Social network popularity prediction method and system based on high-order nonlinear dependence

Abstract

The application discloses a social network popularity prediction method based on high-order nonlinear dependence, comprising the following steps: obtaining topic-related data and preprocessing the topic-related data, wherein the topic-related data comprises topic ranking and post information; inputting the preprocessed data into a trained popularity prediction model to output a topic popularity prediction result; wherein the training of the popularity prediction model comprises the following steps: obtaining topic-related data within a set time length and preprocessing the topic-related data; calculating high-order polynomial features of a preprocessed historical sequence by using Volterra features to generate multi-order tensorization interaction features; setting a learnable discrete Volterra coefficient matrix, independently performing polynomial integral modeling on each order of the tensorization interaction feature channel, projecting the linear aggregation of the outputs of each channel to the original feature dimension space of an input time sequence to obtain the topic popularity prediction result.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of social network analysis and complex system modeling, and particularly relates to a social network popularity prediction method and system based on high-order nonlinear dependence. BACKGROUND

[0002] Topic popularity prediction is an important research direction in social network analysis and computational social science. Existing research has made extensive studies on the popularity prediction problem in social networks and has achieved good results, but there are still many deficiencies.

[0003] Firstly, due to the large scale and complex structure of social networks, in the topic popularity prediction problem, a topic is usually related to a large number of posts, and its popularity is affected by a large number of post information. Existing research usually focuses on the popularity evolution process of a single post information in the social network, but cannot analyze the propagation of each related post one by one to predict the popularity of the topic.

[0004] Secondly, in social networks, the popularity of a topic is not only affected by post information, but also follows the natural evolution law of topics in social networks. External incentives and natural evolution are coupled, which makes it more difficult to model and predict the popularity of topics in social networks. Existing methods are difficult to model both factors, which hinders the further improvement of the accuracy of popularity prediction.

[0005] Finally, deep learning is the dominant method for modeling such complex time series data. However, current deep learning models usually perform as a black box, composed of linear and nonlinear functions, which cannot explicitly capture the inherent dynamic structure in real-world nonlinear systems, limiting their interpretability.

[0006] In summary, the main problems of existing models in topic popularity prediction include the large number of posts affecting the popularity of topics, and the popularity change is affected by many factors. These problems limit the effectiveness and interpretability of the model in practical applications, affecting the understanding and trust of users on the prediction results of the model. SUMMARY

[0007] In order to solve the problems that the existing model is limited by the number of posts affecting the popularity of the topic and the popularity change is affected by many factors in the prediction of the popularity of the topic, the application provides a social network popularity prediction method based on high-order nonlinear dependence, which is equivalent to a complex dynamic system by proposing a time series prediction model, and the macroscopic characteristics of the social network are realized by using the historical sampling data. Under the guidance of this idea, the prediction of the popularity of the topic in the social network is regarded as an output prediction problem of a complex dynamic system under external excitation, and a polynomial integral network is used for modeling, so as to realize the prediction of the popularity of the topic and effectively improve the prediction accuracy.

[0008] According to an aspect of the application, a social network popularity prediction method based on high-order nonlinear dependence is provided, comprising:

[0009] Obtain topic-related data and preprocess, the topic-related data including topic ranking and post information;

[0010] The preprocessed data is input into the trained popularity prediction model, and the topic popularity prediction result is output; wherein the training of the popularity prediction model comprises:

[0011] Obtain the topic-related data within a set time length and preprocess;

[0012] Calculate the high-order polynomial features of the preprocessed historical sequence using Volterra features, and generate multi-order tensor interaction features;

[0013] Set a learnable discrete Volterra coefficient matrix, independently model each order of tensor interaction feature channel with a polynomial integral, and project the linear aggregation of the output of each channel to the original feature dimension space of the input time sequence to obtain the topic popularity prediction result.

[0014] As a further technical solution, setting a learnable discrete Volterra coefficient matrix, independently modeling each order of feature channel with a polynomial integral, comprises:

[0015] The output of channel j is calculated as: wherein is a constant term, is a learnable coefficient matrix, is a Volterra feature, representing an n-order tensor interaction feature.

