Impact maximization method based on pass-through and autoregressive impact estimation
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF SCI & TECH OF CHINA
- Filing Date
- 2025-05-29
- Publication Date
- 2026-06-05
Smart Images
Figure CN120632808B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of information processing technology, and in particular to an impact maximization method based on direct and autoregressive impact estimation. Background Technology
[0002] With the rapid development of social media and content-sharing platforms, the methods and scale of information dissemination have undergone profound changes. In research on information diffusion in social networks, the Influence Maximization Problem (IM) is a key topic. Its goal is to select a small number of seed nodes in the network and maximize the overall scope of influence through the diffusion process.
[0003] Existing solutions to the influence maximization (IM) problem can be categorized into three types based on their approach: greedy algorithms, heuristic algorithms, and learning / reinforcement learning algorithms.
[0004] Greedy algorithms were initially based on Monte Carlo simulations to estimate the influence of nodes and, relying on the submodularity of the propagation function, selected the node with the highest marginal benefit in each round. These methods are theoretically guaranteed to achieve an approximate optimal solution of (1-1 / e). However, Monte Carlo simulations are computationally extremely expensive, especially on large-scale networks, making them inefficient and a bottleneck for practical applications.
[0005] To address this, a greedy algorithm based on Reverse Influence Sampling (RIS) has been proposed. This method significantly improves solution efficiency by randomly sampling the set of influenced nodes (RR sets) in the network and then searching backwards for the nodes most likely to influence these sets. RIS-like methods combine high efficiency and scalability, and theoretically provide probabilistic approximation guarantees. However, their performance is highly dependent on specific propagation models (such as independent cascade models and linear threshold models), limiting their adaptability in practical applications with complex or unknown propagation mechanisms.
[0006] Heuristic algorithms mainly fall into two categories: those based on centrality and those based on community structure. Centrality-based heuristics measure the "importance" of nodes in the network structure by designing various centrality metrics (such as degree centrality and betweenness centrality), and directly select the top k nodes with the highest centrality as the seed set. However, this type of method often ignores the issue of overlapping influence among nodes, leading to excessive redundancy among seed nodes and poor actual diffusion performance. Improved voting mechanism algorithms (such as discounting and sparsity) introduce strategies that consider the overlapping of node influence regions. While this improves the rationality of seed distribution to some extent, it remains locally greedy and lacks global optimality guarantees. Community-based heuristics first divide the network into communities, then select nodes with important positions within or across communities as seeds. Although this method can guarantee seed dispersion to some extent, it often relies on heuristic experience to locally greedily select nodes, lacking accurate modeling of the true diffusion capacity of nodes. It struggles to maximize influence from a global perspective, ultimately resulting in mediocre performance in actual diffusion.
[0007] Learning-based methods (including reinforcement learning and supervised learning) have been widely used in recent years to solve the influence maximization problem. Reinforcement learning methods typically combine graph neural networks (GNNs) to learn seed node selection strategies through interaction with the environment. However, reinforcement learning methods suffer from difficulties in convergence during training, sensitivity to reward design, and insufficient generalization ability when facing complex real-world propagation environments. Supervised learning methods based on node ranking attempt to select seeds by directly predicting node importance, but they also struggle to effectively handle the problem of overlapping influence between nodes, resulting in limited overall diffusion effects. Furthermore, the DeepIM model, based on latent space optimization, introduces a generative model to reduce the dimensionality of the node space and optimizes within the lower-dimensional latent space to solve the influence maximization problem. While this improves efficiency to some extent, the weak generalization ability of deep learning models on out-of-distribution data means that the decoder of the generative model can easily map latent variables to invalid or low-quality seed sets, affecting the final diffusion effect.
[0008] On the other hand, most existing methods are designed and optimized around the standard influence maximization (IM) setting, lacking good adaptability to diverse practical application needs (such as target influence maximization, extended node budget constraints, target node isolation, etc.), resulting in insufficient flexibility and scalability, making it difficult to effectively cope with complex and ever-changing real-world tasks. Summary of the Invention
[0009] To overcome the shortcomings of the existing technologies, this invention provides an influence maximization method based on direct-pass and autoregressive influence estimation. Addressing the problems of low efficiency, weak generalization ability, insufficient global optimality, and poor scalability in the existing technologies, this invention proposes an influence maximization method that can balance diffusion effect, computational efficiency, and application flexibility.
