CN109657160A - In-degree information estimation method and system based on random walk access frequency - Google Patents

Abstract

The invention discloses an incoming degree information estimation method based on random walk access frequency, which comprises the following steps of 1: randomly selecting a seed node which is randomly walked from a directed network of the information of the degree of admission to be estimated, wherein the seed node is any node of the network, then implementing random walk, and randomly selecting a subsequent node which is randomly walked from a neighbor node of the current node; step 2: in the random walk process, the number x of times each node i is repeatedly visited is recorded_i(ii) a And step 3: when the number N of walking steps is equal to the number N of nodes of the network, counting the number x of times each node i is visited_i(ii) a And 4, step 4: estimating and outputting the in-degree information according to the counted number of times that each node i is visited; when the method is used for solving the problem of nondirectional weakness in the directed network, the degree of entry information is estimated by counting the number of times each node is visited in the random walk process, the error of the estimated degree of entry information is small, and the estimation efficiency is high.

Description

In-degree information estimation method and system based on random walk access frequency

technical field

The invention belongs to the field of social network topology information estimation, and in particular relates to an in-degree information estimation method and system based on random walk access frequency.

Background technique

At present, the scale of online social networks is huge, providing researchers with a platform to study complex networks, real group characteristics, and behaviors. And because of its large scale, researchers cannot conduct network-wide information collection or access for analysis. Generally, only part of the information of the network can be obtained by means of random walks. Using the acquired network information to restore the topology of the network is the basis for subsequent complex network analysis and group characteristic analysis. However, an important part of how to recover the network topology through the acquired network information is the estimation of the network in-degree distribution, because in the random walk process, the in-degree information is latent and hidden. With the estimation of the in-degree information, that is, the estimation of the in-degree distribution of the network, the network topology can be restored, and the characteristics of the entire network can be further obtained.

The traditional in-degree information estimation method uses the out-degree information that can be collected in the random walk process. It is assumed that when the in-degree edges and out-degree edges of nodes in the network are highly symmetrical, that is, when the degree of network anisotropy is high (no The tropism is the proportion of undirected edges), and the estimation method EST_out based on the out-degree information can be obtained:

in, represents the estimated in-degree distribution of the network, Represents an estimate of the out-degree distribution of the network, and q _d (k ^out ) is the out-degree distribution of samples obtained by random walk sampling.

However, for online social networks, the relationship or behavior between users is directional. For example, "following behavior" can be two relationships of "following" or "being followed"; "election behavior" can be "election" or The "elected" relationship and so on. Therefore, the edges of the network can be divided into "in-degree edges" and "out-degree edges", which are used to describe the relationship (edge) "pointing" to the node and the relationship (edge) that the node points to other nodes, respectively. And in most cases, the undirection in directed networks is not strong. Therefore, the estimation of the in-degree information obtained by using the formula (1) will cause a large deviation, so it is necessary to solve the problem of in-degree information estimation in the directed network.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is: since the estimation method for network in-degree information in the prior art is an estimation method based on the out-degree information when the degree of network anisotropy is relatively high, the method can be used when the degree of network in-degree is relatively high. In a high social network, the estimated in-degree information has a large error, so it is impossible to understand the user behavior in the network and restore the network topology through the in-degree information. In-degree information estimation method based on random walk access frequency with small degree information estimation error.

In order to solve this problem, the technical scheme adopted in the present invention is:

A method for estimating in-degree information based on random walk access frequency, comprising the following steps:

Step 1: Randomly select the seed node of the random walk from the directed network of the in-degree information to be estimated, the seed node is any node of the network, and then implement the random walk, and the subsequent nodes of the random walk are determined by the neighbors of the current node. Nodes are randomly selected;

Step 2: In the process of random walk, record the number of times xi that each node _i is repeatedly visited;

Step 3: When the number of walking steps n is equal to the number of nodes N of the network, count the times x _i that each node i is visited;

Step 4: Estimate the in-degree information according to the counted number of visits to each node i and output;

where m _i is the number of nodes visited x _i times during the random walk.