[0016] As a further technical solution, after obtaining the output of each channel, it further comprises:

[0017] The outputs of each channel are spliced together using a linear transformation layer, and the spliced output is projected to the original feature dimension space of the input time sequence:​

[0018] ,

[0019] where W and b are learnable weight matrix and bias, represents the prediction result of the original space, represents the vector formed by splicing all channel outputs at time t.

[0020] As a further technical solution, the Volterra characteristic is used to calculate the high-order polynomial features of the historical sequence, including:

[0021] The normalization operation is performed at each time point in the sequence respectively;

[0022] The normalized sequence is flattened into a vector, and the i-th Kronecker product operation is used to generate , and then the Volterra characteristic is obtained.

[0023] As a further technical solution, the preprocessing includes:

[0024] The topic-related data obtained is sequenced;

[0025] The sequenced data is cleaned, and the abnormal values and missing values are processed and normalized.

[0026] According to an aspect of the present application, a social network popularity prediction system based on high-order nonlinear dependence is provided, comprising:

[0027] A data preprocessing module is configured to obtain topic-related data and perform preprocessing, wherein the topic-related data includes topic ranking and post information;

[0028] A popularity prediction module is configured to input the preprocessed data into a trained popularity prediction model and output a topic popularity prediction result, wherein the training of the popularity prediction module includes:

[0029] Obtain topic-related data within a set time period and perform preprocessing;

[0030] Use the Volterra characteristic to calculate the high-order polynomial features of the preprocessed historical sequence, and generate multi-order tensor interaction features;

[0031] Set a learnable discrete Volterra coefficient matrix, model the polynomial integral of each order of tensor interaction feature channel independently, project the linear aggregation of each channel output to the original feature dimension space of the input time sequence, and obtain the topic popularity prediction result.

[0032] As a further technical solution, the popularity prediction module is further configured to execute the following instructions:

[0033] The output of the channel j The calculation process is as follows: Wherein is a constant term, is a learnable coefficient matrix, is a Volterra feature, representing an n-order tensorized interaction feature.

[0034] As a further technical solution, the popularity prediction module is further used to execute the following instructions:

[0035] The outputs of the respective channels are spliced together using a linear transformation layer, and the spliced outputs are projected to the original feature dimension space of the input time sequence:

[0036] ,

[0037] Wherein, W and b are learnable weight matrix and bias, represents the prediction result of the original space, represents a vector formed by splicing the outputs of all channels at time t.

[0038] As a further technical solution, the popularity prediction module is further used to execute the following instructions:

[0039] The normalization operation is performed at each time point in the sequence respectively;

[0040] The normalized sequence is flattened into a vector, and the i-th Kronecker product operation is used to generate , and then the Volterra feature is obtained.

[0041] According to an aspect of the present application, a non-transitory computer readable storage medium is provided, which stores computer instructions for executing the social network popularity prediction method based on high-order nonlinear dependence.

[0042] Compared with the prior art, the present application has the following advantages:

[0043] (1) Accurate prediction of topic popularity: the model of the present application can comprehensively consider the content features and time sequence data of related posts, i.e. the information of forwarding and commenting quantity, decouple the independent influence of natural evolution and external incentive, and realize high-precision prediction of topic popularity by effectively using the related information.

[0044] (2) Model interpretability: This invention can not only make accurate predictions, but also intuitively express the relationships between variables. The model parameters can reflect the specific contribution and mutual influence of each variable to the prediction results, help users understand the internal mechanism of the model, and conduct detailed impact analysis on variables, quantifying the degree of influence of different variables on the predicted popularity of the topic.

[0045] (3) Proposal and Validation of the Prediction Model: This invention utilizes the variable relationships and influence analysis provided by the model to formulate a specific prediction scheme. By using historical relevant posting information and topic ranking data from the Weibo platform, the effectiveness of the model in predicting topic popularity is verified. The actual results are compared with the predicted results, for example... Figure 5 As shown. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart illustrating the social network popularity prediction method based on higher-order nonlinear dependencies provided in an embodiment of the present invention.

[0048] Figure 2 This is a schematic diagram of the training process of the popularity prediction model provided in an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of the algorithm for the popularity prediction model provided in an embodiment of the present invention.

