Information recommendation method, device, equipment, medium and program product

Abstract

The application provides an information recommendation method and device, equipment, medium and program product, which can be applied to the fields of artificial intelligence and big data. The method comprises the following steps: acquiring a time sequence of dynamic network snapshots in a historical period and a predetermined community quantity; extracting anchor point information, node stability degree information and network topology structure information of a global structure from the time sequence of dynamic network snapshots; iteratively optimizing a randomly initialized parameter matrix based on the anchor point information, the node stability degree information and the network topology structure information until an iteration termination condition is reached, so as to obtain a target parameter matrix; performing matrix multiplication on a node community attribution matrix at a T moment and a community transition matrix from a T-1 moment to the T moment, so as to generate an expected community attribution matrix of each node at a T+1 moment; and recommending target product information of a product type corresponding to a k community to a target user based on a probability that each user belongs to the k community at the T+1 moment.

Description

Technical Field

[0001] This application relates to the fields of artificial intelligence technology and big data technology, and more specifically, to an information recommendation method, apparatus, device, medium, and program product. Background Technology

[0002] Dynamic network evolution analysis has significant application value in the financial field. In customer management systems, banks need to understand how customer interests in different financial products evolve over time. A customer group constitutes a dynamic network, where nodes represent customers and edges represent attention to or transaction behavior related to product categories within a specific time period. This network exhibits significant dynamic characteristics: some customers maintain stable product preferences over a long period, while others experience a shift in interest from basic savings to investment and wealth management, and then to insurance planning. Capturing both the overall structured evolutionary patterns of the community and accurately characterizing the transfer behavior of individual nodes between different communities in time-series network data presents a significant challenge to existing methods.

[0003] In realizing the concept of this application, the inventors discovered at least the following problems in the related technology: the information recommendation is inaccurate when the bank's interest in different financial products evolves over time. Summary of the Invention

[0004] In view of this, this application provides an information recommendation method, apparatus, device, medium, and program product.

[0005] One aspect of this application provides an information recommendation method, comprising: obtaining a time sequence of dynamic network snapshots within a historical period and a predetermined number of communities, wherein nodes in the dynamic network represent users, the dynamic network snapshots represent the product preference similarity between different users at any historical moment, the predetermined communities represent the product types preferred by users, the historical period includes T moments, where T is an integer greater than 1, and the predetermined number of communities is K, where K is an integer greater than 1.

[0006] The anchor information, node stability information, and network topology information of the global structure are extracted from the time series of the above dynamic network snapshots. Among them, the anchor information is used to characterize the product preference type at each historical moment; the node stability information is used to characterize the stability of user behavior over time; and the network topology information is used to characterize the association relationship established between different users at each historical moment based on the similarity of product preferences.

[0007] Based on the anchor point information, node stability information, and network topology information of the aforementioned global structure, the randomly initialized parameter matrix is ​​iteratively optimized until the iteration termination condition is met, resulting in the target parameter matrix. The target parameter matrix includes the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T. Each element in the node community affiliation matrix represents the probability that each user belongs to the k-th community at time T. Each element in the community transition matrix represents the probability that a user in any community will transition to the k-th community from time T-1 to time T; k is greater than or equal to 1 and less than or equal to K.

[0008] Multiply the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T to generate the expected community affiliation matrix for each node at time T+1; and

[0009] Based on the probability that each user belongs to the k-th community at time T+1, target product information corresponding to the product type of the k-th community is recommended to the target user.

[0010] According to embodiments of this application, extracting anchor information, node stability information, and network topology information from the time-series sequence of the aforementioned dynamic network snapshots includes extracting an initial dynamic network snapshot at the initial moment from the time-series sequence of the dynamic network snapshots; clustering the initial dynamic network snapshots according to a predetermined number of communities to obtain a clustering indicator matrix; wherein each element in the clustering indicator matrix represents the degree of preference of each user for historical product types at the initial moment; and determining the degree of preference of each user for historical product types at the initial moment as anchor information of the global structure.

[0011] According to embodiments of this application, the extraction of anchor point information, node stability information, and network topology information from the time-series dynamic network snapshot includes determining the degree of any node at time t by summing the product preference similarities between any node in the dynamic network snapshot at time t and all nodes in the dynamic network except for any node; and determining the node stability information at time t by ratio of the number of nodes that maintain association relationships between any node in the dynamic network snapshot from time t-1 to time t and all nodes in the dynamic network except for any node to the degree of any node at time t.

[0012] In embodiments of this application, based on the anchor information, node stability information, and network topology information of the aforementioned global structure, a randomly initialized parameter matrix is ​​iteratively optimized until the iteration termination condition is met to obtain a target parameter matrix. This includes: based on the anchor information of the aforementioned global structure and the initial dynamic network snapshot at the initial moment, the randomly initialized parameter matrix is ​​iteratively optimized to obtain the node community affiliation matrix, the first basis matrix, and the second basis matrix at the initial moment, such that the target difference is less than a predetermined difference threshold. The target difference includes the difference between the product of the node community affiliation matrix and the first basis matrix at the initial moment and the aforementioned initial dynamic network snapshot, and the difference between the product of the node community affiliation matrix and the second basis matrix at the initial moment and the clustering indicator matrix at the initial moment. Based on the anchor information, node stability information, and network topology information of the aforementioned global structure, the node community affiliation matrix, the aforementioned first basis matrix, and the aforementioned second basis matrix at the initial moment are iteratively optimized to obtain the aforementioned target parameter matrix. This ensures that the expected product preference of a user corresponding to any node in the dynamic network at any historical moment, calculated based on the target parameter matrix, matches the time series sequence of the dynamic network snapshot, and the changing trends of product preferences among related nodes in the dynamic network are similar.

[0013] According to an embodiment of this application, the method further includes obtaining a dynamic network snapshot at time T+1; updating the time series sequence of the dynamic network snapshot using the dynamic network snapshot at time T+1 to obtain an updated time series sequence of the dynamic network snapshot; iteratively optimizing a randomly initialized parameter matrix based on the updated time series sequence of the dynamic network snapshot until the iteration termination condition is met to obtain the actual node community affiliation matrix at time T+1; and adjusting the constraint parameters used for the iterative optimization operation in response to the error between the actual node community affiliation matrix at time T+1 and the expected community affiliation matrix of each node at time T+1 being greater than a predetermined error threshold; wherein the constraint parameters include a first parameter for constraining the global structure of the dynamic network and a second parameter for constraining the temporal evolution of the dynamic network.

[0014] Another aspect of this application provides an information recommendation device, comprising: an acquisition module, configured to acquire a time sequence of dynamic network snapshots within a historical period and a predetermined number of communities, wherein nodes in the dynamic network represent users, the dynamic network snapshots represent the product preference similarity between different users at any historical moment, the predetermined communities represent the product types preferred by users, the historical period includes T moments, where T is an integer greater than 1, and the predetermined number of communities is K, where K is an integer greater than 1.

[0015] The extraction module is used to extract anchor information, node stability information, and network topology information of the global structure from the time series of the above dynamic network snapshots. Among them, the anchor information is used to characterize the product preference type at each historical moment; the node stability information is used to characterize the stability of user behavior over time; and the network topology information is used to characterize the association relationship established between different users at each historical moment based on the similarity of product preferences.

[0016] The optimization module is used to iteratively optimize the randomly initialized parameter matrix based on the anchor point information, node stability information, and network topology information of the aforementioned global structure, until the iteration termination condition is met, to obtain the target parameter matrix. The target parameter matrix includes the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T. Each element in the node community affiliation matrix represents the probability that each user belongs to the k-th community at time T. Each element in the community transition matrix represents the probability that a user in any community will transition to the k-th community from time T-1 to time T; k is greater than or equal to 1 and less than or equal to K.

[0017] The generation module is used to perform matrix multiplication on the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T to generate the expected community affiliation matrix for each node at time T+1; and

[0018] The recommendation module is used to recommend target product information of the product type corresponding to the k-th community to the target user based on the probability that each user belongs to the k-th community at time T+1.

[0019] Another aspect of this application provides an electronic device, comprising:

[0020] One or more processors;

[0021] Memory, used to store one or more programs.

[0022] When one or more programs are executed by one or more processors, the one or more processors implement the method described above.

[0023] Another aspect of this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed, are used to implement the method described above.

