CN109657160B - Method and system for estimating incoming degree information based on random walk access frequency number - Google Patents
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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 for random walk from a directed network of the information of the degree of entrance to be estimated, wherein the seed node is any node of the network, then implementing random walk, and randomly selecting a subsequent node for random walk from neighbor nodes of a 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 steps for walking is equal to the number N of nodes of the network, counting the number x of times each node i is accessed 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
Technical Field
The invention belongs to the field of social network topology information estimation, and particularly relates to an incoming degree information estimation method and system based on random walk access frequency.
Background
The current online social network is huge in scale, and provides a platform for researching complex networks, real group characteristics and behaviors for researchers. And because of their large size, researchers are unable to perform full network information gathering or acquisition for analysis. Generally, partial information of the network can be acquired only by means of random walk. The recovery of the topological structure of the network by using the acquired network part information is the basis for subsequent complex network analysis, group characteristic analysis and the like. However, an important part in how to recover the network topology through the acquired network part information is to estimate the network admission distribution, because the admission information is potentially hidden in the random walk process. The recovery of the network topology structure can be carried out only by the estimation of the in-degree information, namely the estimation of the network in-degree distribution, thereby further obtaining the characteristics of the whole network.
In the conventional method for estimating the incoming degree information, by using the outgoing degree information which can be collected in the random walk process, when the incoming degree edge and the outgoing degree edge of a node in a network are highly symmetrical, that is, when the network nondirectivity degree is high (nondirectivity, that is, the ratio of the nondirectional edges), an estimation method EST _ out based on the outgoing degree information can be obtained:
wherein the content of the first and second substances,
represents an estimate of the in-degree distribution of the network,
estimation of a degree-out distribution representing a networkMeter, q d (k out ) Is the out-degree distribution of the samples obtained by random walk sampling.
However, for online social networks, the relationships or behaviors between users are directional, e.g., "follow-up behavior" may be both relationships "follow" or "are followed"; the "election behavior" may be an "election" or "elected" relationship, and so on. Thus, the edges of the network may be divided into "in-degree edges" and "out-degree edges" to describe the relationships (edges) that "point" to the node and the relationships (edges) that point to other nodes, respectively. And in most cases the anisotropy in a directed network is not strong. Therefore, the estimation of the degree of entry information obtained by equation (1) causes a large deviation, and therefore, it is necessary to solve the problem of estimating the degree of entry information in the directed network.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: because the estimation method of the network entry information in the prior art is an estimation method through the exit information when the network nondirectivity degree is higher, when the method is applied to a social network with higher directivity, the estimated entry information has larger error, so that the user behavior in the network cannot be well known and the network topological structure cannot be restored through the entry information, and the random walk access frequency-based entry information estimation method with smaller entry information estimation error for the directed network is provided.
In order to solve the problem, the technical scheme adopted by the invention is as follows:
a method for estimating the incoming degree information based on the random walk access frequency number comprises the following steps:
step 1: randomly selecting a seed node for random walk from a directed network of the information of the degree of entrance to be estimated, wherein the seed node is any node of the network, then implementing random walk, and randomly selecting a subsequent node for random walk from neighbor nodes of a current node;
step 2: in the random walk process, the number x of times each node i is repeatedly visited is recorded i ；
And 3, step 3: when the walking step number N is equal to the node number NWhen the node I is accessed, counting the times x of accessing each node I i ；
And 4, step 4: estimating and outputting in-degree information according to the counted number of times that each node i is accessed;
wherein m is i Is visited x in the random walk process i The number of secondary nodes.
The invention also provides a network admission information estimation system based on the random walk access frequency number, which is characterized in that: the method comprises a processor and a memory connected with the processor, wherein the memory stores a program of an incoming degree information estimation method based on random walk access frequency, and the program of the incoming degree information estimation method based on random walk access frequency realizes the steps of the method when being executed by the processor.
Compared with the prior art, the invention has the following beneficial effects:
the method for estimating the access information based on the random walk access frequency number has the advantages that research finds that when the step number of the random walk is the same as the number of network nodes, the number (frequency number) of the accessed nodes in the random walk process is approximately in direct proportion to the access information, so that the access information is estimated by counting the number of the accessed nodes in the random walk process when the problem of nondirectional failure in a directed network is solved, the error of the estimated access information is small, and the estimation efficiency is high.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the comparison of the estimated results obtained in different real networks with the real distribution, wherein (a) Wikipedia election network (WEL), (b) Edinburgh vocabulary association network (EAT), (c) Stanford hyperlink network (SFH), and (d) Amazon recommendation network (AMR);
FIG. 3 is a diagram of D obtained by an estimation method of in-degree information and out-degree information on different real networks KS And (4) comparing the values. Wherein (a) wiki election network (WEL), (b) Edinburgh vocabulary association network (EAT), (c) Stanford hyperlink network (SFH), and (d) Amazon recommendation network (AMR). 100 simulations were performed on each network.
Detailed Description
Fig. 1 to 3 show an embodiment of an incoming degree information estimation method based on random walk access frequency according to the present invention.
First, a method for estimating the degree of entry information will be described, in which the number of steps of random walk is the same as the number of network nodes, and the number of times (frequency) that a node is accessed during the random walk is approximately proportional to its degree of entry.
