User preference trend recommendation method and system based on causal dependency relationship

Abstract

The invention discloses a user preference trend recommendation method and system based on a causal dependency relationship. A user preference trend is taken as a modeling core, a long-term signal is enhanced through frequency domain analysis, preference granularity is balanced through multi-scale fusion, and a community detection and causal intervention mechanism is introduced to eliminate trend deviation, so that the technical problem that a stable long-term interest mode, trend interference and multi-scale interest change are difficult to capture in the prior art is solved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of preference trend recommendation, in particular to a user preference trend recommendation method and system based on causal dependency. BACKGROUND

[0002] With the rapid development of e-commerce, social media and content platforms, personalized recommendation systems have become one of the core technologies to improve user experience and information matching efficiency. Especially the sequential recommendation system (SR), by modeling the time sequence characteristics of user interaction behavior, can more accurately predict the user's future interest and behavior trend, so it has been widely used in platforms such as Amazon, Yelp, Netflix, etc. Traditional SR models are mostly based on the idea of correlation learning, using recurrent neural networks or self-attention mechanisms to capture sequence dependencies. Although this kind of method can better model user short-term preferences, it still has limitations when facing the following problems: 1. Data sparsity: limited user-item interaction samples make it difficult for the model to capture stable long-term interest patterns; 2. Trend interference: external factors such as manifold trends, price fluctuations and platform exposure mechanisms will interfere with the user's true preferences, and the model is prone to learn false correlation information, i.e. pseudo-correlation; 3. Multi-scale interest changes: user interests have dynamic changes at different time scales, including both long-term stable preferences and short-term context-driven temporary interests. SUMMARY

[0003] The application provides a user preference trend recommendation method and system based on causal dependency, which solves the technical problems of difficulty in capturing stable long-term interest patterns, trend interference and multi-scale interest changes in the prior art.

[0004] The application provides a user preference trend recommendation method based on causal dependency, comprising: performing frequency domain filtering on the user interaction sequence X to obtain a frequency domain filtered user behavior ; dividing the user behavior into global long-term preference representation, local long-term preference representation and short-term preference representation according to different time scales, and fusing the global long-term preference representation, the local long-term preference representation and the short-term preference representation to obtain a unified user preference representation ; performing community detection on the constructed item-item graph to obtain a trend cluster of the items ; through the expression The attention weight matrix is ​​calculated. ;in, and For a two-layer linear mapping, the items are embedded in the representation. With trend clusters Linear transformation into a matrix, For scaling parameters; Through expression The calculated trend preference enhancement representation ; Through expressions Calculate the user preference score ;in, For activation functions; User preferences The item embedding representation The trend cluster The fusion is performed to obtain the fused representation. ; Through expression The degree of personalized trend matching between user u and target item i in the current community c is calculated. ;in, It is a learnable linear transformation matrix. It is a trainable bias; Through expressions Calculate the trend consistency score ; Through expressions Calculate user preference trends .

[0005] Specifically, the frequency domain filtering of the user interaction sequence X is performed to obtain the frequency domain filtered user behavior. ,include: Perform a Fast Fourier Transform on the user interaction sequence X to obtain the complex spectrum F; The complex spectrum F is low-pass filtered to obtain the low-frequency component in the frequency domain. ; For the low-frequency components in the frequency domain Perform an inverse fast Fourier transform to obtain the low-frequency components in the time domain. ; Subtract the time-domain low-frequency component from the user interaction sequence X. High-frequency components are obtained. ; Through expressions Calculate the fused features ;in, These are learnable parameters; The fused features Regularization and normalization are performed, and residual connections are introduced to obtain the final user behavior. .

[0006] Specifically, the user behavior is analyzed according to different time scales. The user preference representation is divided into global long-term preference representation, local long-term preference representation, and short-term preference representation. These three representations are then merged to obtain a unified user preference representation. ,include: Through expressions The key components of global long-term preferences were calculated. ;in, It is a one-dimensional convolution operation. It is batch normalization; The key components of global long-term preferences Input a Transformer encoder to explicitly capture the interactions between positional embeddings in the global action sequence, resulting in a global long-term preference representation. ; Regarding the user behavior Perform sliding window filtering to uncover highly relevant preferences within a local area. ; Preference for all time locations Perform average pooling to obtain the local long-term preference representation. ; From the user behavior The embedding vectors of the most recent N interactions are extracted and average pooled to obtain the short-term preference representation. ; The global long-term preference representation The local long-term preference representation and the aforementioned short-term preference representation By performing weighted fusion, a unified representation of user preferences is obtained. .

[0007] Specifically, community detection is performed on the constructed item-item graph to obtain trend clusters of items. ,include: Community detection is performed on the constructed item-item graph using the Leiden algorithm to obtain trend clusters of items. .

[0008] Specifically, it also includes: The formula is solved iteratively using the Sinkhorn-Knopp algorithm. The optimal transfer matrix is ​​obtained; where, This represents the Euclidean distance between trend clusters. is an entropy regularization parameter, is the trend strength of the i-th item in the last time slice, and the weight assigned to the current j-th item, is the optimal transmission matrix; The generalized trend representation fused with multi-time slice information is recursively interpolated by accumulating the optimal transmission matrix layer by layer ; The attention weight matrix is calculated by the expression , comprising: The generalized attention weight matrix is calculated by the expression ; The trend preference enhancement representation is calculated by the expression , comprising: The generalized trend preference enhancement representation is calculated by the expression ; The user preference score is calculated by the expression , comprising: The generalized user preference score is calculated by the expression ; The user preference trend is calculated by the expression , comprising: The corrected user preference trend is calculated by the expression .