[0024] Another aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0025] According to embodiments of this application, the time-series sequence of dynamic network snapshots and the number of predetermined communities within a historical period are obtained. Nodes in the dynamic network represent users, dynamic network snapshots represent the similarity of product preferences among different users at any historical moment, and predetermined communities represent the product types preferred by users, thereby achieving unified modeling of global structural features and local transfer information. Anchor point information of the global structure, node stability information, and network topology information are extracted from the time-series sequence of dynamic network snapshots; thus, in time-series network data, both the global community structure evolution pattern and the transfer behavior of individual nodes between different communities can be captured. Based on the anchor point information, node stability information, and network topology information of the global structure, the randomly initialized parameter matrix is ​​iteratively optimized until the iteration termination condition is met, obtaining the target parameter matrix; thereby achieving a complete balance system composed of four constraints: structural reconstruction prevents deviation from real data, global alignment prevents local noise dominance, temporal continuity prevents excessive smoothing, and topological smoothing prevents fragmented communities. Based on the probability that each user belongs to the k-th community at time T+1, target product information corresponding to the product type of the k-th community is recommended to the target user; thus, accurate prediction of user product preferences is achieved, improving the accuracy of information recommendation. Attached Figure Description

[0026] The above and other objects, features and advantages of this application will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0027] Figure 1 An application scenario diagram of the information recommendation method according to an embodiment of this application is shown.

[0028] Figure 2 A flowchart of an information recommendation method according to an embodiment of this application is shown.

[0029] Figure 3 A block diagram of an information recommendation device according to an embodiment of this application is shown.

[0030] Figure 4 A block diagram of an electronic device suitable for implementing an information recommendation method according to an embodiment of this application is shown. Detailed Implementation

[0031] The embodiments of this application will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this application. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of this application for ease of explanation. However, it will be apparent that one or more embodiments may be implemented without these specific details. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0032] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0033] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0034] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0035] In the embodiments of this application, the collection, updating, analysis, processing, use, transmission, provision, disclosure, and storage of data (e.g., including but not limited to user personal information) comply with relevant laws and regulations, are used for legitimate purposes, and do not violate public order and good morals. In particular, necessary measures have been taken to prevent unauthorized access to user personal information data and to safeguard user personal information security and network security.

[0036] In the embodiments of this application, the user's authorization or consent was obtained before obtaining or collecting the user's personal information.

[0037] Embodiments of this application provide an information recommendation method, apparatus, device, medium, and program product.

[0038] Figure 1 An application scenario diagram of the information recommendation method according to an embodiment of this application is shown. It should be noted that... Figure 1 The diagram shown is merely a system architecture applicable to embodiments of this application, intended to help those skilled in the art understand the technical content of this application, but does not imply that embodiments of this application cannot be used in other devices, systems, environments, or scenarios.

[0039] like Figure 1As shown, the system architecture 100 according to this embodiment may include a first terminal device 101, a second terminal device 102, a third terminal device 103, a network 104, and a server 105. The network 104 serves as a medium for providing communication links between the first terminal device 101, the second terminal device 102, the third terminal device 103, and the server 105. The network 104 may include various connection types, such as wired and / or wireless communication links, etc.

[0040] Users can use the first terminal device 101, the second terminal device 102, and the third terminal device 103 to interact with the server 105 via the network 104 to receive or send messages, etc. Various communication client applications can be installed on the first terminal device 101, the second terminal device 102, and the third terminal device 103, such as shopping applications, web browser applications, search applications, instant messaging tools, email clients, and / or social media platform software, etc. (for example only).

[0041] The first terminal device 101, the second terminal device 102, and the third terminal device 103 can be various electronic devices with displays and support web browsing, including but not limited to smartphones, tablets, laptops, and desktop computers.

[0042] Server 105 can be a server that provides various services, such as a backend management server that supports websites browsed by users using the first terminal device 101, the second terminal device 102, and the third terminal device 103 (this is just an example). The backend management server can analyze and process data such as received user requests, and feed back the processing results (such as web pages, information, or data obtained or generated according to user requests) to the terminal devices.

[0043] It should be noted that the information recommendation method provided in this application embodiment can generally be executed by server 105. Correspondingly, the information recommendation method system provided in this application embodiment can generally be set up in server 105. The information recommendation method provided in this application embodiment can also be executed by a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105. Correspondingly, the information recommendation method system provided in this application embodiment can also be set up in a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105. Alternatively, the information recommendation method provided in this application embodiment can also be executed by the first terminal device 101, the second terminal device 102, and the third terminal device 103, or it can also be executed by other terminal devices that are different from the first terminal device 101, the second terminal device 102, and the third terminal device 103. Accordingly, the information recommendation method system provided in this application embodiment can also be set in the first terminal device 101, the second terminal device 102, and the third terminal device 103, or in other terminal devices different from the first terminal device 101, the second terminal device 102, and the third terminal device 103.

[0044] It should be understood that Figure 1 The number of terminal devices, networks, and servers in the system is only a limited number. Depending on implementation needs, there can be any number of terminal devices, networks, and servers.

[0045] Figure 2 A flowchart of an information recommendation method according to an embodiment of this application is shown.

[0046] like Figure 2 As shown, the method includes operations S201 to S205.

[0047] In operation S201, the time sequence of dynamic network snapshots and the number of predetermined communities within a historical period are obtained. Nodes in the dynamic network represent users, and dynamic network snapshots represent the similarity of product preferences among different users at any given historical moment. Predetermined communities represent the product types preferred by users. The historical period includes T moments, where T is an integer greater than 1. The number of predetermined communities is K, where K is an integer greater than 1.

[0048] Dynamic network snapshot systems are represented as time series. Each time series It is an adjacency matrix, and the elements of the adjacency matrix are... Represents a node With nodes At any moment The association strength, referring to product preference similarity, is a non-negative real-valued continuous indicator calculated based on user behavior data, rather than a probability value. Specifically, this similarity is calculated based on the intensity of users' attention to the same product combinations (e.g., browsing time, click frequency) and similar holding combinations (e.g., holding quantity, transaction frequency). A higher value indicates more similar product preferences between the two nodes, while a value of zero indicates no association between them. Here, T represents the total number of observation periods, and N represents the total number of nodes in the network. Indicates a time index. Indicates the node index.

[0049] When recommending products based on user preferences, adjacency matrix elements Quantization Node With nodes At any moment The product preference similarity is based on the intensity of attention to the same product portfolio and similar holding portfolios. For example, the intensity of attention can be browsing time or click frequency, and the holding portfolio can be the holding amount or transaction frequency.

[0050] In operation S202, anchor information, node stability information, and network topology information of the global structure are extracted from the time-series sequence of the dynamic network snapshot. Among them, anchor information is used to characterize the product preference type at each historical moment; node stability information is used to characterize the stability of user behavior over time; and network topology information is used to characterize the association relationship established between different users at each historical moment based on the similarity of product preferences.

[0051] The anchor information for the global structure can be the product preference types at various historical moments. During dynamic evolution, the macro-level community structure of a network typically exhibits relative stability; for example, the main savings, financial management, and investment habits of a user group do not change completely in the short term. Establishing a global anchoring mechanism can prevent the algorithm from being dominated by local noise or the behavior of individual anomalous nodes, ensuring that the learned community structure remains rational and continuous at the macro-level.

[0052] Node stability information can represent the stability of user preferences over time. In dynamic networks, the evolutionary behavior of different nodes exhibits significant heterogeneity. Some nodes demonstrate high stability, with their adjacency relationships and community affiliations remaining continuous in adjacent time steps; while others undergo drastic changes, potentially completing community transfers within a short period. Applying a uniform temporal smoothing constraint to all nodes leads to two problems: insufficient constraints on stable nodes fail to effectively filter noise, while excessive constraints on changing nodes mask the true transfer signals. Therefore, an adaptive mechanism is needed to apply constraint strength differently based on the evolutionary characteristics of the nodes.

[0053] Network topology information can be the associations established between different users at different historical moments based on the similarity of product preferences. The basic assumption of network analysis is that connected node pairs in a network should tend to be similar in their latent semantic space. This assumption remains valid in dynamic scenarios and has significant business implications. In user scenarios, users with similar initial interaction behaviors often maintain similar product preference trajectories. Utilizing network topology to guide the learning process can strengthen consistency within the community and promote the smoothness of product preference trajectories.