The present invention also provides a system for estimating network in-degree information based on random walk access frequency, which is characterized by comprising a processor and a memory connected to the processor, and the memory stores a random walk based access frequency. The program of the in-degree information estimation method based on the random walk access frequency is executed by the processor to implement the steps of the above-mentioned method.

Compared with the prior art, the beneficial effects achieved by the present invention are:

The present invention is based on the in-degree information estimation method of random walk access frequency. Through research, it is found that when the number of steps of random walk is the same as the number of network nodes, the number of times (frequency) of nodes visited in the process of random walk is approximately the same as the number of nodes in the random walk. The in-degree information is proportional to the in-degree of , so for the problem of low undirection in the directed network, the in-degree information is estimated by counting the number of times each node is visited in the random walk process, and the estimated in-degree information The error is smaller and the estimation efficiency is higher.

Description of drawings

Fig. 1 is the flow chart of the present invention;

Figure 2 is a schematic diagram of the comparison between the estimated results obtained in different real networks and the real distribution, in which (a) Wiki Electoral Network (WEL), (b) Edinburgh Lexical Association Network (EAT), (c) Stanford Hyperlink Network (SFH) ), and (d) the Amazon Referral Network (AMR);

Figure 3 shows the comparison of D _KS values obtained by in-degree information and out-degree information estimation methods on different real networks. where (a) Wiki Electoral Network (WEL), (b) Edinburgh Lexical Association Network (EAT), (c) Stanford Hyperlink Network (SFH), and (d) Amazon Recommendation Network (AMR). 100 simulations were performed on each network separately.

Detailed ways

FIG. 1 to FIG. 3 show an embodiment of the method for estimating in-degree information based on random walk access frequency according to the present invention.

Firstly, when the number of steps of the random walk is the same as the number of network nodes, the number of times (frequency) that a node is visited in the process of random walk is approximately proportional to its in-degree, and then the method of estimating the in-degree information is obtained.

Assuming that n-step random walk is implemented in the directed network, the seed node of the random walk is 1, the seed selection strategy is random selection, and the subsequent nodes are randomly selected by the neighbor nodes of the current node. Then for any in-degree of The node i of the node i can be approximately modeled by n Bernoulli trials:

Among them, X _i represents the random variable of the number of visits of node i in the random walk, and p _i is the probability that node i may be visited in the random walk (ie, the probability of sampling). So, the expectation of _Xi can be expressed as:

E[X _i ]=np _i . (3)

Literature: Lu X, Malmros J, Liljeros F, et al. Respondent-driven sampling on directed networks[J]. Electronic Journal of Statistics, 2013, 7(1): 292-322. Given that in directed networks, any The in-sampling probability pi of node _i is approximately the same as its in-degree proportional, that is:

where <kin> represents the average ⁱⁿ -degree of the network, and N is the number of nodes in the network. _Bringing (4) into (3) can express the expectation of Xi as:

If the number of steps n of the random walk is set to N, then

That is to say, the number of times (frequency) that the node is visited during the random walk at this time is approximately the same as its in-degree proportional. Therefore, a scaled in-degree information estimate can be obtained approximately:

where m _i is the number of nodes visited x _i times during the random walk. In this embodiment, the estimation method of the in-degree information is called EST_rw.

The specific in-degree information estimation method is as follows:

A method for estimating in-degree information based on random walk access frequency, comprising the following steps:

Step 1: Randomly select the seed node of the random walk from the directed network of the in-degree information to be estimated, the seed node is any node of the network, and then implement the random walk, and the subsequent nodes of the random walk are determined by the neighbors of the current node. Nodes are randomly selected;

Step 2: In the process of random walk, record the number of times xi that each node _i is repeatedly visited;

Step 3: When the number of walking steps n is equal to the number of nodes N of the network, count the times x _i that each node i is visited;

Step 4: Estimate the in-degree information according to the counted number of visits to each node i and output;

where m _i is the number of nodes visited x _i times during the random walk.