[0009] The application also provides a user preference trend recommendation system based on causal dependency, comprising: A frequency domain filtering module is configured to perform frequency domain filtering on a user interaction sequence X to obtain a frequency domain filtered user behavior ; A multi-scale user preference analysis module is configured to divide the user behavior into a global long-term preference representation, a local long-term preference representation and a short-term preference representation according to different time scales, and fuse the global long-term preference representation, the local long-term preference representation and the short-term preference representation to obtain a unified user preference representation ; A community detection module is configured to perform community detection on the constructed item-item graph to obtain a trend cluster of items ; An attention weight matrix calculation module is configured to calculate an attention weight matrix The attention weight matrix is calculated ; wherein, and is a two-layer linear mapping that embeds the item representation into the trend cluster is a linear transformation into a matrix, is a scaling parameter; The trend preference augmented representation computing module is configured to calculate the trend preference augmented representation ; ; The user preference score computing module is configured to calculate the user preference score ; wherein, is an activation function; The fusion module is configured to fuse the user preference representation , the item embedding representation , and the trend cluster to obtain a fused representation ; The personalized trend matching degree computing module is configured to calculate the personalized trend matching degree of the target item i in the current community c for the user u ; wherein, is a learnable linear transformation matrix, is a trainable bias; The trend consistency score computing module is configured to calculate the trend consistency score ; The user preference trend recommendation module is configured to calculate the user preference trend .

[0010] Specifically, the frequency domain filtering module comprises: A fast Fourier transform submodule is configured to perform fast Fourier transform on the user interaction sequence X to obtain a complex frequency spectrum F; A low-pass filtering submodule is configured to perform low-pass filtering on the complex frequency spectrum F to obtain a frequency domain low-frequency component ; An inverse fast Fourier transform submodule is configured to perform inverse fast Fourier transform on the frequency domain low-frequency component to obtain a time domain low-frequency component ; A high-frequency component obtaining submodule is configured to subtract the time domain low-frequency component from the user interaction sequence X to obtain a high-frequency component ;​​​​ The feature fusion submodule is used to fuse features via expressions. Calculate the fused features ;in, These are learnable parameters; The end-user behavior acquisition submodule is used to process the fused features. Regularization and normalization are performed, and residual connections are introduced to obtain the final user behavior. .

[0011] Specifically, the multi-scale user preference analysis module includes: The global long-term preference key component acquisition submodule is used to obtain key components through expressions. The key components of global long-term preferences were calculated. ;in, It is a one-dimensional convolution operation. It is batch normalization; The global long-term preference representation acquisition submodule is used to obtain the key components of the global long-term preference. Input a Transformer encoder to explicitly capture the interactions between positional embeddings in the global action sequence, resulting in a global long-term preference representation. ; The filtering submodule is used to filter the user behavior. Perform sliding window filtering to uncover highly relevant preferences within a local area. ; The local long-term preference representation obtains a submodule for preferences across all time locations. Perform average pooling to obtain the local long-term preference representation. ; Short-term preference representation acquisition submodule, used to obtain from the user behavior The embedding vectors of the most recent N interactions are extracted and average pooled to obtain the short-term preference representation. ; The user preference representation weighted fusion submodule is used to process the global long-term preference representation. The local long-term preference representation and the aforementioned short-term preference representation By performing weighted fusion, a unified representation of user preferences is obtained. .

[0012] Specifically, the community detection module is used to perform community detection on the constructed item-item graph using the Leiden algorithm to obtain trend clusters of items. .

[0013] Specifically, it also includes: The optimal transfer matrix acquisition module is used to iteratively solve the formula using the Sinkhorn-Knopp algorithm. The optimal transfer matrix is ​​obtained; where, This represents the Euclidean distance between trend clusters. It is the entropy regularization parameter. It represents the trend strength of the i-th item in the previous time slice, and the weight assigned to the j-th item in the current time slice. It is the optimal transfer matrix; The generalized trend representation generation module is used to recursively interpolate and generate a generalized trend representation that fuses information from multiple time slices by accumulating the optimal transfer matrix layer by layer. ; The attention weight matrix calculation module is specifically used to calculate the attention weight matrix using an expression. The generalized attention weight matrix is ​​calculated. ; The trend preference enhancement representation calculation module is specifically used to calculate the trend preference through an expression. The generalized trend preference enhancement representation is calculated. ; The user preference score calculation module is specifically used to calculate the user preference score using an expression. Calculate the generalized user preference score ; The user preference trend recommendation module is specifically used to recommend users based on expressions. The corrected user preference trend was calculated. .

[0014] One or more technical solutions provided in this invention have at least the following technical effects or advantages: 1. Taking user preference trends as the core of modeling, this approach enhances long-term signals through frequency domain analysis, balances preference granularity through multi-scale fusion, and introduces community detection and causal intervention mechanisms to eliminate trend bias. This addresses the technical challenges of capturing stable long-term interest patterns, trend interference, and multi-scale interest changes in existing technologies. Specifically, frequency domain filtering decomposes the time-domain signal into frequency-domain components, clearly separating global trends from low-frequency components and fine-grained changes from high-frequency components. Multi-scale user preferences first categorize user historical interaction sequences into three representation strategies based on different time scales: global long-term preferences, local long-term preferences, and short-term preferences. Subsequently, an adaptive fusion mechanism is designed to generate a unified user preference representation, thus more comprehensively describing user behavioral motivations and preference expressions. By introducing causal intervention and trend preference mechanisms, the approach more effectively captures users' true intentions and significantly mitigates the problem of historical preference misleading due to trend drift, thereby improving the accuracy and robustness of recommendations.

[0015] 2. By introducing the Fast Fourier Transform (FFT) into user behavior sequence modeling, low-pass filtering is used to extract long-term stable preferences, while high-pass filtering suppresses short-term noise, achieving interest separation at the signal level. This strategy effectively enhances the expressive power of long-term trends and alleviates the preference drift problem caused by sparse user interactions. Simultaneously, due to the low computational complexity of FFT and IFFT (Inverse Fast Fourier Transform), the stability of the model can be improved without increasing the system burden. Therefore, this invention achieves the advantages of more complete long-term preference expression, stronger noise resistance, and lower computational cost while maintaining structural simplicity.

[0016] 3. Based on the temporal characteristics of user behavior, this invention constructs a global long-term preference (M) model. GL Local long-term preference (M) LL ) and short-term preferences (M S A three-layer structure is used, and dynamic fusion is achieved through adaptive weights (α, β, γ). Among these, the global long-term preference... It models the complete historical sequence of user behavior, reflecting users' overall preferences for specific types, themes, or items of content. This is achieved through designing localized long-term preferences. This represents a user's sustained preference tendencies within a specific time window. Short-term preferences... It is represented by the user's most recent N interactions, indicating the user's recent preference tendencies. This design can automatically balance the influence of preferences at each level according to the behavioral characteristics of different users, avoiding the adaptation problems caused by manually setting windows, and capturing both global trends and immediate intentions at the same time. Therefore, it has the technical advantages of strong multi-scale adaptability, more accurate characterization of interest evolution, and more stable recommendation results.

