CN109547265A - Complex network local immunity method and system based on random walk sampling - Google Patents
Complex network local immunity method and system based on random walk sampling Download PDFInfo
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- 230000003053 immunization Effects 0.000 claims abstract description 56
- 238000002649 immunization Methods 0.000 claims abstract description 54
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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Abstract
The invention discloses a complex network local immunity method and a system based on random walk sampling, which comprises the following steps of 1: random walk sampling is carried out in a network to be immunized to obtain a certain number of local samples, and local sample degree distribution q in the random walk process is calculatedd(k) (ii) a Step 2: according to local sample degree distribution q in the random walk processd(k) Estimating the mean of a networkAnd step 3: estimating a degree cutoff value k of an immunization threshold based on target immunization from the estimated network mean valuecut(ii) a And 4, step 4: if a certain node i is obtained in the random walk process, the degree of the node i is kiIf k isi≥kcutAnd the node i is used for immunizing the immune node. The method can quickly implement immunity on the complex network without sequencing the information of the whole network, and the performance of the method exceeds that of the classical mature human immunity and random immunity methods.
Description
Technical Field
The invention belongs to the field of internet social network analysis, and particularly relates to a complex network local immunity method and system based on random walk sampling.
Background
With the rapid development of online social platforms, online public sentiment control has important significance for instantly suppressing the propagation of false messages, limiting network users from developing large-scale virtual activities, controlling computer worms and viruses, and the like. The propagation control aiming at the online social network is essentially a problem of quickly selecting important immune nodes from the network propagation perspective. Therefore, how to select the important immune nodes is very important for controlling the network propagation.
In general, the "degree" of a network node is used as an evaluation index, and it is considered that the node with a higher degree has a higher efficiency in information diffusion. Therefore, under the condition that the global information is known, all nodes are arranged from large to small according to the degree, and are sequentially selected for immunization, so that an immunization strategy target immunization method (TS) with excellent performance in a scale-free network is obtained. However, a global policy such as target immunization requires knowledge of the information (degrees of all nodes) of all network nodes to complete the ranking, which is difficult to satisfy in practical applications. For example, when public opinion control is performed on an online social network, it is almost impossible to crawl network-wide information in consideration of the unprecedented size of the online social network. Thus, local immunization strategies such AS "acquaintance immunization protocol" (AS) and "random immunization protocol" (RS) have emerged. As the name suggests, random immunity is to randomly select nodes in a network for immunization (namely based on random node sampling), while acquainted human immunity is to randomly select a node and then randomly select any neighbor of the node for immunization (namely based on random node edge sampling) by utilizing the characteristic that second-order average degree is greater than first-order average degree in a scale-free network.
There are many improvements to the three above-mentioned classes of classical immunization strategies, but the major problems remain: the strategy based on the global information has good performance and high efficiency, but the network global information is difficult to obtain; although the local immunization strategy does not need network global information, the difference between the immunization efficiency and a global method of target immunization is large.
Disclosure of Invention
The invention aims to solve the technical problem that higher immunization efficiency can be obtained without acquiring network global information, and provides an immunization method and system based on random walk sampling.
In order to solve the problem, the technical scheme adopted by the invention is as follows:
an immunization method based on random walk sampling comprises the following steps:
step 1: random walk sampling is carried out in a network to be immunized to obtain a certain number of local samples, and local sample degree distribution q in the random walk process is calculatedd(k)；
Step 2: according to local sample degree distribution q in the random walk processd(k) Estimating the mean of a network
And step 3: estimating a degree cutoff value k of an immunization threshold based on target immunization from the estimated network mean valuecut；
And 4, step 4: if a certain node i is obtained in the random walk process, the degree of the node i is kiIf k isi≥kcutAnd the node i is used for immunizing the immune node.
