CN113222774A - Social network seed user selection method and device, electronic equipment and storage medium - Google Patents
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Abstract
The invention discloses a social network seed user selection method and device, electronic equipment and a storage medium. The method comprises the following steps: modeling a social network and user behaviors to obtain a time-aware social network propagation model; according to the social network propagation model, selecting any user for reverse propagation simulation for multiple times, recording activated users in the reverse propagation simulation, and forming reverse reachable sets RRsets by the users; and according to the reverse reachable sets RRsets, representing the approximate influence of any user in the user set by using the intersection number of the user set and the reverse reachable sets RRsets, and greedy selecting a preset number of users based on the approximate influence to serve as seed users in the social network. The method has high efficiency and robustness.
Description
Technical Field
The invention relates to the problem of influence maximization, in particular to a social network seed user selection method and device, electronic equipment and a storage medium.
Background
With the development of social networks, a large amount of social media (such as microblogs, WeChats, Facebook, and the like) have become part of daily life, and more people share and spread information by using social networks; meanwhile, some merchants hope to carry out marketing on company products by means of the propagation effect of the social network, so that higher income is obtained, and therefore, the virus type marketing problem on the social network is greatly concerned. For example, emarker estimates that advertisers worldwide spend approximately 350 billion in social network marketing in 2013 and 2017; fortune states that advertising on social networks cost over $ 500 billion in 2020.
Specifically, the propagation process on the social network is as follows: a batch of influential users are selected as seed users, information is transmitted to friends or fans through mouths of the users, and the friends of the users receive the information with a certain probability (reflecting the influence degree among the users) and continuously transmit influence to surrounding users. In this way, messages are continually flooded out in a cascading fashion until no new users on the social network are affected. The most typical application of the process is social network marketing behavior, as shown in fig. 1, some seed users (such as net red) are selected to perform marketing promotion of a specific product, and through the influence propagation of the seed users, new users continuously receive marketing information and propagate the marketing information to surrounding users, so that the purpose of marketing promotion is achieved.
Conventional techniques consider how to select a certain number of users to maximize the number of users affected throughout the social network, i.e., the influence maximization problem. However, they assume that propagation between all users does not require time, nor does they take into account the effect of propagation time on the probability of success of propagation, e.g., propagation of information between close users has a shorter time, and a short propagation has a greater probability of success.
Therefore, for the limitation of the traditional method, the method considers the effect of time factors in the social network aiming at the influence maximization problem on the social network, formalizes the influence maximization problem under the time limit, and provides a simple and efficient algorithm based on the greedy thought.
Disclosure of Invention
The embodiment of the invention aims to provide a social network seed user selection method and device, electronic equipment and a storage medium, so as to solve the problem that a time factor is not considered in the conventional scheme.
According to a first aspect of the embodiments of the present invention, there is provided a social network seed user selection method, including:
modeling a social network as a directed probability graph G ═ V, E, P, wherein V represents a set of all users, E is a set of social relationships among all users, and P represents a set of propagation probabilities on all edges and represents an original activation probability among the users;
modeling the user behaviors in the social network by considering the propagation time among users and the influence of the propagation time on the propagation probability to obtain a user behavior model, wherein the rules of the user behavior model are as follows: each activated user has only one chance to try to activate their social friends, the time required to activate the friends obeys a geometric distribution or a poisson distribution, and the success probability of activating the friends is the product of the original activation probability among the users and a time delay function;
based on the social network and the user behavior model, selecting users of the social network part as initial activated users, and activating the users according to rules in the user behavior model by the users so that more users are activated and perform activation behaviors until no new user is activated or the preset time is reached to obtain a time-aware social network propagation model;
according to the social network propagation model, selecting any user for reverse propagation simulation for multiple times, recording activated users in the reverse propagation simulation, and forming reverse reachable sets RRsets by the users;
and according to the reverse reachable sets RRsets, representing the approximate influence of any user in the user set by using the intersection number of the user set and the reverse reachable sets RRsets, and greedy selecting a preset number of users based on the approximate influence to serve as seed users in the social network.