[0017] 4. This invention innovatively introduces a community detection and causal intervention mechanism (do-operator). First, an item-item graph is constructed for each time slice. By dividing the item-item graph into communities, potential trend variables are constructed. Furthermore, this invention establishes a decision-making mechanism based on a causal inference graph and a structural causal model, clearly characterizing the causal dependencies between user historical behavior, candidate items, trend variables, and recommendation results. By applying a do-operator operation to this causal structure, spurious correlations caused by trend variables can be eliminated, making the prediction process closer to the true user interest generation mechanism.

[0018] 5. During the inference phase, the minimum cost matrix is ​​found in each time slice, thus obtaining the optimal transfer matrix. By accumulating the transfer matrices layer by layer, a trend evolution path from the initial time slice to the current time slice is constructed, thereby capturing user group behavior trends in a structured manner. Attached Figure Description

[0019] Figure 1 A schematic diagram of a causal graph in an embodiment of the present application; Figure 2 A schematic diagram of a principle of a user preference trend recommendation method based on causal dependency provided in an embodiment of the present application; Figure 3 A flowchart of frequency domain filtering in a user preference trend recommendation method based on causal dependency provided in an embodiment of the present application; Figure 4 A flowchart of multi-scale user preference analysis in a user preference trend recommendation method based on causal dependency provided in an embodiment of the present application; Figure 5 A flowchart of community detection in a user preference trend recommendation method based on causal dependency provided in an embodiment of the present application; Figure 6 A flowchart of optimal transmission in a user preference trend recommendation method based on causal dependency provided in an embodiment of the present application. DETAILED DESCRIPTION

[0020] The embodiment of the present application provides a user preference trend recommendation method and system based on causal dependency, and solves the technical problems of being difficult to capture stable long-term interest patterns, trend interference and multi-scale interest changes in the prior art.

[0021] The technical solution in the embodiment of the present application is to solve the above technical problems, and the general idea is as follows: The embodiment of the present application proposes a sequence recommendation method based on frequency domain filtering, multi-scale user preference and causal reasoning, including frequency domain filtering (FDF), multi-scale user preference (MSUP) and causal reasoning based on community detection (CICD). Wherein, the frequency domain filtering (FDF) captures the periodic structure and trend change in the user behavior sequence. It designs a conversion strategy containing fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) to generate a frequency-enhanced behavior representation as a complementary feature of dynamic user interest. Multi-scale user preference (MSUP) constructs a multi-level interest representation of the user from multiple time scales to more comprehensively depict the behavior motivation and preference evolution of the user. These preferences are adaptively fused through learnable weights, thereby realizing fine modeling of dynamic user behavior. The causal reasoning based on community detection (CICD) analyzes the relationship between the user behavior path and the trend factor by constructing a causal graph. The constructed causal graph is as follows: Figure 1As shown in the figure, the nodes represent variables, and the edges represent the causal relationship between two nodes. Among them, each node represents a variable in the causal graph, which consists of five variables. Including H: user historical interaction sequence; C: dynamic factor, representing the current potential trend; In this embodiment, the user historical sequence S is divided into T equal length time slices , and the trend extracted from each time slice is taken as the trend cluster to represent the potential confounding variable C. I: target item; Y: interaction score between user and target item. : the tendency of user preference. Each edge in the figure represents the causal relationship between the connected nodes, and the specific meaning is: : it represents that the target item I will be affected by the potential trend C in a certain period, and the interaction pattern of the trend item is largely determined by its matching degree with the user's intention. For non-trend items, they are also affected by the representation of trend items. Therefore, the potential trend also affects the representation of non-trend items. : the tendency representation can be calculated by a specific way to the representation of the item involved in the corresponding trend, such as mean merging. Y: the final prediction score Y is affected by the target item I, the tendency representation and the historical interaction sequence H. In addition, CICD combines the causal intervention method to eliminate the confounding bias introduced by the trend variable, so as to restore the real interest preference of the user. CICD as the key content in the invention, effectively solves the problem of false correlation caused by trend interference, enhances the robustness and explainability of the recommendation result in the dynamic environment. Specifically, the invention estimates the real causal effect under intervention by introducing the causal intervention mechanism (do-operator), that is . By breaking the influence path of the potential confounding variable C constructed in the causal graph on the target item I and , the false correlation introduced by the trend factor is eliminated. Figure 1 The red line in the figure represents the causal graph G' after intervention, which removes the influence of confounding variables on target items by "blocking" confounding variables C, and estimates the intervention result from the observation data, and the derivation formula is . Wherein, represents the trend distribution conditioned on the user history h, which is constructed according to the trend cluster obtained by time slicing. Take as the user preference score. Similarly, represents the interaction score between the user and the target item i given the user history h and the trend c, which is defined as the trend consistency score. In addition, the invention also includes an optimal transport algorithm to capture the dynamic trend evolution of users between adjacent time slices to enhance the performance of explainability. In this embodiment, the definition of optimal transport is that the set of time slices is , and the trend distribution of adjacent time slices t and t+1 is and wherein , is the normalized weight of the i-th trend cluster, are the Dirac measure and the center embedding of the i-th trend cluster in the t-th time slice, respectively. There exists an optimal transport matrix that minimizes the transport cost between time slices. Specifically, in the inference phase, the optimal transport method is adopted and combined with the regularized Sinkhorn-Knopp algorithm to recursively interpolate the generalized trend representation that fuses multi-time slice information by constructing the minimum cost transport matrix of adjacent time slice trend distributions, so as to infer the trend of the future time slice and realize the fusion of the recommendation score consistent with the user preference and the trend.

[0022] In order to better understand the above technical solutions, the above technical solutions will be described in detail below in conjunction with the drawings in the specification and specific embodiments.

[0023] As shown in Figure 2 , the user preference trend recommendation method based on causal dependency relationship provided by the embodiment of the application comprises: performing frequency domain filtering on the user interaction sequence X to obtain the user behavior filtered in the frequency domain . The present step is specifically described as follows. Figure 3 Performing frequency domain filtering on the user interaction sequence X to obtain the user behavior filtered in the frequency domain , comprising: performing fast Fourier transform on the user interaction sequence X to obtain a complex frequency spectrum F; specifically, the low-pass filtering strategy based on FFT aims to extract the long-term trend of user preference. First, let the historical behavior sequence embedding of the user be , wherein B is the batch size, L is the length of the historical interaction, and d is the embedding dimension. Apply FFT to the X to convert the sequence embedding from the time domain to the frequency domain to obtain the complex frequency spectrum F, and the expression is ; wherein is the length of the real frequency part.