[0054] In operation S203, based on the anchor point information, node stability information, and network topology information of the global structure, the randomly initialized parameter matrix is ​​iteratively optimized until the iteration termination condition is met, resulting in the target parameter matrix. The target parameter matrix includes the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T. Each element in the node community affiliation matrix represents the probability that each user belongs to the k-th community at time T; each element in the community transition matrix represents the probability that a user in any community will transition to the k-th community from time T-1 to time T; k is greater than or equal to 1 and less than or equal to K.

[0055] The node community affiliation matrix is ​​defined as follows:

[0056] (1)

[0057] Among them, the node community affiliation matrix elements Represents a node At any moment Belongs to the community The intensity or probability, Indicates time The node community affiliation matrix is ​​given by N, where N represents the total number of nodes in the network and K represents the number of predetermined communities.

[0058] When recommending products based on user preferences Community representatives Typical product preference patterns include: savings and wealth management, fund investment, and insurance planning. Quantization Node For the community The degree of belonging.

[0059] The community transition matrix can be defined as:

[0060] (2)

[0061] Among them, community transfer matrix elements Description from time At the time ,Community Transfer to the community The probability or intensity, Indicates from time At the time The community transition matrix, where K represents the number of predetermined communities.

[0062] In operation S204, a matrix multiplication is performed on the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T to generate the expected community affiliation matrix of each node at time T+1.

[0063] At any moment The node community affiliation matrix can be predicted from the previous node community affiliation matrix using the community transition matrix, and is defined as:

[0064] (3)

[0065] in, Indicates time The node community affiliation matrix This represents the node community affiliation matrix at time t-1. Indicates from time At the time The community transition matrix is ​​given by N, where N represents the total number of nodes in the network and K represents the number of predetermined communities.

[0066] Community Transfer Matrix elements Larger indicates at time Many users come from the community Turn to community Through analysis The temporal changes can identify a standardized path for recommending products based on user preferences.

[0067] In operation S205, based on the probability that each user belongs to the kth community at time T+1, target product information corresponding to the product type of the kth community is recommended to the target user.

[0068] Based on time series and what I have learned , Let represent the community transition matrix at any time t between time 1 and time T, and predict . Community distribution at any time:

[0069] (4)

[0070] in, This represents the expected community affiliation matrix at time T+1, with elements... Represents a node At time T+1, it belongs to the community. The predicted intensity, H T This represents the node community affiliation matrix at time T. This represents the community transition matrix from time T-1 to time T.

[0071] When recommending products based on user preferences, this prediction can anticipate changes in each user's product preferences one cycle in advance, providing a basis for preparing recommended content, adjusting product inventory, and allocating customer service resources.

[0072] In this application, the embodiments capture both the global community structure evolution pattern and accurately characterize the transfer behavior of individual nodes between different communities in a time-series network, thereby achieving accurate prediction of user product preferences and improving the accuracy of information recommendation.

[0073] Before performing the main optimization of the dynamic network, three types of key prior information need to be systematically extracted from the network snapshot data at various time points. This prior information provides structured constraints and guidance for the optimization process and is an important component of algorithm design. The prior information mainly includes three categories: node stability, which is used to characterize typical nodes in the macroscopic community structure to measure the stability of user behavior over time; and network topology information, which reflects the similarity relationships between nodes through the graph Laplacian matrix. User product preferences are only the basic data source for constructing behavioral vectors and network structure; the prior information is further extracted structural information based on this, used to guide the subsequent optimization process.

[0074] According to an embodiment of this application, extracting anchor information of the global structure from the time series of dynamic network snapshots may include: extracting the initial dynamic network snapshot at the initial moment from the time series of dynamic network snapshots; clustering the initial dynamic network snapshots according to a predetermined number of communities to obtain a clustering indicator matrix; wherein each element in the clustering indicator matrix represents the degree of preference of each user for historical product types at the initial moment; and determining the degree of preference of each user for historical product types at the initial moment as the anchor information of the global structure.

[0075] When extracting the initial dynamic network snapshot at the initial time from the time-series sequence of dynamic network snapshots, in some embodiments, the k-medoids clustering algorithm can be used to analyze the time. adjacency matrix Perform clustering and select The most representative node is selected as the cluster center.

[0076] The k-medoids algorithm, based on the median distance mechanism, exhibits better stability against outliers and heterogeneity. Cluster centers are actual nodes with clear business implications, and can be directly used for analyzing typical customer profiles or risk level benchmarks.

[0077] The clustering indicator matrix is ​​defined as follows:

[0078] (5)

[0079] in, Indicates time The k-medoids clustering indicator matrix, where each element represents the degree of preference of each user for historical product types at the initial time; It means if and only if the node Assigned to the There are three clusters, where N represents the total number of nodes in the network and K represents the number of predefined communities.

[0080] In the user-product interaction network, global structural anchor points identify typical user prototypes, such as "long-term, stable deposit type." These representative nodes provide stable reference points for the algorithm's macro-level interest distribution, thereby improving the accuracy of product recommendations.

[0081] According to embodiments of this application, extracting node stability information of the global structure from the time-series sequence of dynamic network snapshots may include: determining the degree of any node at time t as the sum of product preference similarities between any node in the dynamic network snapshot at time t and all nodes in the dynamic network except for any node; and determining the node stability information at time t as the ratio of the number of nodes that maintain association relationships between any node in the dynamic network snapshot from time t-1 to time t and all nodes in the dynamic network except for any node to the degree of any node at time t.

[0082] By designing the node stability matrix This quantifies the continuity of behavior of each node across adjacent time steps. For a node at time t, the stability index is defined as:

[0083] (6)

[0084] in, This indicates how much continuity the local connectivity of node i at time t has maintained compared to time t-1, that is, "what proportion of the nodes connected to node i at time t are also connected at time t-1"; Represents a node With nodes At any moment The strength of the association, Represents a node With nodes At any moment -1 correlation strength Let represent the sum of similarities between node i at time t and its N neighboring nodes j. This represents the number of neighbors that maintain a connection at both the current time t and the adjacent time t-1, where N represents the total number of nodes in the network. Indicates the node index. A value close to 1 indicates a high degree of continuity in adjacency relationships, while a value close to 0 indicates drastic changes in adjacency relationships. The stability indices of all nodes form a diagonal matrix. That is, the diagonal matrix of node stability In equation (6), i ≠ j.

[0085] It should be noted that the number of neighbors represents the weighted cumulative sum of the association strengths of neighboring nodes that have a relationship at both time t and time t-1. It is a continuous real value, not an integer count. When a node... At any moment and time All with nodes When there is a strong correlation, A larger product of the factors indicates a higher contribution to the cumulative sum. If the association strength is zero or close to zero at any given time, the contribution of that node to the cumulative sum is close to zero, which is equivalent to nodes that are not continuously connected not being included. Therefore, this cumulative amount semantically reflects the total association strength contributed by neighboring nodes that maintain a continuous connection across two adjacent time points. A larger value indicates more continuously connected neighboring nodes and a stronger association.

[0086] Based on this, the stability index measures the proportion of the local connectivity of node i at time t that continues from time t-1. The value is between [0,1], with a value close to 1 indicating a high degree of continuity in the adjacency relationship and a value close to 0 indicating a drastic change in the adjacency relationship.

[0087] Therefore, in this embodiment, the stability index is defined as the sum of the neighbor strengths of node i that remain connected in two adjacent time intervals, divided by the total connection strength of node i at the current time t. For example, the "proportion" of connections from historical continuity in the connection relationships at time t can take values ​​between [0,1]. A value close to 1 indicates highly continuous neighbor relationships, while a value close to 0 indicates drastic changes in adjacency relationships. A high value indicates that the user's preferences are consistently aligned with those of a similar group of users / products; a low value indicates that the user's product preferences are shifting.

[0088] Introduce a penalty term into the objective function:

[0089] (7)

[0090] The optimization objective function is equivalent to:

[0091] (8)

[0092] in, Indicates time The node community affiliation matrix Indicates time The node community affiliation matrix Indicates from time At the time Community transfer matrix, This represents the diagonal matrix representing the nodal stability at time t. yes The OK, Indicates time Stability indicators This represents the weight parameters for the temporal continuity constraint. , The trace of a matrix is ​​the sum of its diagonal elements. This represents the Hadamard product (element-by-element multiplication). This represents the 2-norm (Euclidean norm) of a vector.