[0010] To achieve the above objectives, the present invention adopts the following technical solution, including:
[0011] Impact maximization methods based on direct-pass and autoregressive impact estimation include:
[0012] Given a propagation network G, the propagation dynamics are modeled based on the propagation trajectory data of the nodes in the network to obtain the propagation model M(x,G;θ), which is used to model the evolution process of node states, where x represents the node state and θ is the model parameter;
[0013] The initial state x of the node is obtained using the propagation model M(x,G;θ). 0 Mapping to the final propagation state y, i.e., the final infection probability of the node, and assigning the node's initial state x... 0 Mapped to a continuous state vector z, an end-to-end propagation surrogate model y = M is constructed. s (z,G;θ);
[0014] With fixed model parameters θ, and aiming to maximize influence, gradient descent is used to initialize the node's initial state x. 0 The corresponding continuous state vector z is optimized, and the seed node set is obtained based on the optimization result.
[0015] Preferably, the propagation trajectory data of a node consists of the infected node and its corresponding infection time; a time window is used to divide the node state trajectory x at different time steps. 0 ,…x t ,…,x T-1 ; Node state trajectory at time step t in, This represents the state of node i at time step t;
[0016] Based on the evolution of node states, a propagation model M(x,G;θ) is constructed using a graph neural network under the given propagation network G, and an autoregressive approach is employed. The model parameter θ is calculated as follows:
[0017]
[0018] Where E[·] represents expectation; p θ (x t+1 |x t ,…,x 0 G) represents the propagation model in xt ,…,x 0 Given G, generate x t+1 The probability of.
[0019] Preferably, based on the propagation mechanism, the propagation model is constructed, and the node state trajectory is updated in the following way:
[0020]
[0021] Where f(·) and g(·) are functions of the propagation model, N(·) represents the set of neighbors of a node, and Δt is the time step size.
[0022] Preferably, a propagation model is constructed based on a neural network, using gated recurrent units combined with a graph neural network to model the evolution process of node states, as shown below:
[0023]
[0024]
[0025] Where N(·) represents the set of neighbors of a node; This is the hidden state of the gated loop unit; This represents the hidden state of node i at time step t; f represents edge-level MLPs out (·) indicates the output layer MLPs;
[0026] At time step t, the graph neural network updates its own hidden representation by aggregating the hidden representations of its neighboring nodes and its own state. The output layer predicts the state of a node at the next time step based on the node's hidden representation.
[0027] Preferably, the initial state x of the node is obtained by using the propagation model M(x,G;θ) and through autoregression. 0 Mapping to the propagation final state y = x T-1 =M(x 0 ,G;θ), the initial state x of the node 0 The discrete values (binary vectors) are relaxed to continuous values (continuous state vectors z), where the continuous state vector z of a node represents the probability of each node being selected. An end-to-end propagation surrogate model y = M is then constructed. s (z, G; θ); With the model parameters θ fixed, the final propagation state y is set with the goal of maximizing influence, and the initial state x of the node is optimized by gradient descent. 0 The corresponding continuous state vector z is then mapped back to a discrete binary vector through a pass-through estimator (STE) to determine the initial state of the node and obtain the seed node set.
[0028] Preferably, the node budget is added as a constraint.
[0029] The present invention also provides a readable storage medium having a computer program stored thereon, which, when executed, implements the aforementioned method for maximizing the impact based on pass-through and autoregressive impact estimation.
[0030] The present invention also provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the aforementioned method for maximizing the impact based on pass-through and autoregressive impact estimation.
[0031] The advantages of this invention are:
[0032] (1) This invention is a further development based on existing technology, which solves the influence maximization (IM) problem by combining straight-through estimation and an autoregressive information diffusion model based on graph neural networks. By designing an end-to-end model and optimization objective, this invention can extend the typical influence maximization (IM) problem to other scenarios, including expanding the definition of budget constraints, target influence maximization, and target isolation.
[0033] (2) This invention proposes an end-to-end propagation proxy model construction method based on graph neural networks. By learning the historical propagation trajectory, the node state evolution is simulated autoregressively in continuous time steps, thereby accurately approximating the propagation process of information in complex networks and providing a differentiable and efficient propagation proxy model for subsequent seed set inference.