[0024] performing low-pass filtering on the complex frequency spectrum F to obtain the frequency domain low-frequency component ; specifically, the long-term trend of user preference is extracted by low-pass filtering, the components above the frequency threshold c are set to zero to generate the low-frequency component , and is applied, wherein is the default cutoff frequency, which can be adjusted according to the sequence length and task requirements.

[0025] performing inverse fast Fourier transform on the frequency domain low-frequency component to obtain the time domain low-frequency component Specifically, the IFFT-based high-pass filtering strategy aims to extract high-frequency components, namely short-term fluctuations or noise. First, it uses IFFT to... Converting back to the time domain, its expression is: ,in It preserves low-frequency trend signals while effectively suppressing high-frequency noise.

[0026] Subtract the low-frequency component of the time domain from the user interaction sequence X. High-frequency components are obtained. This process ensures complete separation of high-frequency components, containing useful local information, thus providing a foundation for subsequent weighted fusion.

[0027] Through expressions Calculate the fused features ;in, These are learnable parameters that can balance low-frequency trends and high-frequency information. Initialization using normal distribution . As a weight, the contribution of high-frequency information is dynamically adjusted. Through backpropagation optimization, the meaning of high-frequency information can be adaptively learned based on data characteristics, such as in high-noise scenarios. It may tend to a smaller value to reduce the impact of noise.

[0028] Features after fusion Dropout regularization and normalization are performed, and residual connections are introduced to obtain the final user behavior. The residual connection preserves the structural information of the original input, and the final output... As an enhanced representation of user behavior, it explicitly integrates global low-frequency and local high-frequency information, effectively capturing the temporal structure and rhythmic changes in user behavior. Frequency domain augmentation serves as a supplementary signal to dynamic user preferences, enhancing the modeling ability for time-sensitive interests.

[0029] User behavior is analyzed according to different time scales. The user preference representation is divided into global long-term preference representation, local long-term preference representation, and short-term preference representation. These three representations are then merged to obtain a unified user preference representation. ; This step will be explained in detail, such as Figure 4 As shown, user behavior is categorized according to different time scales. The user preference representation is divided into global long-term preference representation, local long-term preference representation, and short-term preference representation. These three representations are then merged to obtain a unified user preference representation. ,include: By expression The global long-term preference key component is calculated ; wherein, is a one-dimensional convolution operation, is batch normalization; The structure is equivalent to a residual enhanced convolution filter network, which can capture consistent signals in time slices in the sequence. The obtained enhanced user behavior representation is filtered by the filter The global frequency filtering is implemented to retain the key components , which are set as .

[0030] The global long-term preference key component is input into the Transformer encoder to explicitly capture the mutual influence between the position embeddings in the global behavior sequence, and the global long-term preference representation is obtained, and its expression is .

[0031] The user behavior is filtered by a sliding window to mine highly correlated preferences in a local range , and its expression is .

[0032] The preferences of all time positions are average-pooled to obtain the local long-term preference representation , and its expression is .

[0033] It should be pointed out that, unlike the global filter, the convolution kernel of the local filter has a smaller receptive field, and is mainly used to extract local patterns of interest in a short time range.

[0034] The embedding vectors of the last N interactions are extracted from the user behavior , and average-pooled to obtain the short-term preference representation , which captures the immediate interest in the user's last one or several interactions, and its expression is When the behavior length is less than N, the entire sequence is averaged. In this embodiment, N=3.

[0035] The global long-term preference representation , the local long-term preference representation , and the short-term preference representation are weighted and fused to obtain a unified user preference representation , making the expression of user preferences more comprehensive.

[0036] To be specific, the formula is The weighted fusion is used to obtain a unified user preference representation . Wherein, are three learnable parameters, respectively controlling the fusion weights of the three preferences, The above parameters are updated adaptively through back propagation during the training process to adapt to the characteristics of different user behavior sequences.

[0037] Community detection is performed on the constructed item-item graph to obtain trend clusters of items ; To be specific, community detection is performed on the constructed item-item graph to obtain trend clusters of items , including: Community detection is performed on the constructed item-item graph by using the Leiden algorithm to obtain trend clusters of items . Specifically, as shown in Figure 5 , for a target item i, the set of items appearing in each slice t is defined as , and the embedding representation of the target item i is . Then, the Leiden algorithm is applied to the constructed item-item graph for community detection, and the items in the slice are clustered into different clusters. The input is a weighted undirected graph G=(V, E, W), where V represents the set of item nodes, E represents the edge set, i.e., the co-occurrence relationship of items in the same user sequence, and W represents the edge weight. Let the time slice set be , and the embedding of the K trend clusters divided into the t-th time slice can be represented as , where is the number of clusters. First, under the fixed community division, the nodes are traversed one by one, and the nodes are moved to the neighbor community that can maximize the increment of modularity. The goal of this stage is to find the optimal community position of each node, denoted as formula . Wherein, is the edge weight between node i and node j; is the degree of node i; is the total weight of the graph; C is the community, ; represents the community to which node i belongs. =1 when and only when node i and j belong to the same community, otherwise 0. Further divide each trend cluster C in the current division result into multiple strongly connected subgraphs to ensure that each trend cluster is connected in structure, effectively eliminating isolated subgroups. Then, each trend cluster is regarded as a super node, a new graph G' with edge weights equal to the sum of the original community edge weights is constructed, and the above process is repeated until the modularity no longer increases. Finally, trend clusters of items are formed on each time slice Thus, the construction of variable C in the causal diagram is completed.

[0038] The attention weight matrix is calculated by the expression , which represents the attention degree of the target item to each trend cluster. Wherein, and are two-layer linear mapping, embedding the item representation and the trend cluster into the matrix , which is a scaling parameter; The trend preference enhancement representation is calculated by the expression ; The user preference score is calculated by the expression ; wherein, is an activation function; The user preference representation , the item embedding representation , and the trend cluster are fused to obtain the fused representation ; specifically, a sequence is constructed, and the sequence is input into a multi-layer Transformer encoder to model the relationship between the three by using a self-attention mechanism, and the final fused representation is output, and its expression is .