[0093] The penalty term constrains the continuity of community affiliation over time. Specifically, it compares the node community affiliation matrix learned at the current time t. Based on the community affiliation matrix of node t-1 at the previous time step and community transfer matrix The predicted results The model penalizes deviations between the two, thus preventing unreasonable and drastic changes in community divisions at adjacent time points. Simultaneously, the penalty term utilizes historical state information to guide the learning of the current community structure, enabling the model to depict the dynamic patterns of community evolution over time.

[0094] In addition, in the formula This represents the stability index of node i in the network structure between two adjacent time points. Its value ranges from [0, 1], with a larger value indicating a more stable neighbor relationship. (Matrix) It is composed of stability indicators of all nodes The resulting diagonal matrix is ​​used to impose constraints of varying strengths on different nodes in the penalty term. Specifically, Larger, more stable nodes are subject to stronger temporal continuity constraints, while nodes with lower stability are allowed to undergo greater changes in their community affiliation, thus enabling adaptive modeling of stable and transitioning nodes.

[0095] for For larger, stable nodes, a stronger constraint is imposed as a penalty, requiring their community affiliation to remain smooth over time to prevent noise interference. For smaller, more variable nodes, the penalty is automatically relaxed, allowing for shifts in community affiliation and capturing genuine transfer behavior. When recommending products to users, this mechanism can distinguish between users with stable long-term preferences and those who rapidly shift their preferences.

[0096] During the optimization process, the stability matrix serves as an adaptive weighting term: stronger temporal continuity constraints are imposed on nodes with high stability, while constraints are appropriately relaxed for nodes experiencing drastic changes. When recommending products to users based on their preferences, stable users are better suited to a strategy of continuous deepening and cross-selling, while users who are shifting their preferences are targeted with precise push notifications of new products in the early stages of preference shifts.

[0097] According to an embodiment of this application, extracting network topology information of the global structure from the time sequence of dynamic network snapshots may include: determining the degree of any node at time t as the sum of product preference similarities between any node in the dynamic network snapshot at time t and all nodes in the dynamic network except for any node; and determining the difference between the degree of any node at time t and the dynamic network snapshot at time t as network topology information.

[0098] Network topology information can be the relationships established between different users at different historical moments based on the similarity of product preferences. The learning process can be guided by the network topology by defining a graph Laplacian matrix.

[0099] (9)

[0100] in, Represents a diagonal matrix. Indicates time The adjacency matrix, Let represent the graph Laplace matrix at time t.

[0101] For any vector The Laplace matrix satisfies the key property:

[0102] (10)

[0103] in, Represents the element in the i-th row. This represents the element in the j-th row.

[0104] Introducing a regularization term into the objective function Expanded as:

[0105] (11)

[0106] in, Denotes the graphical Laplace matrix at time t. Indicates time The node community affiliation matrix yes The OK, yes The j-th line, Represents the node affiliation matrix transpose, Represents a node With nodes At any moment The strength of the association, Represents a node With nodes At any moment The strength of the association, Represents the topology smoothing constraint weight parameters. >0, Let N represent the 2-norm (Euclidean norm) of a vector, and let N represent the total number of nodes in the network.

[0107] The regularization term, in matrix form, is transformed into a more intuitive node-level computation. This term essentially penalizes the weighted sum of squared differences in the representations of all neighboring nodes' communities. If two nodes had a strong connection in the network at the previous time step, then... If they are larger, then their community representation at the current moment is greater. and The representations should be as close as possible. The network topology from the previous time step is used to constrain the current community representation, so that nodes with strong connections or similar behaviors in the historical network have similar community affiliation representations at the current time step.

[0108] Formula (11) penalizes the previous time step. There are connected node pairs at the current time. The differences in the latent representation space reflect the basic assumption of network analysis: neighboring nodes should tend to be similar in the latent semantic space.

[0109] In user-product interaction networks, network topology regularization constraints maintain the proximity of users with similar interest patterns in the potential space, smoothly depicting the user's preference transfer trajectory.

[0110] According to an embodiment of this application, based on the anchor point information of the global structure and the initial dynamic network snapshot at the initial time, the randomly initialized parameter matrix is ​​iteratively optimized to obtain the node community affiliation matrix, the first basis matrix, and the second basis matrix at the initial time, so that the target difference is less than a predetermined difference threshold; wherein, the target difference includes the difference between the product of the node community affiliation matrix and the first basis matrix at the initial time and the initial dynamic network snapshot, and the difference between the product of the node community affiliation matrix and the second basis matrix at the initial time and the clustering indicator matrix at the initial time.

[0111] For the initial optimization objective, for the first snapshot (t=1) of the dynamic network time series, due to the lack of prior historical information, the optimization framework adopts a simplified bi-objective form.

[0112] (12)

[0113] in, Let be the first basis matrix at the initial time. Let be the second basis matrix at the initial time. This is the initial node community affiliation matrix. For global alignment weight parameters, , Denotes the Frobenius norm. This represents a network snapshot at the initial moment. This represents the differences in network structure reconstruction. This represents the k-medoids clustering indicator matrix at the initial time step. This indicates global mode alignment differences.

[0114] The network structure reconstruction difference term requires the node community affiliation matrix at the initial time step. Through the first basis matrix Accurate reconstruction / approximation of the initial dynamic network snapshot This is the difference between the product of the node community affiliation matrix and the first basis matrix at the initial moment and the initial dynamic network snapshot. Its theoretical basis is Non-negative Matrix Factorization (NMF), which extracts latent community features through low-rank decomposition. In the client network, this term ensures... This accurately reconstructs the actual interaction intensity of customers with each product category during the current period; in the risk network, it ensures that the initial risk association topology is accurately reconstructed. The closer the reconstructed result is to the real network structure, the smaller this term's value. This term ensures that the latent representation learned by the model can truly reflect the node connection relationships in the current network, thereby extracting the potential community structure within the network.

[0115] The global mode alignment difference term will be the node community affiliation matrix at the initial time. k-medoids clustering indicator matrix anchored to the initial time step This is the difference between the product of the node community affiliation matrix and the second basis matrix at the initial time and the clustering indicator matrix at the initial time. (Parameters) Adjusting the strength of this constraint reflects the degree of confidence in the global clustering results. A second basis matrix is ​​introduced at the initial time step. Rather than reuse The reason is that network structure reconstruction focuses on the accurate restoration of local connection density, while global pattern alignment emphasizes the maintenance of the macroscopic community framework, and decoupling design avoids mutual interference between the two. When recommending products based on user preferences, the differences in network structure reconstruction and global pattern alignment ensure that the initial community structure is closely aligned with the typical user prototype.

[0116] According to the embodiments of this application, based on the anchor point information of the global structure, the node stability information, and the network topology information, the node community affiliation matrix, the first basis matrix, and the second basis matrix at the initial moment are iteratively optimized to obtain the target parameter matrix.

[0117] For iterative optimization of network structure reconstruction:

[0118] (13)

[0119] in, Let the adjacency matrix at time t be denoted as . Denotes the first basis matrix. Represents the node community affiliation matrix. Represents the node community affiliation matrix transpose, Describing the Frobenius norm, for example .

[0120] The iterative optimization term for network structure reconstruction ensures the node community affiliation matrix. Based on the actual observation data at the current time t, through the first basis matrix Adjacency matrix for exact approximation of time t First basis matrix It can be interpreted as Basic connection modes, Each row represents the combined weight of the corresponding node for these patterns. If the iterative optimization term for network structure reconstruction is ignored, the optimization result may appear smooth or idealized under other constraints, resulting in a serious disconnect from actual network data. The iterative optimization term for network structure reconstruction forms the cornerstone of the entire optimization framework, ensuring that all prior constraints are based on data fidelity.

[0121] First basis matrix It is the basic connectivity pattern matrix learned through the nonnegative matrix factorization (NMF) framework. Indicates the number of communities reserved. This represents the total number of nodes in the network. The first basis matrix... The row corresponds to the first Basic connection modes, node community affiliation matrix Each row represents the corresponding node's relationship to this The combined weights of the basic connection patterns. The optimization objective of the first basis matrix is ​​to make the node community affiliation matrix... With the first basis matrix The product reconstructs the current moment as accurately as possible. adjacency matrix (See Formula (13)) thus ensuring that the learned community structure faithfully reflects the actual node relationships at the current moment.