According to a second aspect of the embodiments of the present invention, there is provided a social network seed user selection apparatus, including:
the social network modeling module is used for modeling the social network into a directed probability graph G (V, E, P), wherein V represents a set formed by all users, E is a set of social relationships among all users, and P represents a propagation probability set on all edges and represents an original activation probability among the users;
the user behavior modeling module is used for modeling the user behavior in the social network by considering the propagation time among users and the influence of the propagation time on the propagation probability to obtain a user behavior model, and the rules of the user behavior model are as follows: each activated user has only one chance to try to activate their social friends, the time required to activate the friends obeys a geometric distribution or a poisson distribution, and the success probability of activating the friends is the product of the original activation probability among the users and a time delay function;
the time-aware social network propagation modeling module is used for selecting partial users of the social network as initial activated users based on the social network and the user behavior model, and the users activate the users according to rules in the user behavior model so that more users are activated and perform activation behaviors until no new user is activated or the preset time is reached, and obtaining a time-aware social network propagation model;
the simulation module is used for selecting any user for reverse propagation simulation for multiple times according to the social network propagation model, recording the activated users in the reverse propagation simulation, and forming reverse reachable sets RRsets by the users;
and the selection module is used for representing the approximate influence of any user in the user set by using the intersection number of the user set and the reverse reachable sets RRsets according to the reverse reachable sets RRsets, and selecting a preset number of users as seed users in the social network based on the approximate influence greedy.
According to a third aspect of embodiments of the present invention, there is provided an apparatus comprising: one or more processors; a memory for storing one or more programs; when executed by the one or more processors, cause the one or more processors to implement a method as described in the first aspect.
According to a fourth aspect of embodiments of the present invention, there is provided a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method according to the first aspect.
According to the technical scheme, the method provided by the embodiment of the invention models the propagation time and the propagation influence of the propagation time on the social network, so that a time-aware social network propagation model is obtained, then reverse propagation simulation is carried out for multiple times based on the model to obtain reverse reachable sets RRsets, and finally seed users are selected according to the reverse reachable sets RRsets.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a diagram of a social network dissemination marketing example in the prior art;
FIG. 2 is a flow diagram of a social network seed user selection method provided by an exemplary embodiment of the present invention;
fig. 3 is a block diagram of a social network seed user selection apparatus according to an exemplary embodiment of the present invention.
Detailed Description
The technical solution of the present invention will be further explained with reference to the accompanying drawings and specific implementation:
FIG. 2 is a block diagram of a social network seed user selection method considering the influence of time factors according to an embodiment of the present invention; referring to fig. 2, an embodiment of the present invention provides a social network seed user selection method, which may include the following steps:
step S11, modeling the social network as a directed probability graph G ═ V, E, P, where V represents a set composed of all users, E is a set of social relationships among all users, and P represents a set of propagation probabilities on all edges, representing original activation probabilities among users;
step S12, modeling the user behavior in the social network by considering the propagation time among users and the influence of the propagation time on the propagation probability to obtain a user behavior model, wherein the rules of the user behavior model are as follows: each activated user has only one chance to try to activate their social friends, the time required to activate the friends obeys a geometric distribution or a poisson distribution, and the success probability of activating the friends is the product of the original activation probability among the users and a time delay function;
step S13, based on the social network and the user behavior model, selecting users in the social network as initial activated users, and activating the users according to rules in the user behavior model, so that more users are activated and perform activation behaviors until no new user is activated or the preset time is reached, and obtaining a time-aware social network propagation model;
step S14, according to the social network propagation model, selecting any user for reverse propagation simulation for many times, recording the activated users in the reverse propagation simulation, and forming reverse reachable sets RRsets by the users;
and step S15, according to the reverse reachable sets RRsets, representing the approximate influence of any user in the user set by the intersection number of the user set and the reverse reachable sets RRsets, and selecting a preset number of users as seed users in the social network based on the approximate influence greedy.
According to the technical scheme, the method provided by the embodiment of the invention models the propagation time and the propagation influence of the propagation time on the social network, so that a time-aware social network propagation model is obtained, then reverse propagation simulation is carried out for multiple times based on the model to obtain reverse reachable sets RRsets, and finally seed users are selected according to the reverse reachable sets RRsets. The embodiment of the invention has high efficiency and robustness under different time settings.
In a specific implementation of step S11, the social network is modeled as a directed probability graph G ═ V, E, P, where V represents a set of all users, E is a set of social relationships among all users, and P represents a set of propagation probabilities on all edges, representing the original activation probabilities among the users;
specifically, each user V is a node in the graph G, V belongs to V, and the social relationship between the users u and V is a directed edge e between the nodes in the graph Gu，vE, propagation probability p with the influence degree of the user u on v being edgeu，vE.g. P. Through the step of modeling the social network into the directed probability graph, various social networks in real life can be effectively represented, and the basis is provided for further analysis on the social network by means of related research of the graph.