[0039] The personalized trend matching degree of the target item i in the current community c for the user u is calculated by the expression ; wherein, is a learnable linear transformation matrix, is a trainable bias; The trend consistency score is calculated by the expression ; this attention-based fusion method can jointly encode the candidate item information and the trend representation, so as to more accurately estimate the preference score of the user under a specific trend condition.

[0040] The user preference trend is calculated by the expression .

[0041] In order to establish the trend evolution path and depict the drift, merging and other behaviors of the trend cluster, as shown in Figure 6 , it also includes: The Sinkhorn-Knopp algorithm is used to iteratively solve the formula to obtain the optimal transport matrix; wherein,​​ This represents the Euclidean distance between trend clusters. It is the entropy regularization parameter. It represents the trend strength of the i-th item in the previous time slice, and the weight assigned to the j-th item in the current time slice. It is the optimal transfer matrix; By accumulating the optimal transfer matrix layer by layer, a generalized trend representation that fuses information from multiple time slices is generated through recursive interpolation. ;For example: ;in, It is the generalized trend of time slice 2, which integrates the historical trend transmission results of time slice 1 and the current trend of time slice 2; П is the optimal transmission matrix for time slices t and t+1; It is the cumulative optimal transfer matrix from time slice T-1 to T; The weights of historical trends are controlled. This process maps historical trends to the current time dimension according to their transmission paths, forming a generalized representation that integrates information from multiple time slices.

[0042] Representing generalized trends As a T+1 trend prediction for a future time slice, a consistency score between items and the trend is calculated. In this case, it is expressed as... The attention weight matrix is ​​calculated. ,include: Through expressions The generalized attention weight matrix is ​​calculated. ; Through expressions The calculated trend preference enhancement representation ,include: Through expressions The generalized trend preference enhancement representation is calculated. ; Through expressions Calculate the user preference score ,include: Through expressions Calculate the generalized user preference score ; Through expressions Calculate user preference trends ,include: Through expressions The corrected user preference trend was calculated. .

[0043] Furthermore, embodiments of the present invention also provide a user preference trend recommendation system based on causal dependency, comprising: a frequency domain filtering module, configured to perform frequency domain filtering on the user interaction sequence X to obtain a user behavior filtered in frequency domain ; Specifically, the frequency domain filtering module comprises: a fast Fourier transform submodule, configured to perform fast Fourier transform on the user interaction sequence X to obtain a complex frequency spectrum F; specifically, the low-pass filtering strategy based on FFT aims to extract the long-term trend of user preference. First, let the history behavior sequence embedding of the user be , where B is the batch size, L is the length of the history interaction, and d is the embedding dimension. Applying FFT to X converts the sequence embedding from the time domain to the frequency domain to obtain the complex frequency spectrum F, which is expressed as ; where is the length of the real frequency part.

[0044] a low-pass filtering submodule, configured to perform low-pass filtering on the complex frequency spectrum F to obtain a low-frequency component in frequency domain ; specifically, the long-term trend of user preference is extracted by low-pass filtering, and the components above the frequency threshold c are set to zero to generate the low-frequency component , and the expression is applied, where is the default cutoff frequency, which can be adjusted according to the sequence length and task requirements.

[0045] an inverse fast Fourier transform submodule, configured to perform inverse fast Fourier transform on the low-frequency component in frequency domain to obtain a low-frequency component in time domain ; specifically, the high-pass filtering strategy based on IFFT aims to extract high-frequency components, i.e. short-term fluctuations or noise. First, convert back to the time domain by IFFT, which is expressed as , where retains the low-frequency trend signal while effectively suppressing high-frequency noise.

[0046] a high-frequency component obtaining submodule, configured to subtract the low-frequency component in time domain from the user interaction sequence X to obtain a high-frequency component ; this process ensures that the high-frequency component is completely separated and contains useful local information, thereby providing a basis for subsequent weighted fusion.

[0047] a feature fusion submodule, configured to calculate the fused feature by the expression ; where is a learnable parameter that can balance the low-frequency trend and high-frequency information, initialized by normal distribution . as the weight, dynamically adjusts the contribution of high-frequency information. By backpropagation optimization, it can adaptively learn the significance of high-frequency information according to the characteristics of the data, for example, in a high-noise scene, It may tend to a smaller value to reduce the influence of noise.

[0048] The final user behavior acquisition submodule is used to perform Dropout regularization and normalization on the fused features , and introduce a residual connection to obtain the final user behavior . The residual connection retains the structural information of the original input, and the final output is an enhanced user behavior representation that explicitly integrates global low-frequency and local high-frequency information, which can effectively capture the temporal structure and rhythmic changes in user behavior. The frequency domain enhanced representation serves as a complementary signal to user dynamic preferences to improve the modeling ability of time-sensitive interests.

[0049] The multi-scale user preference analysis module is used to divide the user behavior into global long-term preference representation, local long-term preference representation and short-term preference representation according to different time scales, and fuse the global long-term preference representation, local long-term preference representation and short-term preference representation to obtain a unified user preference representation . Specifically, the multi-scale user preference analysis module comprises: The global long-term preference key component acquisition submodule is used to calculate the global long-term preference key component by the expression ; wherein is a one-dimensional convolution operation, is batch normalization. The structure is equivalent to a residual enhanced convolution filter network that can capture consistent signals in time slices in the sequence. The obtained enhanced user behavior representation is subjected to filter to perform global frequency filtering to retain key components , which are set to here.

[0050] The global long-term preference representation acquisition submodule is used to input the global long-term preference key component into the Transformer encoder to explicitly capture the mutual influence between position embeddings in the global behavior sequence to obtain the global long-term preference representation , whose expression is .

[0051] The filtering submodule is used to perform sliding window filtering on the user behavior to mine highly correlated preferences within a local range , the expression of which is .

[0052] The local long-term preference representation obtaining sub-module is used for averaging and pooling the preferences of all time positions to obtain the local long-term preference representation , the expression of which is .

[0053] It should be noted that, unlike the global filter, the convolution kernel of the local filter has a smaller receptive field and is mainly used to extract local patterns of interest in a short time range.