In order to further optimize the technical scheme, the invention also makes the following improvements:
further, in step 2, according to the local sample degree distribution q in the random walk processd(k) Estimating the mean of a networkThe method comprises the following steps:
step 2.1 obtaining local sample degree distribution q according to the random walk processd(k) And (3) calculating an estimated value of the overall degree distribution of the network:
wherein k represents the degree of a node in the network;
step 2.2: and (3) calculating an average degree estimated value of the network according to the estimated value of the overall degree distribution of the network:
further, the cutoff value k of the immunization threshold based on target immunization is estimated in step 2cut
Wherein p isc(k) For the purpose of the overall cumulative distribution function of the network, is an estimate of the immune threshold for immunization of a target,λ is the "virus" in the network, the propagation rate of the information.
The invention also provides a complex network local immune system based on random walk samples, which comprises a processor and a memory connected with the processor, wherein the memory stores a program of a complex network local immune method based on random walk samples, and the program of the complex network local immune method based on random walk samples realizes the steps of the method when being executed by the processor.
Compared with the prior art, the invention has the following beneficial effects:
a complex network local immunity method based on random walk sampling,the average degree of the network is estimated through the distribution of the local sample degree in the random walk process, so that the immune threshold value of the target immunity is estimated, and whether a node is an immune node or not is judged by comparing the degree of the node in the random walk process with the threshold value. The method does not need to rely on sequencing the information of the whole network degree, but estimates the degree truncation value k through the random walk samples obtained in the immune processcutAnd through kcutAnd comparing the local information of the current wandering node, namely the degree of the current node, to decide whether to implement immunization. The local immunity strategy provided by the invention can quickly implement immunity on a complex network, and the performance of the strategy exceeds that of a classical acquaintance immunity and random immunity method.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 shows the "prevalence reduction" ρ obtained by simulation of different immunization strategies on a real networkf/ρ0；
FIG. 2a is the result of an Advogato network;
FIG. 2b is the result of the BrightKite network;
FIG. 2c is the result of the Epinions network;
figure 2d shows the results for the MSM network.
Detailed Description
FIGS. 1 and 2 show the method for local immunization of a complex network based on random walk sampling, which comprises
Step 1: random walk sampling is carried out in a network to be immunized to obtain a certain number of local samples, and local sample degree distribution q in the random walk process is calculatedd(k) (ii) a Local sample size measurement for general random walk samplingThe number of the network nodes is about 5%, and the number of local samples taken in the experiment in the embodiment is 5%;
step 2: according to local sample degree distribution q in the random walk processd(k) Estimating the mean of a network
Step 2.1 obtaining local sample degree distribution q according to the random walk processd(k) And (3) calculating an estimated value of the overall degree distribution of the network:
if the local sample degree distribution obtained in the random walk process is qd(k) Then using the degree distribution p of the networkd(k) It is shown as
Wherein,is a normalization constant for ensuring qd(k) Is 1 and k is the degree of a node in the network.
Therefore, from the above formula, the conclusion q can be drawnd(k)∝k·pd(k) I.e. byThus, q can be distributed from the local samplesd(k) And (3) obtaining an estimation of the overall degree distribution of the network:
step 2.2: and (3) calculating an average degree estimated value of the network according to the estimated value of the overall degree distribution of the network:
and step 3: estimating a degree cutoff value k of an immunization threshold based on target immunization from the estimated network mean valuecut；
In the embodiment, an immunity 'cutoff value' k is determined by combining an immunity threshold of target immunity and network degree distribution and average degree obtained by estimationcut。
The approximate solution of the immune threshold for target immunization of an arbitrary connectivity index (connection exposure) scale-free network is known as:
wherein,for immunological threshold, m ═<k>And 2, lambda is the propagation rate of viruses, information and the like in the network. Immune threshold gcThe node number is the number of nodes which need immunity and prevent or eliminate the information or virus from spreading in the network, and for the target immunity, the nodes which finally select immunity are arranged according to the degree from large to small and then ranked in the ranking gcThe node before N. Therefore, in order to obtain performance similar to target immunity, it is necessary to determine whether a certain node is in g before degree ranking without depending on global ranking in the random walk processcN nodes:
network population distribution p obtained from previous estimationd(k) The cumulative degree distribution p of the network can be easily obtainedc(k)，Then, the ranking is at the top g, as viewed from the cumulative distributioncThe degree of N nodes will be equal to or greater than some kcutValue, i.e.