[0122] For iterative optimization under global mode alignment:

[0123] (14)

[0124] in, This represents the k-medoids clustering indicator matrix. Describes the second basis matrix. Represents the node community affiliation matrix. Represents the node community affiliation matrix transpose, Describing the Frobenius norm, for example ; This represents the global alignment weight parameter. >0.

[0125] The iterative optimization term under global pattern alignment will include the community affiliation matrix. Anchored to k-medoids clustering indicator matrix This ensures that the resulting community structure remains continuous and robust at the overall level. Macro-level organizational patterns in dynamic networks typically exhibit relative stability, and iterative optimization terms under global pattern alignment avoid excessive perturbation of the macro-framework due to local fluctuations through global anchoring. Parameters Regulation constraint strength: Relatively large Suitable for networks with highly durable macroscopic structures, enhancing global stability; smaller Suitable for networks whose structure may undergo significant reorganization, preserving adjustment space. Employs a second basis matrix. Rather than reuse This allows global pattern alignment to be performed in an independent feature subspace, avoiding conflicts with local structure reconstruction.

[0126] Second basis matrix It is an independent basis matrix used for global pattern alignment. Its optimization objective is to make the node community affiliation matrix... With the second basis matrix The product should be as close as possible to the initial time. -medoids clustering indicator matrix (See Formula (14)) thereby anchoring the learned community structure to the macro clustering framework at the global level, preventing excessive deviation of the macro community structure due to local noise.

[0127] The first and second basis matrices are independent of each other and act on the two objectives of local structure reconstruction and global structure anchoring, respectively. The decoupled design avoids mutual interference between the two.

[0128] According to the embodiments of this application, the expected product preference of a user at any historical moment corresponding to any node in the dynamic network calculated based on the target parameter matrix obtained above matches the time series sequence of the dynamic network snapshot, and the changing trends of product preferences among nodes with related relationships in the dynamic network are similar.

[0129] For time series At this moment, construct a complete four-objective optimization framework: (15)

[0130] in, Let the adjacency matrix at time t be denoted as . Denotes the first basis matrix. This represents the node community affiliation matrix at time t. Indicates time The node community affiliation matrix Represents the node community affiliation matrix transpose, This represents the k-medoids clustering indicator matrix. Describes the second basis matrix. This represents the diagonal matrix representing the nodal stability at time t. Indicates from time At the time Community transfer matrix, Denotes the graph Laplace matrix at time t-1. For global alignment weight parameters, This represents the weight parameters for the temporal continuity constraint. These are the topology smoothing constraint weight parameters. , The Hadamard product represents element-wise multiplication. It is the Frobenius norm. , The trace of a matrix is ​​the sum of its diagonal elements. This represents the iterative optimization of network structure reconstruction. This indicates iterative optimization under global pattern alignment. This represents an adaptive temporal continuity constraint. This represents a topological smoothing constraint.

[0131] The adaptive temporal continuity constraint term achieves an accurate characterization of the heterogeneity of dynamic network evolution through a temporal smoothing mechanism that adapts to node stability. Its equivalent form is:

[0132] (16)

[0133] in for The Rows represent nodes At any moment Actual community affiliation; Indicates time The node community affiliation matrix Indicates from time At the time Community transfer matrix, This represents the expected community affiliation of the i-th row based on the previous time step and the transition matrix. For nodes Stability indicators Let N be the vector 2-norm (Euclidean norm), and let N represent the total number of nodes in the network.

[0134] The physical meaning of the adaptive temporal continuity constraint term is as follows: The expected state at the current moment based on historical patterns and transitional patterns. Quantify the discrepancy between reality and expectations. Apply differentiated constraints to different nodes. For stable nodes ( The stability index is large, so strong temporal continuity constraints are applied to limit deviations from historical expectations and maintain stable evolution. For variable nodes ( It has a small stability index, imposes weak temporal continuity constraints, allows for flexible adjustment, and can capture rapid changes or abrupt changes. Parameters Adjusting the overall time series smoothing intensity: Larger Suitable for slowly evolving networks, producing more continuous trajectories; smaller Suitable for rapidly evolving networks, retaining state transition capabilities.

[0135] The topological smoothness constraint term is based on a core assumption of network analysis: directly connected nodes should have high similarity in the latent representation space. According to the quadratic form property of the graph Laplacian matrix, this term can be expanded as follows:

[0136] (17)

[0137] in, Represents the node community affiliation matrix. Represents the node community affiliation matrix transpose, This represents the Laplace matrix of the graph at time t-1. for The Rows represent nodes At any moment The actual community affiliation Represents a node With nodes At any moment -1 correlation strength The trace of a matrix is ​​the sum of its diagonal elements. Let N be the vector 2-norm, also known as the Euclidean norm, and let N represent the total number of nodes in the network.

[0138] For the node pairs that were connected at the previous time t-1 ,if If the larger value represents a strong connection, then a penalty will be imposed at the current time t. This ensures that adjacent nodes remain similar in the latent space. The graph Laplacian matrix from the previous time step t-1 is used. Instead of the graph Laplace matrix at the current time t There are two reasons: First, the adjacency matrix at time t First, network structure constraints have been reconstructed to avoid circular dependencies; second, the continuous impact of historical correlations on the current time t. Parameters Overall strength of topological smoothing: Relatively large Suitable for networks with significant local clustering structures, enhancing consistency within communities; smaller Suitable for sparsely connected or highly dynamic networks, avoiding excessive constraints.

[0139] In the spatial dimension, network structure reconstruction constraints ensure faithful reproduction of local connection patterns, while global pattern alignment constraints maintain the stability of the macroscopic community framework. Together, they achieve a balance between local accuracy and global consistency. In the temporal dimension, adaptive temporal continuity constraints are implemented through the community transition matrix. and node stability diagonal matrix The modeling nodes exhibit differentiated evolution patterns, and topological smoothing constraints are achieved through the graph Laplacian matrix. Implicit reinforcement of local consistency among neighboring nodes, working together to achieve a balance between individual evolutionary flexibility and topological continuity. Four constraints constitute a complete system of checks and balances: structural reconstruction prevents deviation from real data, global alignment prevents local noise dominance, temporal continuity prevents over-smoothing, and topological smoothing prevents fragmented communities. Parameters It provides a fine-tuning mechanism, which can be determined through cross-validation of historical data or by combining domain knowledge, such as user behavior inertia and the speed of risk contagion. This maximizes the model's accuracy in depicting dynamic processes.

[0140] Furthermore, the complete optimization problem can be formulated as follows:

[0141] (18)

[0142] in, It is a joint function of four objectives. Let be the first basis matrix. This is the second basis matrix. Let be the node community affiliation matrix at time t. From time At the time Community transfer matrix.

[0143] The Lagrange multiplier method is used to handle non-negative constraints. By introducing non-negative Lagrange multipliers, the constrained optimization problem is transformed into an unconstrained form. The iterative update rules for each variable are derived based on the Karush-Kuhn-Tucker (KKT) conditions. The KKT conditions include gradient conditions (first-order optimality), complementary relaxation conditions, primal feasibility, and dual feasibility, ensuring that the obtained solution satisfies the first-order optimality requirement.

[0144] An alternating optimization strategy is adopted to iteratively optimize the four variable matrices in an alternating manner:

[0145] In each step, update one variable while keeping the others fixed until convergence.

[0146] For the first basis matrix The objective term only involves the first term, and its gradient is:

[0147] (19)

[0148] The solutions for the positive and negative parts are , The update rules are as follows:

[0149] (20)

[0150] in, Let be the first basis matrix. Represents the node community affiliation matrix. Represents the node community affiliation matrix transpose, Let be the adjacency matrix at time t. The Hadamard product represents element-wise multiplication.

[0151] For the second basis matrix The target item only involves the second item, and the update rule is:

[0152] (twenty one)

[0153] in, This is the second basis matrix. Represents the node community affiliation matrix. Represents the node community affiliation matrix transpose, For a moment k-medoids clustering indicator matrix, The Hadamard product represents element-wise multiplication.

[0154] For the node community affiliation matrix All four terms are involved, and the total gradient is:

[0155] (twenty two)

[0156] The update rules are as follows:

[0157] (twenty three)

[0158] in, Let be the first basis matrix. This is the second basis matrix. Represents the node community affiliation matrix. Represents the node community affiliation matrix transpose, Let the adjacency matrix at time t be denoted as . Indicates time k-medoids clustering indicator matrix, This represents the degree diagonal matrix at time t. Let be the diagonal matrix for node stability. For community transfer matrix, For global alignment weight parameters, This represents the weight parameters for the temporal continuity constraint. These are the topology smoothing constraint weight parameters. , This represents the Hadamard product (element-by-element multiplication).