[0054] The short-term preference representation obtaining sub-module is used for intercepting embedding vectors of the last N interactions from the user behavior and performing average pooling to obtain the short-term preference representation , which captures the immediate interest in the last one or several interaction behaviors of the user, the expression of which is When the behavior length is less than N, the entire sequence is averaged. In this embodiment, N = 3.

[0055] The user preference representation weighted fusion sub-module is used for weighted fusion of the global long-term preference representation , the local long-term preference representation and the short-term preference representation to obtain a unified user preference representation , so that the expression of the user preference is more comprehensive.

[0056] In this embodiment, the user preference representation weighted fusion sub-module is specifically used for weighted fusion through the formula to obtain a unified user preference representation . Wherein, are three learnable parameters, respectively controlling the fusion weights of the three preferences, The above parameters are updated adaptively through back propagation in the training process to adapt to the characteristics of different user behavior sequences.

[0057] The community detection module is used for community detection on the constructed item-item graph to obtain a trend cluster of items ; Specifically, the community detection module is specifically used for community detection on the constructed item-item graph through the Leiden algorithm to obtain a trend cluster of items . Specifically, as shown in Figure 5 , for a target item i, the set of items appearing in each slice t is defined as , and the embedding representation of the target item i is Then, the Leiden algorithm is applied to the constructed item-item graph for community detection, clustering items in the slices into different clusters. The input is a weighted undirected graph G=(V, E, W), where V represents the set of item nodes, E represents the set of edges (i.e., the co-occurrence relationships of items in the same user sequence), and W represents the weight of the edges. Let the time slice set be... The embedding of the K trend clusters divided into the t-th time slice can be represented as: ,in This refers to the number of clusters. First, under a fixed community division, nodes are traversed one by one, and each node is moved to a neighboring community that maximizes the increment in modularity. The goal of this stage is to find the optimal community location for each node, denoted by the formula... .in, Let the edge weight be the weight between node i and node j; Let i be the degree of node i; C represents the total weight of the graph; C represents the community. ; This represents the community to which node i belongs. =1 if and only if nodes i and j belong to the same community, otherwise 0. Each trend cluster C in the current partitioning result is further divided into multiple strongly connected subgraphs to ensure that each trend cluster... Structurally connecting these groups effectively eliminates isolated subgroups. Then, each trend cluster is... Treating each node as a supernode, a new graph G' with edge weights equal to the sum of edge weights between the original communities is constructed for the next iteration, and the above process is repeated until modularity no longer increases. Finally, a graph is formed at each time slice. Thus, the construction of variable C in the causal graph was completed.

[0058] The attention weight matrix calculation module is used to calculate the attention weight matrix using an expression. The attention weight matrix is ​​calculated. This indicates the degree of attention the target item receives from each trend cluster. Among them, and For a two-layer linear mapping, items are embedded in the representation. With trend clusters Linear transformation into a matrix, For scaling parameters; Trend preference enhancement representation calculation module, used to calculate through expressions The calculated trend preference enhancement representation ; The user preference score calculation module is used to calculate user preference scores using expressions. Calculate the user preference score ;in, For activation functions; The fusion module is used to represent user preferences. , item embedding representation , trend cluster fusion, obtaining a fused representation ; specifically, constructing a sequence and inputting the sequence into a multi-layer Transformer encoder to model the relationship among the three using a self-attention mechanism, and outputting a final fused representation, which is expressed as .

[0059] a personalized trend matching degree calculation module configured to calculate a personalized trend matching degree of the user u to the target item i in the current community c by using the expression ; wherein is a learnable linear transformation matrix, is a trainable bias; a trend consistency score calculation module configured to calculate a trend consistency score by using the expression This attention-based fusion method can jointly encode the candidate item information and the trend representation, so as to more accurately estimate the preference score of the user under a specific trend condition.

[0060] a user preference trend recommendation module configured to calculate a user preference trend by using the expression .

[0061] In order to establish a trend evolution path and depict the behaviors such as drift and merging of the trend cluster, the method further includes: an optimal transport matrix obtaining module configured to obtain an optimal transport matrix by using a Sinkhorn-Knopp algorithm to iteratively solve the formula ; wherein represents an Euclidean distance between the trend clusters, is an entropy regularization parameter, is a trend intensity of the i-th item in the previous time slice, and a weight assigned to the current j-th item, is the optimal transport matrix; a generalized trend representation generating module configured to recursively interpolate a generalized trend representation fused with multi-time slice information by accumulating the optimal transport matrix layer by layer ; for example: ; wherein is a generalized trend of the time slice 2, which fuses the historical trend transport result of the time slice 1 and the current trend of the time slice 2; П is the optimal transport matrix of the time slice t and t+1; is the cumulative optimal transport matrix from the time slice T-1 to T; ​​​Control the weight of historical trends. The process maps historical trends to the current time dimension by transmission path, forming a generalized representation that integrates multi-time slice information.

[0062] Generalized trend representation As a trend prediction for the future time slice T+1, the consistency score of the item with the trend is calculated. In this case, the attention weight matrix calculation module is specifically configured to calculate the generalized attention weight matrix by the expression The trend preference enhancement representation calculation module is specifically configured to calculate the generalized trend preference enhancement representation by the expression The user preference score calculation module is specifically configured to calculate the generalized user preference score by the expression The user preference trend recommendation module is specifically configured to calculate the corrected user preference trend by the expression .

[0063] The loss function of the recommendation system (FMCRec model) provided by the embodiment of the application is described below: In the model training process, the classical Bayesian personalized ranking (BPR) loss function is used to optimize the model to improve the ranking performance, and the expression is ; wherein, represents a training triple, is a Sigmoid function, and the preference scores of the positive sample and the negative sample are respectively: , ; wherein, , are the item embeddings of the positive sample and the negative sample, respectively, and the trend scores of the positive sample and the negative sample are respectively , , to ensure that the model has good discrimination between the relative scores of the positive sample pair and the negative sample pair.

[0064] In order to prevent the model from overfitting, the embodiment introduces regularization constraints, and the final loss function is ; wherein, represents the set of all trainable parameters in the model, is a regularization coefficient.