[0050] Figure 4 This is a structural block diagram of the popularity prediction model provided in an embodiment of the present invention.

[0051] Figure 5 This is a comparison chart of the predicted results and the actual results provided in the embodiments of the present invention. Detailed Implementation

[0052] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0053] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the protection scope of the present application. In addition, the technical features in each embodiment or in a single embodiment provided by the present application can be combined with each other at will to form new technical solutions, and the combination is not restricted by the sequence of steps and / or the mode of structural composition, but should be based on the fact that those skilled in the art can realize it. When the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist, and is not within the protection scope required by the present application.

[0054] The main problems of the existing model in topic popularity prediction include that the number of posts affecting the topic popularity is huge, and the popularity change is affected by many factors, which limits the effectiveness and interpretability of the model in actual application, and affects the understanding and trust of users on the prediction results of the model. Therefore, the present application provides a social network popularity prediction method based on high-order nonlinear dependence, which regards the topic popularity prediction in a social network as an output prediction problem of a complex dynamic system under external excitation, and uses a polynomial integral network for modeling, realizes accurate prediction of the evolution law of topic popularity under the action of related posts, and effectively improves the prediction accuracy of topic popularity.

[0055] The social network popularity prediction method based on high-order nonlinear dependence provided by the embodiments of the present application, as shown in Figure 1 Firstly, topic related data including topic ranking and post information is acquired and preprocessed, and then the preprocessed data is input into the trained popularity prediction model to output topic popularity prediction results.

[0056] The training of the popularity prediction model includes:

[0057] Data preprocessing: acquiring topic related data within a set time length and preprocessing the topic related data;

[0058] Multi-dimensional feature construction: high-order polynomial features of the preprocessed historical sequence are calculated by using Volterra features to generate multi-order tensor interaction features;

[0059] Multi-channel linear transformation: a learnable discrete Volterra coefficient matrix is set, polynomial integral modeling is independently performed on each order of tensorization interaction feature channel, and the outputs of each channel are linearly aggregated and projected to the original feature dimension space of the input time sequence to obtain the topic popularity prediction result.

[0060] The popularity prediction model provided by the application aims to accurately predict the future popularity of topics and related post information, intuitively express variable relationships, perform detailed variable influence analysis, and provide effective system optimization strategies, thereby improving the accuracy of prediction and helping various organizations and individuals better understand social network dynamics, thereby making more intelligent choices in information dissemination, decision making, and resource allocation.

[0061] First, as shown in Figure 2 and 3 indicate that after the topic-related data is preprocessed, the topic-related data is input into the popularity prediction model, the topic-related data including the number of reposts, the number of comments, the number of likes, whether it is a repost, the sentiment score, and the topic ranking. The popularity prediction model processes the topic-related data to predict the topic popularity in the future period of time and the important parameters such as the number of reposts, the number of likes, and other post information related to the future topic that we need.

[0062] Further, the topic-related data is serialized, for example, the topic ranking is serialized to obtain where t is the length of the observed historical data, is the ranking of the topic popularity at time t. For another example, other post information is serialized to obtain where t is the length of the observed historical data, d is the dimension of each observation at time t, represents a d-dimensional vector composed of each observation at time t, and R represents the real number field.

[0063] It should be noted that after the topic-related data is serialized, each feature sequence is a sequence with a length of T and a dimension of 1, and has a shape of [T, 1]; D feature sequences are spliced into a multi-dimensional feature sequence to obtain a multi-dimensional feature sequence with a shape of [T, D].

[0064] As a preferred, the data preprocessing cleans, processes outliers and missing values of the input data set, ensures data quality, normalizes the data, makes the input data have more stable gradients, and reduces the magnitude difference between features, thereby improving the accuracy of the model.

[0065] Next, in the multidimensional feature construction step, this embodiment of the invention utilizes Volterra features to calculate the high-order polynomial features of the historical sequence (i.e., the concatenated multidimensional feature sequence). For the input historical sequence, a normalization operation is performed on each time point t in the sequence from 0 to h-1, such that... ,here and These represent the mean and standard deviation used for data normalization, respectively. Next, we will discuss the normalized series. Flattened into a vector For i from 1 to k, let This step involves calculating the Kronecker product, where... This represents the Kronecker product operation, where `i` indicates performing the Kronecker product `i` times. Ultimately, it returns the Volterra feature. It represents the tensorized interaction of past states from order 1 to order k.