[0159] For community transfer matrix The target item only involves the third item, and the update rule is:

[0160] (twenty four)

[0161] in, From time arrive Community transfer matrix, Represents the community affiliation matrix. Indicates time The node community affiliation matrix express matrix transpose, For a moment The diagonal matrix of node stability, This represents the Hadamard product (element-by-element multiplication).

[0162] The multiplicative update rule has three important theoretical properties. First, nonnegativity is preserved: all variables are initialized to be nonnegative, and the multiplicative form of the update rule naturally preserves nonnegativity, ensuring that all variables remain nonnegative throughout the iteration process. Second, the objective function monotonically decreases: each update step strictly reduces (or keeps constant) the overall objective function value, ensuring stable convergence of the algorithm and avoiding oscillations or divergence. Third, the Karush-Kuhn-Tucker condition is satisfied: the convergence point satisfies the Karush-Kuhn-Tucker optimality condition of the original problem, providing a theoretical guarantee for local optima.

[0163] The relative rate of change of the objective function is used as the convergence criterion:

[0164] (25)

[0165] in, For the first The objective function value of the next iteration. For example, a preset threshold. Desirable In practical applications, k-medoids clustering results are used for initialization, and parameters are set appropriately. The algorithm typically converges within 50-100 iterations.

[0166] for Each node The network of communities has a single iteration complexity of O(n). The space complexity of the main storage matrix is ​​O(n). This can be optimized using the following strategy: utilizing the adjacency matrix. The sparsity is optimized using sparse matrices; matrix operations can be parallelized; incremental updates are used when new data arrives. On a network scale of millions of customers, standard servers can complete single-time processing in minutes, meeting the needs of batch offline analysis.

[0167] According to embodiments of this application, the information recommendation method based on the joint global structure and local node transfer may further include: obtaining a dynamic network snapshot at time T+1; updating the time sequence of the dynamic network snapshot using the dynamic network snapshot at time T+1 to obtain an updated time sequence of the dynamic network snapshot; iteratively optimizing a randomly initialized parameter matrix based on the updated time sequence of the dynamic network snapshot until the iteration termination condition is met to obtain the actual node community affiliation matrix at time T+1; and adjusting the constraint parameters used for the iterative optimization operation in response to the error between the actual node community affiliation matrix at time T+1 and the expected community affiliation matrix of each node at time T+1 being greater than a predetermined error threshold; wherein the constraint parameters include: a first parameter for constraining the global structure of the dynamic network and a second parameter for constraining the temporal evolution of the dynamic network.

[0168] After learning all historical moments, the learned patterns are used to predict future states. Based on the learning results at the last observation time T, a community affiliation prediction for the future time T+1 is generated.

[0169] (26)

[0170] in, Indicates the last observation time The node community affiliation matrix Indicates from time arrive Community transfer matrix, Indicates prediction Moment Community Affiliation Matrix.

[0171] The prediction matrix of the first Line number Column elements:

[0172] (27)

[0173] Where T represents the total number of observation periods, N represents the total number of nodes in the network, and K represents the number of pre-defined communities. Indicates the node index. Indicates a community index. Let represent the probability that node i belongs to community m at time T. This represents the probability that community m will migrate to community k from time T-1 to time T. This represents the predicted probability that node i belongs to community k at time T+1.

[0174] Prediction results A "soft assignment" is given, where each node has a correlation strength or probability value for each community, preserving complete uncertainty information. In scenarios requiring explicit category labels, hard classification can be achieved by taking the maximum value.

[0175] (28)

[0176] in, This represents the predicted probability that node i belongs to community k at time T+1. This represents the predicted community affiliation label of node i in the k-medoids clustering indicator matrix at time T+1.

[0177] Soft allocation is suitable for generating diverse recommended content or detailed risk assessments, while hard classification is suitable for clarifying decision-making criteria and business operations.

[0178] Prediction error monitoring involves comparing predicted values ​​with actual learned values.

[0179] (29)

[0180] in, express The actual node community affiliation matrix at any given time. Indicates prediction Moment Community Affiliation Matrix It is the Frobenius norm. This error can be used to monitor whether there are any abnormalities in the system's evolution. A sudden increase in prediction error indicates that the system has experienced external shocks or changes in its internal mechanisms, requiring timely attention and analysis.

[0181] The constraint parameters are adaptively adjusted based on prediction error feedback, dynamically adjusting the global pattern alignment weights used to constrain the global structure of the dynamic network. and the temporal continuity constraint weight parameters used to constrain the temporal evolution of dynamic networks If the time series prediction error is large, it can be reduced. This reduces the temporal continuity constraints, allowing for faster adaptation to new patterns. If the structural reconstruction error is large, adjustments may be necessary. or This closed-loop mechanism makes the method a dynamic system capable of continuous learning and self-adjustment, making it more suitable for handling complex and ever-changing networks in the real world.

[0182] According to an embodiment of this application, the complete algorithm flow includes the following steps:

[0183] The system consists of four phases: system initialization, time-series evolution learning, prediction generation, and closed-loop update.

[0184] During system initialization: Input data: Time series Number of communities reserved ,parameter Preset threshold ,For example Desirable .

[0185] Global pattern recognition: for the initial time series sequence Perform k-medoids clustering to obtain the clustering indicator matrix. When recommending products based on user preferences, identify... Representative users of a typical product preference pattern.

[0186] Variable initialization: Randomly initialize the first basis matrix, the second basis matrix, and the node community affiliation matrix as non-negative matrices. or ,in This indicates a truncated normal distribution (keeping only non-negative values).

[0187] Initial optimization: Optimization using a simplified bi-objective function: .

[0188] Using the above multiplication update rule, iterate until the change in the objective function is less than a preset threshold. This establishes a stable initial state for subsequent time series analysis.

[0189] In the temporal evolution learning phase: For Perform the following steps.

[0190] Prior information calculation: Calculate the clustering indicator matrix Node stability Construct a diagonal matrix Graph Laplace matrix .

[0191] Variable initialization: using an iterative strategy , , Or prediction strategy (If a prediction has already been generated in the previous time step). The evolution matrix is ​​initialized to... or .

[0192] Alternating optimization: Repeat the following updates until the objective function changes less than a preset threshold. Or reach the maximum number of iterations (e.g., 100):

[0193] (30)

[0194] (31)

[0195] in, Denotes the first basis matrix. This represents the second basis matrix.

[0196] (32)

[0197] (33)

[0198] Convergence criterion: Calculate the relative rate of change of the objective function.

[0199] (34)

[0200] like or reach If the current optimization fails, the result will be saved. Now, let's move on to the next moment.

[0201] In the prediction generation phase: future state projection can be based on the last observation time. The learning results generate future moments. Community affiliation prediction:

[0202] (35)

[0203] Output results: The complete learning results are output, including the node community affiliation matrix sequence. Community transition matrix sequence Expected community affiliation matrix Clustering indicator matrix ).

[0204] During the closed-loop update phase: when the adjacency matrix... Upon arrival, a closed-loop feedback mechanism is activated.

[0205] Warm start initialization: Accelerating a new round of optimization by leveraging prediction results: , , , .

[0206] Prediction error monitoring: Completed After time-based optimization, the prediction error is calculated:

[0207] (36)

[0208] like If the error level significantly exceeds the historical error level (e.g., exceeding the mean plus twice the standard deviation), an anomaly detection warning is triggered, indicating that the system may have experienced structural changes or external shocks.

[0209] Hyperparameter adaptive tuning

[0210] Hyperparameters are adjusted based on prediction error feedback. If the time series error remains consistently high: (Reduce temporal constraint hyperparameters to enhance adaptability). If the structural reconstruction error is too high: (Enhanced global anchoring improves stability). The adjustment range is determined through cross-validation using historical data to avoid parameter drift.

[0211] In the complete process of recommending products based on user preferences—specifically, data preparation and network construction—user behavior data can be extracted from business systems, including product browsing history, product purchase history, and product ownership status. For example, product browsing history can include browsing duration and frequency; product purchase history can include transaction amount and frequency; and product ownership status can include the amount held and the duration of holding. Choosing a time granularity, such as monthly or quarterly, divides the time series into... One observation window.