[0034] (3) This invention proposes a continuous relaxation and direct estimation mechanism for the initial state of a node, which relaxes the initial state of the node from a discrete binary vector to a continuous state vector to support gradient-based optimization, and introduces a direct estimator to achieve mapping to discrete seed selection while maintaining the trainability of the propagation model.
[0035] (4) This invention proposes a continuous inference strategy for jointly optimizing the seed set. Based on freezing the parameters of the propagation proxy model, and combined with a differentiable optimization objective function, the seed probability vector is iteratively updated in the continuous space to realize the joint optimization of the seed set in the high-dimensional space, thereby improving the global quality and diffusion ability of seed selection.
[0036] (5) This invention proposes a seed inference mechanism that can adapt to various task settings. The inference mechanism has flexible target adaptation capabilities and can dynamically adjust the optimization strategy according to different actual application scenarios (such as changes in node budget constraints, adjustments to the influence target area, modifications to constraints, etc.) to achieve support for multiple diffusion optimization tasks under a unified framework.
[0037] (6) Compared with the greedy algorithm based on Monte Carlo simulation, the heuristic method with improved voting mechanism and reinforcement learning methods, this invention optimizes the seed node selection process, improves the convergence speed and stability of the model training stage, and realizes a more efficient decision-making process for the target scenario in the inference stage, thereby having a faster solution speed and better resource utilization efficiency in large-scale networks, and improving computational efficiency.
[0038] (7) The present invention introduces an adaptation mechanism for different propagation models and diverse real-world scenarios (such as budget constraints, propagation of specific target nodes, etc.), which can maintain stable performance under different propagation environments and application conditions, and has good scalability and practicality, enhancing generalization and adaptability.
[0039] (8) While maintaining theoretical interpretability, this invention also takes into account the feasibility of engineering implementation, and can effectively solve the core technical problems in applications such as information dissemination, advertising, and public opinion intervention in reality.
[0040] (9) This invention not only overcomes the shortcomings of existing methods in terms of efficiency, diffusion effect and scalability, but also can adapt to more complex and varied practical application needs, and has significant application value and promotion prospects.
[0041] (10) Extensive experiments were conducted on real-world datasets to compare the invention with various advanced methods. The experimental results show that the model of the present invention achieves excellent performance on almost all datasets, significantly surpassing existing advanced solutions, thus verifying the advantages and effectiveness of the model of the present invention and enhancing the effect of maximizing influence. Attached Figure Description
[0042] Figure 1 This is a schematic diagram of the influence maximization method based on direct-pass and autoregressive influence estimation of the present invention.
[0043] Figure 2 This is a comparison chart of experimental results from an embodiment of the present invention. Detailed Implementation
[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0045] Example 1
[0046] This invention presents an influence maximization method based on straight-through and autoregressive influence estimation. It employs a model-based optimization framework, STARIM (Straight-Through and Autoregressive Influence Estimation for Influence Maximization), to solve the influence maximization problem. Assuming the probabilistic nature of information propagation, STARIM uses a graph neural network to model the continuous evolution of node states in an autoregressive manner. It also combines straight-through estimation to construct an end-to-end propagation proxy model, thereby efficiently inferring the seed node set in a continuous optimization space. The overall framework is as follows: Figure 1 As shown, STARIM consists of two parts:
[0047] In the propagation dynamics modeling stage, such as Figure 1 As shown in part (a) of the diagram. First, the propagation network G and multiple propagation trajectory data are taken as input. Each propagation trajectory consists of a series of infected nodes and their corresponding infection times. Then, the propagation trajectory data is divided into node state trajectories x at different time steps using time windows. 0 ,…,x T-1 The propagation model uses graph neural networks (GNNs) to fit these propagation trajectories through autoregression, that is, predicting the infection probability of each node at each time step based on historical states, thereby approximating the real propagation trajectory on a given network.
[0048] Seed node inference phase, such as Figure 1 As shown in section (b) of the diagram. The initial state x of the node... 0 The binary vector is relaxed into a continuous state vector z to support gradient-based optimization. Subsequently, a pass-through estimator is used to map the continuous state vector z back to the discrete state x. 0 The propagation model based on GNNs can predict the initial state x of nodes using an autoregressive approach. 0 The corresponding final infection probability y, combined with direct-through estimation, constructs an end-to-end transmission proxy model y=M. s (z, G; θ). Finally, the propagation surrogate model M is frozen. s The model parameters are set, and the continuous state vector z of the nodes is updated according to the custom optimization objective. The seed node set is selected through multiple rounds of iterative optimization to maximize the diffusion effect of the seed node set.