[0066] Then, in the multi-channel linear transformation step, for the already calculated multidimensional features... Each channel k independently models the nonlinear interactions and memory effects of the system. A learnable discrete Wolterra coefficient matrix is ​​set within each channel. To capture non-linear relationships.

[0067] Specifically, for the output of channel j The calculation process is as follows: ,in It is a constant term. It is a learnable coefficient matrix. This is a Volterra feature. After obtaining the output of each channel, a multi-channel linear transform layer is used to concatenate them together, and the output is projected back onto the original space: , ,in It is the number of channels. It is the dimension of the target time series. Indicates the first The output vectors of each channel at time t and , This represents the vector formed by concatenating the outputs of all channels at time t. and It consists of learnable weight matrices and biases.

[0068] Preferably, the multi-channel linear transformation layer uses polynomial approximation to provide a nonlinear representation of the latent function. Therefore, the method of the present invention does not depend on the activation function, does not require the design of a complex neural network structure, and only requires a simple linear layer to predict the coefficients of higher-order polynomials.

[0069] As preferred, the Volterra feature construction describes the matrix form polynomial expansion of the corresponding nonlinear dynamic system through the discrete Volterra coefficient matrix, thereby converting the nonlinear problem of time series analysis into a linear problem of learning polynomial coefficients, improving the model interpretability, and the multi-channel linear transformation provides a nonlinear representation for the potential function using polynomial approximation without activation function, and only through linear layer learning high-order polynomial coefficients.

[0070] As preferred, the popularity prediction effectively captures the complex spatio-temporal nonlinear interaction in the dynamic system by integrating high-order polynomials and time integration into the neural network, avoids the black box effect brought by traditional methods, improves the model interpretability, and facilitates user understanding of the working principle of the model.

[0071] On this structure, the present application calculates the discrete Volterra coefficient matrix through polynomial expansion, converts nonlinear time series modeling into linear polynomial coefficient learning, and then uses a multi-channel linear layer to predict the discrete Volterra coefficient matrix to obtain an accurate prediction of the topic popularity at the future time. Experimental results show that the method is effective. Through the prediction of the topic popularity, the present application can improve the dynamic understanding of the social network, help various organizations and individuals analyze the propagation trend of the topic in the social network, assist users in formulating a propagation strategy in advance, and optimize resource allocation.

[0072] The implementation basis of each embodiment of the present application is the programmed processing of a device with processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the present application are packaged into various modules. Based on this actual situation, on the basis of the above-mentioned embodiments, the embodiments of the present application provide a social network popularity prediction system based on high-order nonlinear dependence, which is used to execute the social network popularity prediction method based on high-order nonlinear dependence in the above-mentioned method embodiments.

[0073] As Figure 4 shown, the system comprises a data preprocessing module for acquiring and preprocessing topic related data, the topic related data comprising topic ranking and post information; a popularity prediction module for inputting the preprocessed data into a trained popularity prediction model and outputting a topic popularity prediction result, the training of the popularity prediction module comprising: acquiring and preprocessing topic related data within a set time length; calculating high-order polynomial features of the preprocessed historical sequence using Volterra feature, generating multi-order tensor interaction features; setting a learnable discrete Volterra coefficient matrix, independently modeling each order of tensor interaction feature channel through polynomial integration, linearly aggregating the outputs of each channel and projecting them to the original feature dimension space of the input time sequence to obtain the topic popularity prediction result.

[0074] The social network popularity prediction system based on high-order nonlinear dependence provided in the embodiment of the application faces the problems that existing models are limited in topic popularity prediction and the number of posts affecting topic popularity and the popularity change is affected by multiple factors, adopts the foregoing modules, proposes a time series prediction model, equivalent to a complex dynamic system, and uses historical sampling data to realize the characterization of the macroscopic characteristics of the social network. Under the guidance of this idea, the topic popularity prediction in the social network is regarded as an output prediction problem of a complex dynamic system under external excitation, and a polynomial integral network is used for modeling, so that the popularity prediction of the topic is realized, and the prediction accuracy is effectively improved.