[0212] For each time window Construct an adjacency matrix .element Quantization Node With nodes At any moment The product preference similarity is calculated as follows:

[0213] (37)

[0214] in For nodes At any moment Product preference feature vector, For node j at time... The product preference feature vector is calculated with the total number of product categories as one dimension. Each dimension's value is weighted by factors such as browsing time, click frequency, and transaction amount. Similarity threshold filtering reduces noise edges, retaining only the most relevant features. (like () edge.

[0215] Model parameter settings: The number of communities can be set. This can be determined through business experience, for example, by categorizing investors as conservative savers, steady investors, balanced investors, growth investors, or aggressive equity investors, or by using clustering quality indicators such as the Silhouette Coefficient. Parameters can also be set. Recommended initial value is (Balancing data fidelity and global anchoring) (Considering user behavior inertia, the temporal evolution should be appropriately smoothed.) (Utilize user-similar network topology, but without over-constraining). Optimization can be achieved on historical data using leave-one-out cross-validation or grid search.

[0216] Model Execution and Result Interpretation: Execute the above algorithm process to obtain the key output matrix.

[0217] Node Community Affiliation Matrix Each line represents a user in The strength of belonging to a community. For users , Quantify the degree of inclination towards each typical product preference pattern. Hard classification is achieved through... Identify the user's primary product preference categories, and use soft allocation to retain diverse preference information.

[0218] Community Transfer Matrix :element Indicates from the community To the community The transition probability or intensity. Through analysis By observing temporal changes, we can identify the dominant path for recommending user product preferences. For example, if we continuously observe... A larger value indicates a shift from "savings-oriented" to "investment-oriented," and The subsequent increase indicates a shift from "financial management" to "investment," suggesting a standardized evolutionary path of "savings → financial management → investment."

[0219] Node stability diagonal matrix : diagonal element Quantization Node Product preference stability. The users are highly stable, making them suitable for long-term relationship maintenance and in-depth cross-selling; Users are highly volatile and in a period of interest transition, so they should be given special attention and personalized guidance.

[0220] Expected Community Affiliation Matrix Predict the product preference distribution for each user one period in advance. For customers... ,like The increase is significant, indicating a rise in their preference for "investment-type" products. Targeted product recommendations can be prepared in advance.

[0221] Business decision support: Based on the above outputs, the following product recommendation strategies can be formulated.

[0222] Precise customer segmentation: based on node community affiliation matrix Divide users into For each group, we design differentiated product portfolios and service solutions.

[0223] Interest Evolution Path Identification: Analysis of Community Transition Matrix Time Series It identifies high-frequency evolution paths, providing a basis for product line planning and customer lifecycle management.

[0224] Timing of Personalized Recommendations: Combining Stability Diagonal Matrix And expected community affiliation matrix Identify users who are about to shift their product preferences (indicating decreased stability and predicted changes in community affiliation) and intervene precisely during the transition window.

[0225] Product recommendation system optimization: Utilize soft allocation results to generate diversified recommendations, recommending featured products to communities with high membership levels and exploratory products to communities with medium membership levels, thereby improving recommendation coverage and conversion rates.

[0226] Figure 3 A block diagram of an information recommendation method apparatus according to an embodiment of this application is shown.

[0227] like Figure 3 As shown, the device 300 includes an acquisition module 301, an extraction module 302, an optimization module 303, a generation module 304, and a recommendation module 305.

[0228] The acquisition module 301 is used to acquire the time sequence of dynamic network snapshots and the number of predetermined communities within a historical period. Nodes in the dynamic network represent users, and dynamic network snapshots represent the similarity of product preferences between different users at any historical moment. Predetermined communities represent the product types preferred by users. The historical period includes T moments, where T is an integer greater than 1. The number of predetermined communities is K, where K is an integer greater than 1.

[0229] The extraction module 302 is used to extract anchor information, node stability information and network topology information of the global structure from the time sequence of dynamic network snapshots. Among them, the anchor information is used to characterize the product preference type at each historical moment; the node stability information is used to characterize the stability of user behavior over time; and the network topology information is used to characterize the association relationship established between different users at each historical moment based on the similarity of product preferences.

[0230] The optimization module 303 is used to iteratively optimize a randomly initialized parameter matrix based on the anchor point information, node stability information, and network topology information of the global structure, until the iteration termination condition is reached to obtain the target parameter matrix. The target parameter matrix includes the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T. Each element in the node community affiliation matrix represents the probability that each user belongs to the k-th community at time T. Each element in the community transition matrix represents the probability that a user in any community will transfer to the k-th community from time T-1 to time T. k is greater than or equal to 1 and less than or equal to K.

[0231] The generation module 304 is used to perform matrix multiplication on the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T to generate the expected community affiliation matrix of each node at time T+1.

[0232] The recommendation module 305 is used to recommend target product information of the product type corresponding to the k community to the target user based on the probability that each user belongs to the k community at time T+1.

[0233] Any one or more of the modules, submodules, units, and subunits according to embodiments of this application, or at least some of their functions, can be implemented in one module. Any one or more of the modules, submodules, units, and subunits according to embodiments of this application can be divided into multiple modules for implementation.

[0234] Any one or more of the modules, submodules, units, and subunits according to the embodiments of this application can be at least partially implemented as hardware circuits, such as field-programmable gate arrays (FPGAs), programmable logic arrays (PLAs), systems-on-a-chip, systems-on-a-substrate, systems-on-package, application-specific integrated circuits (ASICs), or implemented in hardware or firmware by any other reasonable means of integrating or packaging circuits, or implemented in software, hardware, and firmware, or in any appropriate combination of any of these three methods. Alternatively, any one or more of the modules, submodules, units, and subunits according to the embodiments of this application can be at least partially implemented as computer program modules, which can perform corresponding functions when the computer program module is run.

[0235] For example, any number of the acquisition module, extraction module, optimization module, generation module, and recommendation module can be combined into one module / unit / subunit, or any one of these modules / units / subunits can be split into multiple modules / units / subunits. Alternatively, at least part of the functionality of one or more of these modules / units / subunits can be combined with at least part of the functionality of other modules / units / subunits and implemented in one module / unit / subunit. According to embodiments of this application, at least one of the acquisition module, extraction module, optimization module, generation module, and recommendation module can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging the circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, at least one of the acquisition module, extraction module, optimization module, generation module, and recommendation module can be at least partially implemented as a computer program module, which can perform corresponding functions when the computer program module is run.

[0236] It should be noted that the apparatus portion for the information recommendation method in the embodiments of this application corresponds to the information recommendation method portion in the embodiments of this application. The description of the apparatus portion for the information recommendation method is specifically referred to in the information recommendation method portion, and will not be repeated here.

[0237] Figure 4 A block diagram of an electronic device suitable for implementing the information recommendation method described above, according to an embodiment of this application, is shown. Figure 4 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of this embodiment.

[0238] like Figure 4 As shown, an electronic device according to an embodiment of this application includes a processor 401, which can perform various appropriate actions and processes according to a program stored in ROM 402 or a program loaded from storage portion 408 into RAM 403. The processor 401 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor, such as an application-specific integrated circuit (ASIC), etc. The processor 401 may also include onboard memory for caching purposes. The processor 401 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of this application.

[0239] RAM 403 stores various programs and data required for the operation of the electronic device. Processor 401, ROM 402, and RAM 403 are interconnected via bus 404. Processor 401 executes various operations of the method flow according to embodiments of this application by executing programs in ROM 402 and / or RAM 403. It should be noted that the programs may also be stored in one or more memories other than ROM 402 and RAM 403. Processor 401 may also execute various operations of the method flow according to embodiments of this application by executing programs stored in said one or more memories.

[0240] According to embodiments of this application, the electronic device may further include an input / output (I / O) interface 405, which is also connected to a bus 404. The electronic device may also include one or more of the following components connected to the input / output (I / O) interface 405: an input section 406 including a keyboard, mouse, etc.; an output section 407 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 408 including a hard disk, etc.; and a communication section 409 including a network interface card such as a LAN card, modem, etc. The communication section 409 performs communication processing via a network such as the Internet. A drive 410 is also connected to the input / output (I / O) interface 405 as needed. A removable medium 411, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 410 as needed so that computer programs read from it can be installed into the storage section 408 as needed.