[0049] I. The specific methods for propagation dynamics modeling are as follows:
[0050] Given a propagation network G, the dynamics of information propagation are modeled based on the propagation trajectory data of nodes in the network. Each trajectory consists of a series of infected nodes and their corresponding infection times. The propagation trajectory data of the nodes is divided into node state trajectories x at different time steps using a time window. 0 ,…x t ,…,x T-1 Where T is the total number of time steps, and the node state trajectory at time step t is... use This represents the state of node i at time step t, and the trajectory of node i's state.
[0051] Based on the evolution of node states, p is modeled using a graph neural network under the given propagation network G. θ (x t+1 |x t ,…,x 1 Finally, a propagation model M(x,G;θ) is constructed using an autoregressive approach. The model parameter θ is calculated by maximizing the following probabilities:
[0052]
[0053] Where E[·] represents expectation; p θ (x t+1 |x t ,…,x 0 G) represents the propagation model in x t ,…,x 0 Given G, generate x t+1 The probability of.
[0054] In this embodiment, the propagation model can be constructed in two ways:
[0055] Implementation Method 1: Constructing a Propagation Model Based on the Propagation Mechanism. Information propagation and message passing in graph neural networks both rely on the topological structure of the graph and achieve information updating and diffusion through interactions between neighbors. They are highly similar in mechanism; the mechanism-based propagation model, which updates node states by performing matrix multiplication, can be seen as a form of message passing. Given that the propagation mechanism is known and probabilistic, the message passing framework of a graph neural network is used to represent the quenched mean-field equation corresponding to the propagation model, modeling and describing the evolution of node states in complex networks. Under this setting, This represents the infection probability of node i at time step t. In fact, for node i at time step t in the propagation network G... The synchronization state update resulting from a single propagation in the mechanism propagation model is equivalent to each node in the graph aggregating the states of its neighbors and performing a computation based on the mechanism model. The state update of the entire network can be uniformly represented as:
[0056]
[0057] Here, f(·) and g(·) are functions of the propagation model, N(·) represents the set of neighbors of a node, Δt is the time step size, and Δt = 1 will be used as the default value. The message passing of the graph neural network is used to simulate the propagation dynamics of the propagation model in discrete time steps.
[0058] The above process is described below using a typical social network propagation model as an example. A typical individual-based SIR model can be constructed using a graph neural network, showing the following propagation dynamics over discrete time steps:
[0059]
[0060] in, It is the adjacency matrix of the network. It is a vector representing the three different states of the SIR model for all nodes in the network. Let represent the three states at time t, where ⊙ represents the element-wise product, the infection rate of an edge is represented as β∈[0,1], and the recovery rate of a node is represented as γ∈[0,1].
[0061] Similarly, the typical Independent Cascade Model (IC) can be viewed as a form where γ is 1 and the infection probabilities between different node pairs are randomly different. A graph neural network can be used to construct the following propagation dynamics over discrete time steps:
[0062]
[0063] in, It is the probability of infection between node pairs, i.e., B i,j Let be the probability of node i infecting node j.
[0064] Implementation Method Two: Constructing a Propagation Model Based on Neural Networks (Data-Driven Mode). For real-world scenarios with complex and unknown diffusion models, a neural network model is trained using the propagation network G and propagation trajectory data to model the implicit dynamics of the actual propagation data. The task of the neural network model is to predict the future dynamic evolution p of the node states in the propagation scenario. θ (x t+1 |x t ,…,x 1Since propagation in real-world scenarios typically exhibits non-Markovian properties—meaning the current state depends not only on the previous state but also on all previous states—a GRU (Gated Recurrent Unit) structure combined with a graph neural network is used to model the evolution of node states. 0 ,…,x T-1 The details are as follows:
[0065]
[0066] Where N(·) represents the set of neighbors of a node, This is the hidden state of the GRU (Gated Circular Unit); This represents the hidden state of node i at time step t; f represents edge-level MLPs out (·) indicates the output layer MLPs.
[0067] At time step t, the graph neural network updates its own hidden representation by aggregating the hidden representations of its neighboring nodes and its own state. The output layer predicts the state of a node at the next time step based on the node's hidden representation.