In the specific implementation of step S12, user behavior in the social network is modeled to obtain a user behavior model, where the rules of the user behavior model are as follows: each activated user has only one chance to try to activate their social friends, the time required to activate the friends obeys a geometric distribution or a poisson distribution, and the success probability of activating the friends is the product of the original activation probability among the users and a time delay function;
specifically, the user behavior in the social network is modeled to obtain a user behavior model, and the rule of the model is that each activated user v (with the activated time t) has only one chance to try to activate the social friend u, and the time delta required for activating the friendtObeying a geometric or Poisson distribution, v being at t + deltatThe success probability of activating friends at any moment is the original activation probability p between usersu，vWith the delay function f (delta)t) Satisfies the following formula:
wherein, f (δ)t) The time delay function taking the propagation time as an independent variable has two forms of an exponential function and a power function, alpha is a hyper-parameter and represents the propagationThe degree of influence of time on the propagation probability, the larger α, the greater its influence. The geometric distribution and the Poisson distribution are commonly used for representing possible time and existence probability, and the exponential function and the power function as a time delay function can represent the characteristic that the propagation probability is reduced along with the increase of the propagation time, and are consistent with the reality.
In a specific implementation of step S13, based on the social network and the user behavior model, selecting users of the social network part as initial activated users, and activating the users according to rules in the user behavior model, so that more users are activated and perform activation behavior until no new user is activated or a predetermined time T is reached, and obtaining a time-aware social network propagation model.
Specifically, at an initial time t0And selecting a part of nodes S e V in G to be marked as an activated state, activating a neighbor node u of the node V which is marked as the activated state for the first time at any time t and t, wherein the activation time and the activation probability are obtained by the user behavior model rule, and if u is successfully activated, marking u as the activated state at the corresponding time. The above process continues until a certain time T has no first activated node or T ═ T. The model considers the propagation time among users and the influence of the propagation time on the propagation probability, corresponds to the existence of information propagation time in real life and the rule that the influence of outdated information is relatively small, researches the propagation process under the preset time T, and meets the actual requirements of advertisers and the like on the advertisement influence effect in the specific time on the social network.
In the specific implementation of step S14, according to the social network propagation model, any user is selected multiple times to perform the back propagation simulation, activated users in the back propagation simulation are recorded, and the users are grouped into the back reachable sets RRsets.
And specifically, according to the social network propagation model, any user on the social network is selected as an initial activated user for multiple times with the same probability, and a reverse activation behavior is started until no new user is reversely activated or the propagation process reaches a preset time.
The following further elaboration of this step, which is illustrated by the following example, can be divided into the following steps:
(1) determining the number N of the reverse propagation simulation according to theoretical proofmIt is defined as follows:
where e is a natural logarithm, δ is a predetermined approximation probability, e is a predetermined error threshold, n is the number of users in the social network G, and k is the number of users to be selected. N is a radical ofmRepresenting a simulation NmAfter the second back propagation process, the ratio of the influence of the selected k users over time T to the influence of the optimal solution has a probability of at least 1- δ to satisfy a predetermined approximation ratio of 1-1/e-e compared to the optimal solution.
(2) In each back propagation simulation, randomly selecting any user z in the social network as an activated user at the initial moment with the same probability, adding z into RRset, and starting to perform back propagation simulation according to the social network propagation model.
(3) At any time t, for a user v which is successfully activated at each time t, if v is not activated at the previous time, v is added into RRset, v tries to activate each internal neighbor friend u (namely friend u has an edge pointing to v in G), and the time delta required for activating friends istObeying a geometric or Poisson distribution, v being at t + deltatThe success probability of activating friends at any moment is pu，v*f(δt) Meaning u has pu，v*f(δt) Has a probability of t + deltatThe moment is successfully activated. If the activation is successful, u will be at t + deltatThe moment is activated. The propagation simulation procedure described above is performed for each reverse neighbor node of v. If v has been activated before t, the user is skipped. If the current time T is not successfully influenced by the user, or T is larger than the given time limit T, the back propagation simulation is ended, otherwise, the next time T +1 is enteredRepeating (3);
(4) repeating the back propagation simulation process NmThen, obtain NmThe RRsets constitute RRsets.
In a specific implementation of step S15, according to the reverse reachable sets RRsets, the number of intersections between the user set and the reverse reachable sets RRsets is used to represent the approximate influence of any user in the user set, and a predetermined number of users are selected based on the greedy influence.