[0075] It should be noted that the system embodiments provided by the application are used to implement the methods in the method embodiments, and are also used to implement the methods in other method embodiments provided by the application. The difference is only that the corresponding function modules are set, and the principle is basically the same as that of the above-mentioned system embodiments provided by the application. As long as the person skilled in the art improves the modules in the above-mentioned system embodiments on the basis of the above-mentioned system embodiments, refers to the specific technical solutions in other method embodiments, obtains the corresponding technical means by combining technical features, and the technical solutions composed of these technical means, as long as the technical solutions have practicality, the corresponding system class embodiments are obtained, which are used to implement the methods in other method class embodiments. For example:

[0076] Based on the content of the above-mentioned system embodiments, as a preferred embodiment, the social network popularity prediction system based on high-order nonlinear dependence provided in the embodiment of the application, the data preprocessing module is further used to execute the following instructions:

[0077] The topic related data is sequenced, and the sequenced data is cleaned, processed for abnormal values, processed for missing values, and normalized.

[0078] Based on the content of the above-mentioned system embodiments, as a preferred embodiment, the social network popularity prediction system based on high-order nonlinear dependence provided in the embodiment of the application, the popularity prediction module further comprises:

[0079] The multi-dimensional feature construction submodule calculates high-order polynomial features from historical sequences, and represents the multi-dimensional features as These features represent the tensorization interaction of the past state from the first order to the order, which can capture the complex dynamic information of different orders in the time series.

[0080] Based on the content of the above-mentioned system embodiments, as a preferred embodiment, the social network popularity prediction system based on high-order nonlinear dependence provided in the embodiment of the application, the popularity prediction module further comprises:

[0081] Multi-channel linear transformation sub-module: setting a learnable discrete coefficient matrix Polynomial integral modeling is independently performed for each channel, thereby effectively capturing the nonlinear interaction and memory effect of the system. The outputs of the independent modeling of each channel are linearly aggregated and projected to the original space, thereby realizing fusion of information of different channels, capturing complex nonlinear dynamics and long-term dependence in the time series data, obtaining a prediction result, and improving the modeling and prediction ability of the model on the time series data.

[0082] Based on the same inventive concept as the foregoing embodiments, the embodiments of the present application also provide a non-transitory computer-readable storage medium storing computer instructions, which cause the computer to perform the social network popularity prediction method based on high-order nonlinear dependence.

[0083] In summary, the present application discloses a social network popularity prediction method based on high-order nonlinear dependence, which realizes prediction of popularity in a future period of time through a trained popularity prediction model. The training of the model includes: first, preprocessing topic-related data, serializing topic rankings and post information (such as the number of reposts, the number of comments, etc.), and completing data cleaning, normalization, etc.; then, calculating high-order polynomial features of the historical sequence through a multi-dimensional feature construction module, and capturing 1st to kth tensorization dynamic interaction using Volterra features; finally, setting a learnable discrete coefficient matrix through a multi-channel linear transformation module, modeling the polynomial integral for each channel independently, projecting to the original space after fusing multi-channel information to generate a prediction result, and completing the training of the popularity prediction model. The present application constructs a neural network model of a complex dynamic system with multiple modules in cooperation, so that the model can effectively decouple the natural evolution of topic popularity and the influence of external incentives, realize high-precision prediction of topic popularity, and provide a feature representation with high precision and interpretability for topic propagation trend prediction in social networks, which can be used in scenarios such as social network dynamic analysis and propagation strategy optimization.

[0084] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent substitutions for part or all of the technical features; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present application.

Claims

1. A social network popularity prediction method based on high-order nonlinear dependence, characterized in that, include: Acquire topic-related data within a set time period and preprocess it. The topic-related data includes topic rankings and posting information. The preprocessed data is input into the trained popularity prediction model, which outputs the topic popularity prediction results for a preset future time period; wherein, the training of the popularity prediction model includes: Acquire topic-related data within a set time period and preprocess it; Using Volterra features, high-order polynomial features of the preprocessed historical sequence are calculated to generate multi-order tensorized interaction features, including: for each time point t in the preprocessed historical sequence from arrive Perform a normalization operation to make ,in and Let these represent the mean and standard deviation used for data normalization, respectively; the normalized series... Flattened into a vector Then perform i Kronecker product iterations to return the Volterra features. , representing the tensorized interaction of past states from order 1 to order k, where This represents the Kronecker product operation; We set up a learnable discrete Volterra coefficient matrix, independently modeled the interaction feature channels of each order of tensor quantization using polynomial integrals, and projected the linearly aggregated outputs of each channel onto the original feature dimension space of the input time series to obtain the topic popularity prediction results.