[0068] Assuming the model infection probability follows a Gaussian distribution, the mean squared error between the predicted and true values is used as the loss function to model the infection probability of a node at each time step. This allows the model to model the evolution of the node infection probability, similar to mean-field dynamics.
[0069] II. The specific method for seed node inference is as follows:
[0070] The propagation model M(x,G;θ) can be used to model the node state evolution process, that is, to model p θ (x t+1 |x t ,…,x 1 Therefore, the initial state x of the node can be determined through autoregression. 0 Mapped to the propagation final state y, therefore given the initial state x 0 An end-to-end propagation model can then be constructed:
[0071] y = x T-1 =M(x 0 ,G;θ)
[0072] Where y is the node infection probability at time step T-1.
[0073] In the scenario of maximizing influence on a graph (propagation network G) with N nodes, each node can be in one of two discrete states: selected or unselected. Let the initial state x of the node be... 0The relaxation process involves relaxing discrete values (binary vectors of 0 or 1) into continuous values, i.e., continuous state vectors z, where the continuous state vector z of a node represents the probability of each node being selected, taking any real number between 0 and 1. This relaxation method supports gradient-based optimization. To connect the continuous and discrete domains, a straight-through estimator (STE) is used, mapping the continuous probabilities back to discrete binary values (0 or 1) during the evaluation process.
[0074] In the forward propagation, the input z represents the continuous state vector of a node. A threshold operation maps the continuous value to a discrete binary value. Specifically, when z > σ, the output is 1 (indicating the node is selected), otherwise the output is 0 (indicating the node is not selected). This operation can be formalized as:
[0075] x 0 =I(z>σ)
[0076] Here, I is an indicator function, and the output is converted to a floating-point type for compatibility with subsequent calculations. Thus, the pass-through estimator STE is compared with the diffusion model M(x). 0 Given G and θ), an end-to-end propagation proxy model can be constructed, mapping the continuous state vector z of a node to the final infection probability through the end-to-end propagation proxy model, i.e.:
[0077] y = x T-1 =M s (z, G; θ)
[0078] During the backpropagation phase, since the thresholding operation is inherently non-differentiable (i.e., its derivative is undefined at the threshold point and zero elsewhere), directly calculating the gradient would hinder optimization. Therefore, STE ignores the discontinuity of this operation, assuming that discretization in forward propagation has no effect on the gradient, and directly passes the output gradient to the input. When the model calculates the loss function as Loss based on the optimization objective, the gradient is calculated as follows:
[0079]
[0080] This pass-through strategy allows gradients to flow through discrete layers, enabling continuous node state vectors z to be effectively updated via gradient descent.
[0081] Furthermore, a scalable optimization objective is designed. This is achieved using an end-to-end agent model M trained with historical propagation data. s, which can estimate the propagation influence of node combinations in a target scenario and infer the optimal node set using gradient descent according to the optimization objective. By expanding the form of the optimization objective, the STEIM of the present invention can solve various IM variants in different scenarios. The expanded optimization objective is to find an optimal combination of seed nodes, under the extended node constraint conditions to maximize the estimated value of the extended propagation influence objective of the model , that is:
[0082]
[0083]
[0084] x 0 = I(z > σ)
[0085] where V is the node set and V i is the i-th node. is the generalized propagation influence objective, for example, by setting a target set of expected influences, maximizing the influence of the seed set on the target population. Various algorithms have been proposed for the target diffusion problem in the prior art, such as the reverse local path algorithm, which defines the propagation ability of nodes to the target nodes. is the generalized budget constraint applicable to a single node. For example, the budget can be set as different centrality measures of the nodes, and K is the actual budget. For the IM problem of setting the node degree as the budget
[64] , can be set as ‖x·A‖1, is the adjacency matrix of the network G, and ‖x·A‖1 < K represents that the L1-norm of the total seed node degree is restricted by the budget K.
[0086] Using the penalty function method, the constraint condition is added as a penalty term to the loss function, and the loss function used in the final optimization process is:
[0087]
[0088] where is the negative value of the objective function, making the estimated value of the generalized propagation influence objective larger; μ > 0 is the penalty coefficient, used to control the importance of the constraint; ensures that the constraint is satisfied as much as possible, and the loss increases when deviating from the constraint.