[0065] ​​​​​​​To verify the performance of the recommendation system provided in this embodiment of the invention, experiments were conducted on three real datasets: Amazon Sports, Amazon, and Yelp. The Yelp data was provided by the Yelp community. Sports belongs to the Sports and Outdoors category in the Amazon dataset. This embodiment selected data from December 7, 2012 to May 31, 2014, removing users and items with fewer than 5 interactions to ensure high-quality experimental data. Phones belongs to the Phones and Accessories category in the Amazon dataset. Data from November 30, 2012 to July 23, 2014 was selected, and users and items with fewer than 5 interactions were removed. Yelp, published by Yelp, the largest review website in the United States, is a subset of Yelp's merchant, review, and user data. Interactions from July 1, 2017 to July 1, 2018 were selected. Similarly, this embodiment removed users and items with fewer than 5 interactions.

[0066] To capture dynamic item trends, this embodiment divides each dataset into (T+1) equal time intervals. The first T slices are used for training, and the last time slice is used for inference. For the validation and test sets, 30% of the users are randomly selected from the (T+1)th slice for validation, and the other 70% are selected for testing.

[0067] The hardware configuration of this embodiment is as follows: Intel(R) Core(TM) i5-10400F CPU @ 2.90GHZ (16GB RAM) and NVIDIA RTX 1650 GPU (4GB VRAM); the software environment is as follows: Windows 10 Professional operating system, CUDA version 11.6, Python version 3.10, and PyTorch 1.13 deep learning framework.

[0068] This embodiment uses two metrics to evaluate the model: NDCG (Normalized Discount Cumulative Gain) and HitRate. NDCG is a metric that measures ranking quality, considering both the relevance and position of each result. It is normalized to a value between 0 and 1, where higher values ​​indicate better ranking quality. HitRate measures the proportion of queries where relevant items appear in the top k ranked results. It indicates whether the next item the user actually wants to interact with appears in the top k recommended results.

[0069] NDCG@10 represents the ranking quality of the top 10 items in the ranking result, and Hit Rate@10 represents whether the relevant items needed by the user are hit in the top 10 ranking results. The higher the values of the two are, the higher the accuracy is. For convenience, they are respectively referred to as N@10 and H@10 hereinafter.

[0070] The embodiment analyzes the comparison experimental results of the FMCRec model and other SOTA models. The specific experimental results are shown in Table 1, in which the best result is highlighted in bold, and the suboptimal result is highlighted in underlined.

[0071] Table 1 Performance comparison of different models

[0072] As shown in Table 1, under each evaluation index, the FMCRec model has a significant improvement compared with the suboptimal baseline model. These results show the superior performance of the FMCRec model in different scenarios. Compared with the MDIT model, the FMCRec model increases N@10 by 2.6% and H@10 by 1.8% in the Sports dataset. The improvement in the Phones dataset is the smallest because the Phones dataset has relatively high density, clear relevance, and the least trend interference. The Reg model uses regularization to reduce model bias by weakening the linear correlation between item popularity and predicted scores, and its strict constraint leads to poor generalization ability. The Zerosum model uses a regularization strategy, but its overly strict debiasing constraint fails to bring significant benefits. Although the regularization method can alleviate the popularity bias, it cannot distinguish real preferences from trend-induced interference from a causal perspective.

[0073] Those skilled in the art will appreciate that embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage, etc.) containing computer usable program code.

[0074] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks

[0075] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks

[0076] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks

[0077] The embodiments of the present application described above are merely used to illustrate the technical solutions of the present application but not limit the present application. Although the present application is described in detail with reference to the preferred embodiments, one skilled in the art should understand that they can make modifications or equivalent replacements to the technical solutions of the present application without departing from the spirit and scope of the present application, and they should be included in the scope of the claims of the present application.

Claims

1. A user preference trend recommendation method based on causal dependency, characterized in that, include: Frequency domain filtering is applied to the user interaction sequence X to obtain the frequency-domain filtered user behavior. ; The user behavior is analyzed according to different time scales. The user preference representation is divided into global long-term preference representation, local long-term preference representation, and short-term preference representation. These three representations are then merged to obtain a unified user preference representation. ; Community detection is performed on the constructed item-item graph to obtain the trend clusters of items. ; Through expression The attention weight matrix is ​​calculated. ;in, and For a two-layer linear mapping, the items are embedded in the representation. With trend clusters Linear transformation into a matrix, For scaling parameters; Through expression The calculated trend preference enhancement representation ; Through expression Calculate the user preference score ;in, For activation functions; User preferences The item is embedded in the representation. The trend cluster The fusion is performed to obtain the fused representation. ; Through expression The degree of personalized trend matching between user u and target item i in the current community c is calculated. ;in, It is a learnable linear transformation matrix. It is a trainable bias; Through expression Calculate the trend consistency score ; Through expression Calculate user preference trends .

2. The user preference trend recommendation method based on causal dependency as described in claim 1, characterized in that, The user interaction sequence X is subjected to frequency domain filtering to obtain the frequency domain filtered user behavior. ,include: Perform a Fast Fourier Transform on the user interaction sequence X to obtain the complex spectrum F; The complex spectrum F is low-pass filtered to obtain the low-frequency component in the frequency domain. ; For the low-frequency components in the frequency domain Perform an inverse fast Fourier transform to obtain the low-frequency components in the time domain. ; Subtract the time-domain low-frequency component from the user interaction sequence X. High-frequency components are obtained. ; Through expression Calculate the fused features ;in, These are learnable parameters; The fused features Regularization and normalization are performed, and residual connections are introduced to obtain the final user behavior. .

3. The user preference trend recommendation method based on causal dependency as described in claim 1, characterized in that, The user behavior is analyzed according to different time scales. The user preference representation is divided into global long-term preference representation, local long-term preference representation, and short-term preference representation. These three representations are then merged to obtain a unified user preference representation. ,include: Through expression The key components of global long-term preferences were calculated. ;in, It is a one-dimensional convolution operation. It is batch normalization; The key components of global long-term preferences Input a Transformer encoder to explicitly capture the interactions between positional embeddings in the global action sequence, resulting in a global long-term preference representation. ; Regarding the user behavior Perform sliding window filtering to uncover highly relevant preferences within a local area. ; Preference for all time locations Perform average pooling to obtain the local long-term preference representation. ; From the user behavior The embedding vectors of the most recent N interactions are extracted and average pooled to obtain the short-term preference representation. ; The global long-term preference representation The local long-term preference representation and the aforementioned short-term preference representation By performing weighted fusion, a unified representation of user preferences is obtained. .