Specifically, whether the user set and each RRset have intersection is sequentially judged according to the reverse reachable sets RRsets, the number of the intersection of the user set and each RRset is recorded, the approximate influence of any user in the user set is obtained, and the users are sequentially selected according to the following greedy rule based on the approximate influence:
when a first user is selected, the user with the greatest approximate influence is selected, when a second user is selected, the user with the greatest approximate influence combined with the first selected user is selected, and so on until a predetermined number of users are selected.
The following further elaboration of this step, which is illustrated by the following example, can be divided into the following steps:
(1) sequentially judging the user set S and each RRset R according to the reverse reachable sets RRsetsiWhether an intersection exists or not is judged, the number of the intersections of the user set and the RRsets is recorded to obtain the approximate influence of any user in the user set, and the approximate influence is as follows:
wherein R isiIs an arbitrary one of the rrsets,
for the indicator function, if S and RiIf there is intersection, it is 1, otherwise it is 0.
(2) Using S*Representing a selected set of seed users, initialized to null, each greedy selection of the relatively approximate most influentialUser of (2) joining S*Until a predetermined number of users are selected, wherein the relative approximate influence is as follows:
Λ(v|S*)＝Λ(S*∪{v})-Λ(S*) (4)
it will be appreciated that the user with the greatest approximate impact is selected when the first user is selected, the user with the greatest approximate impact in conjunction with the first selected user is selected when the second user is selected, and so on until a predetermined number of users are selected. By the selection mode and the reverse propagation simulation times NmThe ratio of the influence of the selected seed user to the optimal solution can be guaranteed to have a probability of at least 1-delta to meet a predetermined approximate ratio of 1-1/e-e, and therefore the selected seed user can be guaranteed to generate the approximately optimal influence in actual activities such as social network marketing.
Corresponding to the embodiment of the social network seed user selection method, the application also provides an embodiment of a social network seed user selection device.
FIG. 3 is a block diagram illustrating a social network seed user selection apparatus, according to an example embodiment. Referring to fig. 3, the apparatus includes:
a social network modeling module 21, configured to model a social network as a directed probability graph G ═ V, E, P, (V, E, P), where V represents a set formed by all users, E is a set of social relationships among all users, and P represents a set of propagation probabilities on all edges, which represents an original activation probability among the users;
the user behavior modeling module 22 is configured to model the user behavior in the social network in consideration of the propagation time between users and the influence of the propagation time on the propagation probability to obtain a user behavior model, where rules of the user behavior model are as follows: each activated user has only one chance to try to activate their social friends, the time required to activate the friends obeys a geometric distribution or a poisson distribution, and the success probability of activating the friends is the product of the original activation probability among the users and a time delay function;
the time-aware social network propagation modeling module 23 is configured to select, based on the social network and the user behavior model, users in a part of the social network as initial activated users, activate the users according to rules in the user behavior model, so that more users are activated and perform activation behaviors until no new user is activated or a predetermined time is reached, and obtain a time-aware social network propagation model;
the simulation module 24 is configured to select any user for multiple times to perform reverse propagation simulation according to the social network propagation model, record activated users in the reverse propagation simulation, and form reverse reachable sets RRsets from the users;
and the selecting module 25 is configured to represent the approximate influence of any user in the user set by using the intersection number of the user set and the reverse reachable sets RRsets according to the reverse reachable sets RRsets, and select a predetermined number of users as seed users in the social network based on the approximate influence greedy.
With regard to the apparatus in the above-described embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be elaborated here.
For the device embodiments, since they substantially correspond to the method embodiments, reference may be made to the partial description of the method embodiments for relevant points. The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the scheme of the application. One of ordinary skill in the art can understand and implement it without inventive effort.
Correspondingly, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when executed by the one or more programs, cause the one or more processors to implement a social network seed user selection method as described above.