[0089] During the optimization process, the parameters θ of the forward diffusion model M s are frozen, and the continuous state vector z of the seed nodes is iteratively updated by the gradient descent method. This reverse optimization utilizes M sThe gradient of (z, G; θ) with respect to z enables the model to explore in a continuous space of node selection probabilities and converge to an optimal configuration that maximizes influence.
[0090] In summary, this invention proposes:
[0091] 1. A seed node inference method based on an end-to-end propagation agent model, which efficiently infers the seed node set under various practical constraints through continuous optimization.
[0092] 2. A method for relaxing the initial state of nodes from a discrete space to a continuous probability space and combining it with a pass-through estimator for optimization, used for differentiable optimization of the seed node set in a continuous space.
[0093] 3. A seed node inference mechanism with task adaptability, supporting various application scenarios such as changes in node budget and influence target, improving the flexibility and scalability of the inference stage.
[0094] In this embodiment, 10 real-world network datasets were collected, including Soc-Dolphins, Celegans, Fb-Pages-Food, Cora, Ego-Facebook, Ca-GrQc, Wiki-Vote, Deezer-Europe, Cit-HepPh, and Soc-Douban. In typical IM scenarios, the STARIM method of this invention was compared with some existing methods, including centrality methods such as H-index and NumCycle; improved heuristic methods such as VoteRank and VoteRank++; methods based on reverse reachability sets such as OPIM and SubSim; methods based on reinforcement learning to solve the common CO problem such as S2V-DQN; methods based on supervised learning for ranking node importance such as RCNN and MRCNN; methods based on reinforcement learning to solve IM problems such as ToupleGDD; and methods based on latent space optimization such as DeepIM.
[0095] STARIM was tested under three different settings: STAR-M is a propagation proxy model based on direct-pass estimation and mechanism propagation; STAR-N is a propagation proxy model based on direct-pass estimation and training a neural network using trajectory data; and GSO-M is a propagation proxy model based on Gumbel-Softmax and mechanism propagation.
[0096] Table 1 below shows the IM performance of different methods on multiple datasets under the IC propagation model. The values in the table represent the percentage of nodes ultimately infected by the seed sets found by each method under different seed ratios. The STARIM framework models information propagation based on the mechanism data generated by the IC propagation model and constructs a robust end-to-end proxy model by combining pass-through estimation. It obtains more stable and efficient experimental results by directly optimizing the selection of node sets through gradient descent.
[0097] Table 1 shows the performance of the IC propagation model.
[0098]
[0099] Table 2 below shows the IM performance of different methods on multiple datasets under the SIR propagation model. Overall, the STARIM framework still achieves significant advantages in this scenario.
[0100] Table 2 shows the performance on the SIR propagation model.
[0101]
[0102] In IM scenarios with enhanced budget constraints, by adjusting the loss function... By defining node centrality as a cost for node selection, the selection of the seed set can still maximize influence under the condition of an expanded node budget. A comparative experiment was conducted between STAR-M and the typical solution BCT. As shown in Table 3, under the IC propagation model, node centrality is used as a budget constraint, and STAR-M is compared with the typical method BCT. Considering that in real-world scenarios, the influence of a node is usually positively correlated with its number of followers, the node out-degree d is... out The total budget constraint is set as the cost of selecting a single node. in Let ρ be the average out-degree of nodes in the network, with values of 0.02, 0.04, 0.06, and 0.08. The budget-constrained augmented IM capabilities of different methods are quantified by comparing the proportion of initially infected nodes to the total number of infected nodes. STAR-M shows a significant advantage over BCT, indicating that the STARIM framework can be extended to scenarios requiring budget-constrained augmented influence maximization.
[0103] Table 3 IM of Node Centrality Constraints
[0104]
[0105] In the scenario of maximizing the target's influence, by using the loss function... Setting the seed set to the sum of infection probabilities of the target node set allows the optimization of the seed set to maximize its influence on the target node set. A comparative experiment was conducted with STAR-M and two other solutions to the target diffusion problem: RLP and Katz index. Figure 2 As shown, under the SIR propagation model, the ratio ρ of the initial infected nodes is set to 0.01 (e.g., Figure 2 (as shown in (a)-(e)) and 0.05 (as shown in...) Figure 2 As shown in (f)-(j), the proportion of the target node set is set to 0.1-0.5. The influence of different methods on the target nodes is quantified by comparing the proportion of initially infected nodes to the final infected target nodes. Katzindex, considering the more global relationship between nodes and the target node set, performs better than RLP in experimental results. STAR-M shows a significant advantage over the other two methods, indicating that the STARIM framework can be extended to scenarios that maximize target influence.