WhereinAnd obtaining the immune threshold of the target immunity for estimation. Thus, using the estimated cumulative degree distribution and average degree, an immune "cutoff value" k is obtainedcut。
It should be noted that in estimating gcIn practical applications, such as during information transmission or virus outbreak, λ is relatively easy to estimate, and if λ cannot be estimated, we can select a certain ranking ratio α to determine kcutThe value of (c):
kcut＝max{k|pc(k)≤1-α}
for example, when immunization is performed on the nodes ranked 10% of the degree, α is 0.1, and the corresponding cutoff value k is obtainedcut。
And 4, step 4: if a certain node i is obtained in the random walk process, the degree of the node i is kiIf k isi≥kcutIf the node i is an immunization node, the node can be immunized.
The method does not need to rely on sequencing the information of the whole network degree, but estimates the degree truncation value k through the random walk samples obtained in the immune processcutAnd through kcutAnd comparing the local information of the current wandering node, namely the degree of the current node, to decide whether to implement immunization. Therefore, the immunity can be quickly and effectively implemented, and public sentiment or viruses can be controlled.
The invention also provides a complex network local immune system based on random walk samples, which comprises a processor and a memory connected with the processor, wherein the memory stores a program of a complex network local immune method based on random walk samples, and the program of the complex network local immune method based on random walk samples realizes the steps of the method when being executed by the processor.
The proposed immunization strategy was then simulated by four real social networks. They are respectively: (1) advogato online social network, (2) Brightkite online social network, (3) relationships mutual social network, and (4) anonymous boy and social network MSM network. In order to make all nodes in the network reachable (reachable), the 4 maximum Connected components (GCC) of the undirected network extracted in this embodiment obtain the final experimental network. The basic network parameters of the experimental network are shown in table 1.
TABLE 1 basic network statistics parameters of the experimental network
| Network | Number of network nodes N | Number of network edges M | Mean estimate < k > |
| Advogato network | 5,158 | 78,852 | 15.297 |
| Brightkit network | 58,109 | 427,712 | 7.360 |
| Epinions networks | 75,877 | 811,478 | 10.694 |
| MSM network | 16,082 | 446,170 | 27.743 |
(1) Evaluation index
To demonstrate the efficiency of the random walk based sampling immunization method, the present example uses a critical immune fraction (critical immune fraction) fcAs a reference index. Critical immune ratio fcCharacterised by the fact that "viruses" are eliminated from being prevalent in the network or "information" propagation is stopped, etc. (i.e. "prevalence's in the network)/(i.e." prevalence's in the network)f0) the minimum node proportion that needs to be immunized. That is to say f obtained by an immunological methodcThe smaller the efficiency of the device.
(2) Comparison method
In the simulation, three traditional immunization methods, namely target immunization TS, mature human immunization AS and random immunization RS, are selected for comparison with an immunization method RWS based on random walk sampling.
Target immunization TS is to arrange the nodes of the whole network from large to small according to illumination intensity and sequentially immunize according to a sequence; mature person immunization, namely randomly selecting a certain node to immunize any random neighbor node of the random nodes; random immunization refers to randomly selecting a certain node to directly immunize.
(3) Model of infectious disease
There are many models of infectious diseases that can describe and study the transmission behavior and dynamic mechanism in the network, and the present embodiment will use standard SIS model (safe-fed-safe) to perform the transmission simulation experiment.
In the SIS model, each node in the network represents an individual, and viruses or information, etc. can propagate among the nodes through edges in the network. The nodes in the model may have one of two states, namely a susceptive state (susceptable) or an Infected state (fed), and the node state may change between the two states with a certain probability: generally, the transmission process of the SIS is updated in parallel (synchronization), that is, at each step time t, if any vulnerable node is connected with an infected node, it will be infected with a probability v and become an infected node; at the same time, any infected node is recovered to be a susceptible node with a probability delta. Thus, the propagation rate λ of the virus or information can be defined as v/δ. In the model operation, we assume that each step time interval Δ t is 1, and the propagation dynamics process will continue until the system reaches a steady state.