Accordingly, the present application also provides a computer-readable storage medium having computer instructions stored thereon, wherein the instructions, when executed by a processor, implement the social network seed user selection method as described above.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (8)
1. A social network seed user selection method, the method comprising:
modeling a social network as a directed probability graph G ═ V, E, P, wherein V represents a set of all users, E is a set of social relationships among all users, and P represents a set of propagation probabilities on all edges and represents an original activation probability among the users;
modeling the user behaviors in the social network by considering the propagation time among users and the influence of the propagation time on the propagation probability to obtain a user behavior model, wherein the rules of the user behavior model are as follows: each activated user has only one chance to try to activate their social friends, the time required to activate the friends obeys a geometric distribution or a poisson distribution, and the success probability of activating the friends is the product of the original activation probability among the users and a time delay function;
based on the social network and the user behavior model, selecting users of the social network part as initial activated users, and activating the users according to rules in the user behavior model by the users so that more users are activated and perform activation behaviors until no new user is activated or the preset time is reached to obtain a time-aware social network propagation model;
according to the social network propagation model, selecting any user for reverse propagation simulation for multiple times, recording activated users in the reverse propagation simulation, and forming reverse reachable sets RRsets by the users;
and according to the reverse reachable sets RRsets, representing the approximate influence of any user in the user set by using the intersection number of the user set and the reverse reachable sets RRsets, and greedy selecting a preset number of users based on the approximate influence to serve as seed users in the social network.
2. The method of claim 1, wherein selecting any user for back propagation simulation a plurality of times according to the social network propagation model comprises:
and according to the social network propagation model, selecting any one user on the social network as an initial activated user for multiple times with the same probability, and starting a reverse activation behavior until no new user is reversely activated or the propagation process reaches a preset time.
3. The method of claim 1, wherein according to the reverse reachable sets RRsets, using the number of intersections of the set of users with the reverse reachable sets RRsets to represent the approximate influence of any user in the set of users, and wherein selecting a predetermined number of users based on greedy of influence comprises:
sequentially judging whether the user set and each RRset have intersection or not according to the reverse reachable sets RRsets, recording the number of the intersection of the user set and each RRset, obtaining the approximate influence of any user in the user set, and sequentially selecting the users according to the following greedy rule based on the approximate influence;
when a first user is selected, the user with the greatest approximate influence is selected, when a second user is selected, the user with the greatest approximate influence combined with the first selected user is selected, and so on until a predetermined number of users are selected.
4. A social network seed user selection apparatus, comprising:
the social network modeling module is used for modeling the social network into a directed probability graph G (V, E, P), wherein V represents a set formed by all users, E is a set of social relationships among all users, and P represents a propagation probability set on all edges and represents an original activation probability among the users;
the user behavior modeling module is used for modeling the user behavior in the social network by considering the propagation time among users and the influence of the propagation time on the propagation probability to obtain a user behavior model, and the rules of the user behavior model are as follows: each activated user has only one chance to try to activate their social friends, the time required to activate the friends obeys a geometric distribution or a poisson distribution, and the success probability of activating the friends is the product of the original activation probability among the users and a time delay function;
the time-aware social network propagation modeling module is used for selecting partial users of the social network as initial activated users based on the social network and the user behavior model, and the users activate the users according to rules in the user behavior model so that more users are activated and perform activation behaviors until no new user is activated or the preset time is reached, and obtaining a time-aware social network propagation model;
the simulation module is used for selecting any user for reverse propagation simulation for multiple times according to the social network propagation model, recording the activated users in the reverse propagation simulation, and forming reverse reachable sets RRsets by the users;
and the selection module is used for representing the approximate influence of any user in the user set by using the intersection number of the user set and the reverse reachable sets RRsets according to the reverse reachable sets RRsets, and selecting a preset number of users as seed users in the social network based on the approximate influence greedy.
5. The apparatus of claim 4, wherein according to the social network propagation model, selecting any user for back propagation simulation a plurality of times comprises:
and according to the social network propagation model, selecting any one user on the social network as an initial activated user for multiple times with the same probability, and starting a reverse activation behavior until no new user is reversely activated or the propagation process reaches a preset time.
6. The apparatus of claim 4, wherein according to the reverse reachable sets RRsets, using the number of intersections of the set of users with the reverse reachable sets RRsets to represent the approximate influence of any user in the set of users, selecting a predetermined number of users based on greedy of influence comprises:
according to the reverse reachable sets RRsets, whether intersection exists between the user set and each RRset is sequentially judged, the number of the intersection of the user set and each RRset is recorded, the approximate influence of any user in the user set is obtained, and the user is sequentially selected according to the following greedy rule based on the approximate influence:
when a first user is selected, the user with the greatest approximate influence is selected, when a second user is selected, the user with the greatest approximate influence combined with the first selected user is selected, and so on until a predetermined number of users are selected.
7. An electronic device, comprising:
one or more processors;
a memory for storing one or more programs;
when executed by the one or more processors, cause the one or more processors to implement the method of any one of claims 1-3.
8. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1-3.
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