The present invention also provides a system for estimating network in-degree information based on random walk access frequency, which is characterized by comprising a processor and a memory connected to the processor, and the memory stores a random walk based access frequency. The program of the in-degree information estimation method based on the random walk access frequency is executed by the processor to implement the steps of the above-mentioned method.

In the following, the proposed directed network in-degree information estimation method is verified by using 4 real directed networks. They are (1) the Wikipedia election network (WEL), the nodes in the network represent users in Wikipedia; the directed edge from node i to node j in the network indicates that user i voted for user j . (2) The Edinburgh Associative Thesaurus network (EAT), in which the network nodes represent English words, and the directed edges from node i to node j are represented. In user experiments, if they are stimulated with word i , it will respond with word j. (3) Stanford hyperlink network (SFH): The nodes in this network represent different web pages on the Stanford University homepage; the directed edge from node i to node j indicates that web page i has hyperlinks to web page j. (4) Amazon recommendation network (AMR): The nodes in this network represent different commodities, and the directed edge from node i to node j indicates that when commodity i is purchased, commodity j is also purchased. In order to make the nodes in the network all reachable (reachable), this embodiment extracts the largest connected component (Giant Connected Component, GCC) of the four networks to obtain the final experimental network. The main network statistics of these experimental networks are shown in Table 1.

Table 1 Basic network statistics of the experimental network

network Node number N side number E Wiki election network 1,300 39,437 Edinburgh Vocabulary Association Network 7,751 235,476 Stanford Hyperlink Network 150,532 1,576,314 Amazon Referral Network 395,234 3,301,092

For the simulation experiments of in-degree information estimation, this embodiment will be carried out in four real networks (WEL, EAT, SFH and AMR). In each simulation, a node in the network is randomly selected as the initial seed node for the random walk, and then at each step the next node for the walk is randomly selected from the neighbors of the current node. Set the number of steps of the random walk as the number of nodes in the network N. In the process of walking, record the repeated visits of the node and the out-degree information of the node. In this example, 100 simulations were performed for each network.

In each simulation, we will use two methods to estimate the in-degree information of the network, namely

(1) Estimation method of in-degree information, EST_rw;

(II) Traditional method based on out-degree information, EST_out.

To compare the performance of the two methods, the K-S statistic is used to measure the similarity of the estimates they produce with the true in-degree information. The specific process is as follows.

First, normalize the data, and project the real in-degree information and the data collected by the estimation method (EST_rw: node access frequency; EST_out: sample node out-degree) to the same scale:

For the convenience of calculation, we can set z _min to 1 and z _max to 100, then the value of y in the above formula will be projected between [1, 100], and the real in-degree information is projected, the value of y in the above formula is the true in-degree of the node; for the EST_rw method, the y value in the above formula is the frequency of the node being visited in N-step random walks; for the EST_out method, the y value in the above formula is the out-degree of the sample node, y _max and y _min correspond to the maximum and minimum values of the observations expressed above, respectively. y _max and y _min correspond to different methods and are different quantities, specifically: if it is the traditional method for comparison EST_out, y _max and y _min indicate the maximum and minimum values of the degree, if it is the proposed EST_rw method For example, y _max and y _min represent the maximum and minimum visit frequency. For the true values used for comparison, y _max and y _min are the maximum and minimum values of the true in-degree.

Then, use the projected data to calculate the projected reality distribution and its estimation by the two methods (for the proposed EST_rw, use equation (7); for EST_out, use equation (1)). Finally, calculate the K-S statistic between the projected true distribution and the estimated distribution obtained by the two methods. K-S statistic is the basis for rejecting the null hypothesis in the Komogorov-Smirnov test (KS test), that is, it is used to judge whether the two distributions have agreement; in this embodiment, it is simply used to measure the true distribution and estimation Similarity between distributions:

D _KS =max _z {|F'(z)-F(z)|}. (9)

Among them, z represents the value range of the in-degree information after projection (after normalization), and F(z) and F'(z) represent the cumulative distribution function of the true in-degree distribution and the estimated distribution (note that it is normalized), respectively. distributionfuncion). D _KS in the formula describes the maximum distance between the two cumulative degree distribution functions. Generally speaking, if the value of D _KS is small, then the estimated distribution has a high similarity with the real distribution in shape and position, otherwise , the similarity between them is low. Therefore, it can be considered that if one estimation method performs better than the other, it will result in a relatively small _DKS value.