4. The user preference trend recommendation method based on causal dependency as described in claim 1, characterized in that, The constructed item-item graph is subjected to community detection to obtain the trend clusters of items. ,include: Community detection is performed on the constructed item-item graph using the Leiden algorithm to obtain trend clusters of items. .

5. The user preference trend recommendation method based on causal dependency as described in claim 1, characterized in that, Also includes: The formula is solved iteratively using the Sinkhorn-Knopp algorithm. The optimal transfer matrix is ​​obtained; where, This represents the Euclidean distance between trend clusters. It is the entropy regularization parameter. It represents the trend strength of the i-th item in the previous time slice, and the weight assigned to the j-th item in the current time slice. It is the optimal transfer matrix; By accumulating the optimal transfer matrix layer by layer, a generalized trend representation that fuses information from multiple time slices is generated through recursive interpolation. ; The expression The attention weight matrix is ​​calculated. ,include: Through expression The generalized attention weight matrix is ​​calculated. ; The expression The calculated trend preference enhancement representation ,include: Through expression The generalized trend preference enhancement representation is calculated. ; The expression Calculate the user preference score ,include: Through expression Calculate the generalized user preference score ; The expression Calculate user preference trends ,include: Through expression The corrected user preference trend was calculated. .

6. A user preference trend recommendation system based on causal dependency, characterized in that, include: The frequency domain filtering module is used to perform frequency domain filtering on the user interaction sequence X to obtain the frequency-domain filtered user behavior. ; The multi-scale user preference analysis module is used to analyze user behavior according to different time scales. The user preference representation is divided into global long-term preference representation, local long-term preference representation, and short-term preference representation. These three representations are then merged to obtain a unified user preference representation. ; The community detection module performs community detection on the constructed item-item graph to obtain trend clusters of items. ; The attention weight matrix calculation module is used to calculate the attention weight matrix using an expression. The attention weight matrix is ​​calculated. ;in, and For a two-layer linear mapping, the items are embedded in the representation. With trend clusters Linear transformation into a matrix, For scaling parameters; Trend preference enhancement representation calculation module, used to calculate through expressions The calculated trend preference enhancement representation ; The user preference score calculation module is used to calculate user preference scores using expressions. Calculate the user preference score ;in, For activation functions; The fusion module is used to represent the user preferences. The item is embedded in the representation. The trend cluster The fusion is performed to obtain the fused representation. ; The personalized trend matching degree calculation module is used to calculate the degree of matching through expressions. The degree of personalized trend matching between user u and target item i in the current community c is calculated. ;in, It is a learnable linear transformation matrix. It is a trainable bias; The trend consistency score calculation module is used to calculate the trend consistency score using an expression. Calculate the trend consistency score ; The user preference trend recommendation module is used to recommend users based on expressions. Calculate user preference trends .

7. The user preference trend recommendation system based on causal dependency as described in claim 6, characterized in that, The frequency domain filtering module includes: The Fast Fourier Transform (FFT) submodule is used to perform a Fast Fourier Transform on the user interaction sequence X to obtain a complex spectrum F; The low-pass filtering submodule is used to perform low-pass filtering on the complex spectrum F to obtain the low-frequency component in the frequency domain. ; The inverse fast Fourier transform submodule is used to process the low-frequency components in the frequency domain. Perform an inverse fast Fourier transform to obtain the low-frequency components in the time domain. ; The high-frequency component acquisition submodule is used to subtract the time-domain low-frequency component from the user interaction sequence X. High-frequency components are obtained. ; The feature fusion submodule is used to fuse features via expressions. Calculate the fused features ;in, These are learnable parameters; The end-user behavior acquisition submodule is used to process the fused features. Regularization and normalization are performed, and residual connections are introduced to obtain the final user behavior. .

8. The user preference trend recommendation system based on causal dependency as described in claim 6, characterized in that, The multi-scale user preference analysis module includes: The global long-term preference key component acquisition submodule is used to obtain key components through expressions. The key components of global long-term preferences were calculated. ;in, It is a one-dimensional convolution operation. It is batch normalization; The global long-term preference representation acquisition submodule is used to obtain the key components of the global long-term preference. Input a Transformer encoder to explicitly capture the interactions between positional embeddings in the global action sequence, resulting in a global long-term preference representation. ; The filtering submodule is used to filter the user behavior. Perform sliding window filtering to uncover highly relevant preferences within a local area. ; The local long-term preference representation obtains a submodule for preferences across all time locations. Perform average pooling to obtain the local long-term preference representation. ; Short-term preference representation acquisition submodule, used to obtain from the user behavior The embedding vectors of the most recent N interactions are extracted and average pooled to obtain the short-term preference representation. ; The user preference representation weighted fusion submodule is used to process the global long-term preference representation. The local long-term preference representation and the aforementioned short-term preference representation By performing weighted fusion, a unified representation of user preferences is obtained. .

9. The user preference trend recommendation system based on causal dependency as described in claim 6, characterized in that, The community detection module is specifically used to perform community detection on the constructed item-item graph using the Leiden algorithm to obtain trend clusters of items. .

10. The user preference trend recommendation system based on causal dependency as described in claim 6, characterized in that, Also includes: The optimal transfer matrix acquisition module is used to iteratively solve the formula using the Sinkhorn-Knopp algorithm. The optimal transfer matrix is ​​obtained; where, This represents the Euclidean distance between trend clusters. It is the entropy regularization parameter. It represents the trend strength of the i-th item in the previous time slice, and the weight assigned to the j-th item in the current time slice. It is the optimal transfer matrix; The generalized trend representation generation module is used to recursively interpolate and generate a generalized trend representation that fuses information from multiple time slices by accumulating the optimal transfer matrix layer by layer. ; The attention weight matrix calculation module is specifically used to calculate the attention weight matrix using an expression. The generalized attention weight matrix is ​​calculated. ; The trend preference enhancement representation calculation module is specifically used to calculate the trend preference through an expression. The generalized trend preference enhancement representation is calculated. ; The user preference score calculation module is specifically used to calculate the user preference score using an expression. Calculate the generalized user preference score ; The user preference trend recommendation module is specifically used to recommend users based on expressions. The corrected user preference trend was calculated. .

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