(4) Simulation of immunological methods
In the simulation, we will experimentally observe the "prevalence" ρ in steady statef(proportion of infected nodes in the network) with the proportion f of immune nodes.
Specifically, we first use a certain immunization strategy to immunize f.N nodes in the experimental network, where N is the number of nodes in the network. Then we set the initial infection fraction (infection fraction) of the network to 50%, i.e. select 50% of the nodes of the network to infect, and make them in the infected state, and then the rest nodes are set in the susceptible state. Then, the propagation rate λ of the SIS process is set to 0.25, the SIS infection process is iterated in the network, and the states of the nodes are updated in parallel. Finally, when the system reaches a stable state, the prevalence rate rho under the immune proportion f can be obtainedf. By adjusting the value of f to carry out simulation, we can obtain rhofThe variation with f; and critical immune ratio fcCan also be easily obtained, i.e. fc＝min{f|ρf＝0}。
The basic setting of the immunization method based on random walk sampling in the simulation is as follows: the seed node and the number of branches of the random walk sample are both 1. The seed node is randomly selected, and the branch walk also randomly selects a neighbor to access. Considering that in the immunization process, generally only one node is judged once, the random walk sampling is implemented without replacement. For any one network, the present embodiment will implement 100 simulations, and all results are the average of the results of 100 simulations.
(5) Results of the experiment
Figure 2 shows the results of numerical simulation of "virus" transmission after implementation of the immunization strategy. It can be seen that, for all real networks, the proposed random walk sampling based immunization method compares with the other two local methods AS and RS, and f of the local immunization method RWS proposed by the inventioncCritical immune ratio f to global target immune method TScMore closely. In particular, f of RWS and TS policiescThe gap in values is only 0.02 in the Advoagto network, 0.01 in the Brightkite network, 0.05 in the epions network, and 0.06 in the MSM network. The above results all show very well that in a real network, the efficiency of the local immune method RWS is similar to the global target immune method TS and superior to the other two classical local strategies, namely the mature human immune method AS and the random immune method RS.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.
Claims (4)
1. A local immunization method of a complex network based on random walk sampling is characterized in that: the method comprises the following steps:
step 1: random walk sampling is carried out in a network to be immunized to obtain a certain number of local samples, and local sample degree distribution q in the random walk process is calculatedd(k)；
Step 2: according to local sample degree distribution q in the random walk processd(k) Estimating the mean of a network
And step 3: estimating a degree cutoff value k of an immunization threshold based on target immunization from an average value of the estimated networkcut；
And 4, step 4: if a certain node i is obtained in the random walk process, the degree of the node i is kiIf k isi≥kcutIf the node i is an immune node, the node i is immunized.
2. The method for local immunization on a complex network based on random walk sampling as claimed in claim 1, wherein: step 2, the local sample degree distribution q in the random walk process is obtainedd(k) Estimating the mean of a networkThe method comprises the following steps:
step 2.1 obtaining local sample degree distribution q according to the random walk processd(k) And (3) calculating an estimated value of the overall degree distribution of the network:
wherein k represents the degree of a node in the network;
step 2.2: and (3) calculating an average degree estimated value of the network according to the estimated value of the overall degree distribution of the network:
。
3. the method of complex network local immunity based on random walk sampling according to claim 2, wherein: estimating degree cutoff value k of immunity threshold based on target immunity in step 3cutThe method is that
Wherein p isc(k) For the purpose of the overall cumulative distribution function of the network, is an estimate of the immune threshold for immunization of a target,m＝<k>and 2, lambda is the propagation rate of virus and information in the network.
4. A complex network local immune system based on random walk sampling is characterized in that: comprising a processor and a memory connected to said processor, said memory storing a program of a random walk sample based complex network local immunization method, which when executed by said processor implements the steps of the method of any of the preceding claims 1 to 3.
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Application publication date: 20190329 |