[0241] According to embodiments of this application, the method flow according to embodiments of this application can be implemented as a computer software program. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowchart. In such embodiments, the computer program can be downloaded and installed from a network via communication section 409, and / or installed from removable medium 411. When the computer program is executed by processor 401, it performs the functions defined in the system of embodiments of this application. According to embodiments of this application, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0242] This application also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0243] According to embodiments of this application, the computer-readable storage medium can be a non-volatile computer-readable storage medium. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0244] For example, according to embodiments of this application, a computer-readable storage medium may include ROM 402 and / or RAM 403 and / or one or more memories other than ROM 402 and RAM 403 as described above.

[0245] Embodiments of this application also include a computer program product comprising a computer program containing program code for performing the methods provided in the embodiments of this application. When the computer program product is run on an electronic device, the program code is used to enable the electronic device to implement the information recommendation method provided in the embodiments of this application.

[0246] When the computer program is executed by the processor 401, it performs the functions defined in the system / apparatus of this application embodiment. According to the embodiments of this application, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0247] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and downloaded and installed via communication section 409, and / or installed from removable medium 411. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0248] According to embodiments of this application, program code for executing the computer programs provided in the embodiments of this application can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0249] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions. Those skilled in the art will understand that the features described in the various embodiments of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, without departing from the spirit and teachings of this application, the features described in the various embodiments of this application can be combined and / or combined in various ways. All such combinations and / or combinations fall within the scope of this application.

[0250] The embodiments of this application have been described above. However, these embodiments are merely illustrative and not intended to limit the scope of this application. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Without departing from the scope of this application, those skilled in the art can make various substitutions and modifications, all of which should fall within the scope of this application.

Claims

1. An information recommendation method, characterized in that, include: Obtain the time-series sequence of dynamic network snapshots and the number of predetermined communities within a historical period. Nodes in the dynamic network represent users, and the dynamic network snapshots represent the product preference similarity between different users at any historical moment. Predetermined communities represent the product types preferred by users. The historical period includes T moments, where T is an integer greater than 1. The number of predetermined communities is K, where K is an integer greater than 1. Anchor point information, node stability information, and network topology information of the global structure are extracted from the time-series sequence of the dynamic network snapshots. The anchor point information is used to characterize the product preference type at each historical moment; the node stability information is used to characterize the stability of user behavior over time; and the network topology information is used to characterize the association relationship established between different users at each historical moment based on the similarity of product preferences. Based on the anchor point information, node stability information, and network topology information of the global structure, the randomly initialized parameter matrix is ​​iteratively optimized until the iteration termination condition is met, resulting in the target parameter matrix. The target parameter matrix includes a node community affiliation matrix at time T and a community transition matrix from time T-1 to time T. Each element in the node community affiliation matrix represents the probability that each user belongs to community k at time T. Each element in the community transition matrix represents the probability that a user in any community will transition to community k from time T-1 to time T. k is greater than or equal to 1 and less than or equal to K. Multiply the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T to generate the expected community affiliation matrix for each node at time T+1; and Based on the probability that each user belongs to the k-th community at time T+1, target product information corresponding to the product type of the k-th community is recommended to the target user.

2. The method according to claim 1, characterized in that, The extraction of anchor information of the global structure, node stability information, and network topology information from the time-series sequence of the dynamic network snapshot includes: Extract the initial dynamic network snapshot at the initial moment from the time sequence of the dynamic network snapshot; Based on the predetermined number of communities, the initial dynamic network snapshots are clustered to obtain a clustering indicator matrix; wherein each element in the clustering indicator matrix represents the degree of preference of each user for historical product types at the initial time; and The degree of preference of each user for historical product types at the initial moment is determined as the anchor information of the global structure.

3. The method according to claim 1 or 2, characterized in that, The extraction of anchor information of the global structure, node stability information, and network topology information from the time-series sequence of the dynamic network snapshot includes: The sum of product preference similarities between any node in the dynamic network snapshot at time t and all nodes in the dynamic network except for that node is determined as the degree of that node at time t; and The node stability information at time t is determined by the ratio of the number of nodes that maintain associations with all nodes in the dynamic network except for any node in the dynamic network from time t-1 to time t to the degree of any node at time t.

4. The method according to claim 1 or 2, characterized in that, The extraction of anchor information of the global structure, node stability information, and network topology information from the time-series sequence of the dynamic network snapshot includes: The sum of product preference similarities between any node in the dynamic network snapshot at time t and all nodes in the dynamic network except for that node is determined as the degree of that node at time t; and The difference between the degree of any node at time t and the dynamic network snapshot at time t is determined as the network topology information.

5. The method according to claim 1, characterized in that, Based on the anchor point information, node stability information, and network topology information of the global structure, the randomly initialized parameter matrix is ​​iteratively optimized until the iteration termination condition is met, resulting in the target parameter matrix, including: Based on the anchor point information of the global structure and the initial dynamic network snapshot at the initial moment, the randomly initialized parameter matrix is ​​iteratively optimized to obtain the node community affiliation matrix, the first basis matrix, and the second basis matrix at the initial moment, such that the target difference is less than a predetermined difference threshold; wherein, the target difference includes the difference between the product of the node community affiliation matrix and the first basis matrix at the initial moment and the initial dynamic network snapshot, and the difference between the product of the node community affiliation matrix and the second basis matrix at the initial moment and the clustering indicator matrix at the initial moment; Based on the anchor point information, node stability information, and network topology information of the global structure, the node community affiliation matrix, the first basis matrix, and the second basis matrix at the initial moment are iteratively optimized to obtain the target parameter matrix. This ensures that the expected product preference of a user corresponding to any node in the dynamic network at any historical moment, calculated based on the target parameter matrix, matches the time series sequence of the dynamic network snapshot, and that the changing trends of product preferences among related nodes in the dynamic network are similar.

6. The method according to claim 1 or 5, characterized in that, The method further includes: Obtain a dynamic network snapshot at time T+1; The time series sequence of the dynamic network snapshot is updated using the dynamic network snapshot at time T+1 to obtain the updated time series sequence of the dynamic network snapshot; Based on the time-series sequence of the updated dynamic network snapshot, the randomly initialized parameter matrix is ​​iteratively optimized until the iteration termination condition is met, resulting in the actual node community affiliation matrix at time T+1; and In response to the error between the actual node community affiliation matrix at time T+1 and the expected community affiliation matrix of each node at time T+1 being greater than a predetermined error threshold, the constraint parameters used for iterative optimization operations are adjusted; wherein, the constraint parameters include: a first parameter for constraining the global structure of the dynamic network and a second parameter for constraining the temporal evolution of the dynamic network.

7. An apparatus based on an information recommendation method, characterized in that, include: The acquisition module is used to acquire the time sequence of dynamic network snapshots and the number of predetermined communities within a historical period. Nodes in the dynamic network represent users, and the dynamic network snapshots represent the product preference similarity between different users at any historical moment. Predetermined communities represent the product types preferred by users. The historical period includes T moments, where T is an integer greater than 1. The number of predetermined communities is K, where K is an integer greater than 1. An extraction module is used to extract anchor point information, node stability information, and network topology information of the global structure from the time-series sequence of the dynamic network snapshot; wherein, the anchor point information is used to characterize the product preference type at each historical moment; the node stability information is used to characterize the stability of user behavior over time; and the network topology information is used to characterize the association relationship established between different users at each historical moment based on the similarity of product preferences. An optimization module is used to iteratively optimize a randomly initialized parameter matrix based on the anchor point information, node stability information, and network topology information of the global structure, until the iteration termination condition is met to obtain a target parameter matrix. The target parameter matrix includes a node community affiliation matrix at time T and a community transition matrix from time T-1 to time T. Each element in the node community affiliation matrix represents the probability that each user belongs to community k at time T. Each element in the community transition matrix represents the probability that a user in any community will transition to community k from time T-1 to time T. k is greater than or equal to 1 and less than or equal to K. The generation module is used to perform matrix multiplication on the node community affiliation matrix at time T and the community transition matrix from time T-1 to time T to generate the expected community affiliation matrix for each node at time T+1; and The recommendation module is used to recommend target product information of the product type corresponding to the k-th community to the target user based on the probability that each user belongs to the k-th community at time T+1.

8. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the method of any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to implement the method of any one of claims 1 to 6.

10. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the method according to any one of claims 1 to 6.

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