the prescribed function or operation, or can be implemented using a combination of dedicated hardware and computer instructions.

[0145] The units involved in the embodiments described in this application may be implemented by software or hardware, wherein the name of a unit does not, in some cases, constitute a limitation on the unit itself.

[0146] The functions described above herein may be performed, at least in part, by one or more hardware logic components. For example, and without limitation, exemplary types of hardware logic components that may 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), and the like.

[0147] The above description is only a partial embodiment of the present application and an illustration of the technical principles used. Those skilled in the art should understand that the scope of disclosure involved in this application is not limited to the technical solutions formed by the specific combination of the above technical features, but also includes other technical solutions formed by any combination of the above technical features or their equivalents without departing from the above disclosed concepts. For example, the above features can be replaced with (but not limited to) technical features with similar functions disclosed in this application.

[0148] In addition, although adopting specific order to describe each operation, this should not be interpreted as requiring these operations to be performed in the specific order shown or in sequential order. Under certain environment, multitasking and parallel processing may be advantageous. Similarly, although comprising some specific implementation details in the above discussion, these should not be interpreted as limiting the scope of the application. Some features described in the context of separate embodiment can also be implemented in a single embodiment in combination. On the contrary, the various features described in the context of a single embodiment also can be implemented in multiple embodiments individually or in the mode of any suitable subcombination.

[0149] Although the subject matter has been described in language specific to structural features and / or methodological logical acts, it should 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, using spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph, wherein the graph embedding signal includes a low-frequency graph embedding signal and a high-frequency graph embedding signal; Performing spatial flipping on the high-frequency image embedding signal; Performing recommendation prediction based on the low-frequency graph embedding signal and the high-frequency graph embedding signal after spatial flipping, respectively, and training and generating a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model; Using the low-frequency collaborative filtering recommendation model or the high-frequency collaborative filtering recommendation model, predicting the user's next interactive item; The specific steps of using spectral GNN to generate a graph embedding signal corresponding to the user-item interaction graph based on the user-item interaction graph include: Based on the original filter function of the spectral GNN, the frequency signal scaling function is used to scale the original filter function to generate a first filter function. The specific steps are as follows: ； ； in, is the eigenvalue after eigenvalue decomposition of the adjacency matrix of the user-item interaction graph, is the original filter function, is the frequency signal scaling function, is the first filter function, 、 and is the scaling parameter, , Used to control the steepness of the waveform. When , it is used to extract low-frequency signals; when When , it is used to extract high-frequency signals; Used to control the position of the waveform; Used to scale the size of the extracted waveform; Respectively using a monomial basis to approximate the first filter function to train and generate a low-frequency filter function and a high-frequency filter function; Based on the user-item interaction graph, a low-frequency graph embedding signal and a high-frequency graph embedding signal corresponding to the user-item interaction graph are generated using a low-frequency filtering function and a high-frequency filtering function respectively.

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

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

4. The collaborative filtering recommendation method based on spectral graph neural network according to claim 1, characterized in that The specific steps of respectively using a monomial basis to approximate the first filter function to train and generate a low-frequency filter function and a high-frequency filter function also use the following formula: ； ； in, is the high-frequency filter 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, Eigenvalues ​​of the adjacency matrix of the user-item interaction graph after eigenvalue decomposition.

5. The collaborative filtering recommendation method based on spectral graph neural network according to claim 1, characterized in that: The specific steps of generating a low-frequency graph embedding signal and a high-frequency graph embedding signal corresponding to the user-item interaction graph using a low-frequency filter function and a high-frequency filter function respectively based on the user-item interaction graph are as follows: ； ； in, is the normalized adjacency matrix of the user-item interaction graph The eigenvector of is the normalized adjacency matrix The eigenvalues ​​after eigenvalue decomposition, represents the normalized adjacency matrix, represents the embedding signals of users and items at layer 0, represents the low-frequency graph embedding signal, represents the high-frequency graph embedding signal, is the high-frequency filter function, is the low-frequency filter function, is the weight parameter of the low-frequency filter function, is the weight parameter of the high-frequency filter function, and n represents the number of layers of the polynomial basis.

6. The collaborative filtering recommendation method based on spectral graph neural network according to claim 4, characterized in that: The specific step of spatially flipping the high-frequency image embedding signal adopts the following formula: ； is the high-frequency image embedding signal before spatial flipping, It is the high-frequency image embedding signal after spatial flipping.

7. The collaborative filtering recommendation method based on 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 signal and the high-frequency graph embedding signal after spatial flipping, and training and generating a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are as follows: ； in, , For users The low-frequency embedding representation of For the project The low-frequency embedding representation of is the low-frequency graph embedding signal, For predicted users About the project interest score.

8. The collaborative filtering recommendation method based on 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 signal and the high-frequency graph embedding signal after spatial flipping, and training and generating a low-frequency collaborative filtering recommendation model and a high-frequency collaborative filtering recommendation model are as follows: ； in, , For users The high-frequency embedding representation of For the project The high-frequency embedding representation of is the high-frequency image embedding signal before spatial flipping, is the high-frequency image embedding signal after spatial flipping, For predicted users About the project interest score.

9. An electronic device, characterized in that: include: processor; a memory having stored thereon one or more computer program instructions executed on the processor; Wherein, when the processor runs the computer program instructions, it executes the collaborative filtering recommendation method based on spectral graph neural network described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that Computer instructions are stored thereon, and when the computer instructions are executed by the processor, the steps of the collaborative filtering recommendation method based on spectral graph neural network described in any one of claims 1 to 8 are executed.

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