2. The social network popularity prediction method based on high-order nonlinear dependence according to claim 1, characterized in that, A learnable discrete Volterra coefficient matrix is ​​set up, and multinomial integral modeling is performed independently for each order of tensor-quantized interaction feature channel, including: For channels Output The calculation process is as follows: ,in It is a constant term. It is a learnable coefficient matrix. It is a Volterra characteristic, indicating The interaction characteristics of tensor quantization.

3. The social network popularity prediction method based on high-order nonlinear dependence according to claim 2, characterized in that, After obtaining the output of each channel, it also includes: A linear transformation layer is used to concatenate the outputs of each channel, and the concatenated output is projected onto the original feature dimension space of the input time series: ， in, b are the learnable weight matrix and bias, This represents the predicted result of the original space. Indicates the output of all channels at time [time]. The vector formed by splicing.

4. The social network popularity prediction method based on high-order nonlinear dependence according to claim 1, characterized in that, Calculating high-order polynomial features of the preprocessed historical sequence using Volterra features, including: Perform normalization at each time point in the sequence; The normalized sequence is flattened into a vector, and then generated by i Kronecker product operations. Thus, the Volterra features were obtained. .

5. The social network popularity prediction method based on high-order nonlinear dependence according to claim 1, characterized in that, The preprocessing includes: The acquired topic-related data is serialized; The serialized data is cleaned, outliers and missing values ​​are handled, and normalization is performed.

6. A social network popularity prediction system based on high-order nonlinear dependencies, characterized in that, include: The data preprocessing module is used to acquire and preprocess topic-related data, including topic rankings and posting information. The popularity prediction module is used to input preprocessed data into the trained popularity prediction model and output the topic popularity prediction result. The training of the popularity prediction module includes: Acquire topic-related data within a set time period and preprocess it; Using Volterra features, high-order polynomial features of the preprocessed historical sequence are calculated to generate multi-order tensorized interaction features, including: for each time point t in the preprocessed historical sequence from arrive Perform a normalization operation to make ,in and Let these represent the mean and standard deviation used for data normalization, respectively; the normalized series... Flattened into a vector Then perform i Kronecker product iterations to return the Volterra features. , representing the tensorized interaction of past states from order 1 to order k, where This represents the Kronecker product operation; We set up a learnable discrete Volterra coefficient matrix, independently modeled the interaction feature channels of each order of tensor quantization using polynomial integrals, and projected the linearly aggregated outputs of each channel onto the original feature dimension space of the input time series to obtain the topic popularity prediction results.

7. The social network popularity prediction system based on high-order nonlinear dependence according to claim 6, characterized in that, The popularity prediction module is also used to execute the following instructions: For channels Output The calculation process is as follows: ,in It is a constant term. It is a learnable coefficient matrix. It is a Volterra characteristic, indicating The interaction characteristics of tensor quantization.

8. The social network popularity prediction system based on high-order nonlinear dependence according to claim 7, characterized in that, The popularity prediction module is also used to execute the following instructions: A linear transformation layer is used to concatenate the outputs of each channel, and the concatenated output is projected onto the original feature dimension space of the input time series: ， in, and It consists of learnable weight matrices and biases. This represents the predicted result of the original space. This indicates the output after aggregating all channels.

9. The social network popularity prediction system based on high-order nonlinear dependence according to claim 6, characterized in that, The popularity prediction module is also used to execute the following instructions: Perform normalization at each time point in the sequence; The normalized sequence is flattened into a vector, and then generated by i Kronecker product operations. Thus, the Volterra features were obtained. .

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the social network popularity prediction method based on higher-order nonlinear dependencies as described in any one of claims 1 to 5.

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