[0106] Example 2
[0107] In addition to the methods described above, embodiments of this application may also be computer program products, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the decision-making behavior decision-making method according to various embodiments of this application as described in Embodiment 1 above.
[0108] The computer program product can be written in any combination of one or more programming languages to perform the operations of the embodiments of this application. The programming languages include object-oriented programming languages such as Java and C++, as well as conventional procedural programming languages such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.
[0109] Example 3
[0110] Embodiments of this application may also be computer-readable storage media storing computer program instructions thereon, which, when executed by a processor, cause the processor to perform the steps in the decision-making behavior decision-making method according to various embodiments of this application described in Embodiment 1 above.
[0111] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may, for example, include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.
[0112] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. An impact maximization method based on direct-pass and autoregressive impact estimation, characterized in that, include: Given a propagation network G, the propagation dynamics are modeled based on the propagation trajectory data of the nodes in the network, resulting in a propagation model. Used to model the evolution of node states. Indicates the node status. These are the model parameters; the propagation network G is a social network; Using propagation models The initial state of the node Mapping to the final state of propagation That is, the final infection probability of the node, and the initial state of the node. Mapped to continuous state vectors Construct an end-to-end propagation agent model ; Fixed model parameters With the goal of maximizing influence, the initial state of the nodes is determined using gradient descent. The corresponding continuous state vector Optimize the process and obtain a set of seed nodes based on the optimization results; The propagation trajectory data of a node consists of the infected node and its corresponding infection time; time windows are used to divide the node state trajectory at different time steps. ; Node state trajectory at time step t ,in, This represents the state of node i at time step t; N represents the total number of time steps; N represents the total number of nodes. Based on the evolution of node states, a propagation model is constructed using a graph neural network under a given propagation network G, and an autoregressive approach is employed. Model parameters The calculation method is as follows: in, Expressing expectations; Indicating the propagation model in Under the conditions of G, generate The probability of.
2. The method for maximizing the impact based on direct-pass and autoregressive impact estimation according to claim 1, characterized in that, Based on the propagation mechanism, a propagation model is constructed, and the node state trajectory is updated in the following way: Where, f( ) and g( ) is a function of the propagation model. The set of neighbors of a node. t represents the time step size.
3. The impact maximization method based on direct-pass and autoregressive impact estimation according to claim 1, characterized in that, A propagation model is constructed based on a neural network. Gated recurrent units are combined with graph neural networks to model the evolution process of node states, as shown below: in, Represents the set of neighbors of node i; Gated loop unit The hidden state; This represents the hidden state of node i at time step t; Represents edge-level MLPs, Indicates the output layer MLPs; e represents an edge; v represents a node; This represents the combined spatial impact of all neighboring nodes of node i on node i at time step t; This represents the directional interaction influence characteristics of neighbor node j on node i at time step t; At time step t, the graph neural network updates its own hidden representation by aggregating the hidden representations of its neighboring nodes and its own state. The output layer predicts the state of a node at the next time step based on the node's hidden representation.
4. The method for maximizing the impact based on direct-pass and autoregressive impact estimation according to claim 1, characterized in that, Using propagation models And by using an autoregressive approach, the initial state of the node is determined. Mapping to the final state of propagation The initial state of the node Relaxing from discrete values (binary vectors) to continuous values (continuous state vectors) The continuous state vector of a node Representing the probability of each node being selected, an end-to-end propagation proxy model is constructed. Fixed model parameters Setting the final state of communication with the goal of maximizing influence The initial state of the node is optimized using gradient descent. The corresponding continuous state vector The optimized continuous state vector By mapping the direct-through estimator (STE) back to discrete binary vectors, the initial state of the nodes is determined, thus obtaining the seed node set.
5. The method for maximizing the impact based on direct-pass and autoregressive impact estimation according to claim 1 or 4, characterized in that, Add the node budget as a constraint.
6. A readable storage medium, characterized in that, It stores a computer program that, when executed, implements the influence maximization method based on direct and autoregressive influence estimation as described in any one of claims 1 to 5.
7. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements the influence maximization method based on pass-through and autoregressive influence estimation as described in any one of claims 1 to 5.