The simulation results on the four real networks are as follows. First, the difference between the estimated distribution and the true distribution is visually compared, and the experimental results are shown in Figure 2. It can be seen that: in contrast, the proposed new method achieves better estimation results than traditional out-degree information-based methods, and is closer to the real in-degree information. In the WEL network, EAT network and SFH network, we can intuitively observe that the distribution obtained by EST_rw is more similar in shape to the real distribution, and the distance between the two is also smaller than the distance between the distribution estimated by EST_out and the real distribution a lot of. For the AMR network, although the shape of the distribution estimated by EST_rw deviates from the real distribution in the first half, on the whole, its overall shape is much closer to the real distribution than the results obtained by EST_out.

Then, quantitatively analyze the estimation results of EST_rw and EST_out, that is, use the indicator D _KS to measure the difference between them and the real distribution. The specific results are shown in Figure 3. It can be seen that in these four real networks, the value of D _KS obtained by EST_rw is smaller than that obtained by EST_out. Specifically, the average value of D _KS obtained by EST_rw is 0.29 smaller in WEL network, 0.60 smaller in EAT network, 0.78 smaller in SFH network, and 0.85 smaller in AMR network than the corresponding result of EST_out. That is, the similarity between the estimated results obtained by EST_rw and the true distribution is higher than the corresponding results of EST_out.

The above results all illustrate very well that the error of the in-degree estimation method EST_rw proposed by the present invention is smaller than that of the out-degree estimation method. At the same time, it can also be obtained that, whether in the model network or in the real network, the distribution estimated by the present invention has a high similarity with the real distribution.

Compared with roaming the whole network (referred to as "global acquisition method"), although the method proposed in the present invention cannot obtain accurate in-degree information by acquiring all or most of the outgoing edges in the network like the global acquisition method. , but the efficiency of the present invention is much higher than the global acquisition method. Because, to get all the outgoing edges of the network, each edge must be traversed at least once, that is to say, at least the number of steps of the random walk to be performed is the total number of edges in the entire network; The number of walking steps is the same as the number of nodes in the network, that is, only the same number of edges as the number of network nodes need to be accessed; therefore, the efficiency of the present invention is <k> times that of the global acquisition method (<k> is the average degree of the network) .

Besides, compared with the out-degree method, the proposed new method does not need to collect additional data such as out-degree in the random walk process, but only needs to record the number of visits; from the perspective of data collection volume , the new method is also more efficient than the out-degree method, which requires less process data to be stored.

The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions that belong to the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (2)

1. A complex network entry information estimation method based on random walk access frequency is characterized in that: the method comprises the following steps:

step 1: randomly selecting a seed node which is randomly walked from a directed network of the information of the degree of admission to be estimated, wherein the seed node is any node of the network, then implementing random walk, and randomly selecting a subsequent node which is randomly walked from a neighbor node of the current node;

step 2: in the random walk process, the number x of times each node i is repeatedly visited is recorded_i；

And step 3: when the number N of walking steps is equal to the number N of nodes of the network, counting the number x of times each node i is visited_i；

And 4, step 4: estimating the degree of entry information p according to the counted number of times each node i is visited_d(x_i) And outputting;

wherein m is_iIs visited x in the random walk process_iThe number of secondary nodes.

2. A complex network entry information estimation system based on random walk access frequency is characterized in that: comprising a processor and a memory connected to said processor, said memory storing a program of a random walk access frequency based approach information estimation method, said program of a random walk access frequency based approach information estimation method being executed by said processor to implement the steps of the method of any of the previous claims 1-3.