Suppose 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 one degree of in is
Can be modeled approximately by n Bernoulli experiments (n Bernoulli trials):
wherein X i Random variable, p, representing the number of times node i is visited in random walks i Is the probability that node i may be visited in a random walk (i.e., the probability of sampling). Therefore, X i The expectation of (c) can be expressed as:
E[X i ]＝np i . (3)
the literature: lu X, malmros J, liljeros F, et al]Electronic Journal of Statistics,2013,7 (1): 292-322, gives the sample probability p of any node i in the directed network i Approximately in line with it
In direct proportion, namely:
wherein < k in And > represents the average in-degree of the network, and N is the number of nodes of the network. Bringing (4) into (3) can bring X i The desired representation of (a) is:
if the number of steps N of the random walk is set to N, then
That is, the number of times (frequency) a node is accessed during the random walk at this time is approximately equal to its in-degree
Is in direct proportion. So one scale (scaling) scaled estimate of the in-degree information can be approximately obtained:
wherein m is i Is visited x in the random walk process i The number of secondary nodes. In this embodiment, the method for estimating the in-degree information is referred to as EST _ rw.
The specific method for estimating the in-degree information comprises the following steps:
a method for estimating in-degree information based on random walk access frequency 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 steps for walking is equal to the number N of nodes of the network, counting the number x of times each node i is accessed i ；
And 4, step 4: estimating and outputting the in-degree information according to the counted number of times that each node i is visited;
wherein m is i Is visited x in the random walk process i The number of secondary nodes.
The invention also provides a network admission information estimation system based on the random walk access frequency number, which is characterized in that: the method comprises a processor and a memory connected with the processor, wherein the memory stores a program of an incoming degree information estimation method based on random walk access frequency, and the program of the incoming degree information estimation method based on random walk access frequency realizes the steps of the method when being executed by the processor.
The proposed method of estimating the inbound information of the directed network is verified below by using 4 real directed networks. They are (1) Wikipedia election network (WEL), in which nodes represent users in Wikipedia; the directed edge from node i to node j in the network indicates that user i votes for user j. (2) Edinburgh Association networks (EAT), where network nodes represent English words and are represented by nodes i to j directed edges, will have a response to word j if stimulated with word i in the user's experiment. (3) Stanford hyperlink network (SFH): the nodes in the network represent different web pages on the Stanford university homepage; a directed edge pointing to node j from node i indicates that web page i has a hyperlink pointing to web page j. (4) Amazon recommendation network (AMR): nodes in the network represent different goods, and a directed edge directed by node i to node j indicates that goods j are purchased at the same time goods i are purchased. In order to make all the nodes in the network reachable (reachable), this embodiment extracts the largest Connected Component (GCC) of the 4 networks to obtain the final experimental network. The main network statistics for these several experimental networks are shown in table 1.
TABLE 1 basic network statistics for an experimental network
| Network | Number of nodes N | Number of edges 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 recommendation network | 395,234 | 3,301,092 |
For simulation experiments of in-degree information estimation, this embodiment will be performed in four real networks (WEL, EAT, SFH and AMR). In each simulation, a node in the network is randomly selected as an initial seed node for random walk, and then each step randomly selects the next walk node from the neighbors of the current node. And setting the number of steps of random walk as the number N of nodes of the network. And recording the repeated access condition of the node and the outbound information of the node in the process of walking. This example performed 100 simulations for each network.
In each simulation, we will use two methods to estimate the in-degree information of the network, i.e. we will use
(I) An estimation method of in-degree information, EST _ rw;
(II) conventional method based on out-of-order information, EST _ out.
To compare the performance of the two methods, K-S statistics were used to measure the similarity of their derived estimates and true in-degree information. The specific process is as follows.
First, the data is normalized (normalization), and the true in-degree information and the data collected by the estimation method (EST _ rw: frequency of node visits; EST _ out: sample node out) are projected onto the same scale:
for computational convenience, we can compare z min Is set to be 1,z max Set to 100, the value of y in the above equation will be projected to [1,100 ]]Projecting the real in-degree information, wherein the y value in the formula is the real in-degree of the node; for the EST _ rw method, the y value in the above formula is the frequency of the nodes accessed in the N-step random walks; for the EST _ out method, the y value in the above equation is the degree of departure of the sample node, y max And y min Corresponding respectively to the maximum and minimum values of the observed values expressed above. y is max And y min The different methods are different quantities, specifically: if it is the conventional method EST _ out for comparison, y max And y min With respect to the maximum and minimum values representing degrees, y is given for the EST _ rw method proposed max And y min Representing the maximum and minimum values of the access frequency. If it is true for comparison, y max And y min The maximum and minimum values of true in-degree.
The projected data is then used to calculate the projected distribution of truth and its estimates by both methods (for the proposed EST _ rw, equation (7) is used; for EST _ out, equation (1) is used), respectively. And finally, calculating K-S statistic between the projected real distribution and the estimated distribution obtained by the two methods. The K-S statistic is the basis for rejecting the null hypothesis in the Komogorov-Smirnov test (KS test), i.e. for determining whether two distributions have consistency (elementary); it is used in this example simply to measure the similarity (similarity) between the true distribution and the estimated distribution:
D KS ＝max z {|F'(z)-F(z)|}. (9)
where z represents a range of values of the post-projection (normalized) entrance information, and F (z) and F' (z) represent cumulative distribution functions (normalized) of the true entrance distribution and the estimated distribution (note that normalized), respectively. In the formula D KS The maximum distance of these two cumulative degree distribution functions is described, in general, if D KS If the value of (a) is small, the estimated distribution has a high similarity in shape and position to the true distribution, otherwise, the similarity between them is low. Therefore, it can be said that if one estimation method performs better than the other, it yields D KS The value is relatively small.
The results of simulation experiments on four real networks are as follows. First, the difference between the estimated distribution and the true distribution is visually compared, and the experimental result is shown in fig. 2. It can be seen that: compared with the traditional method based on the out-degree information, the new method has the advantages that the estimation result is better, and the method is closer to the real in-degree information. In the WEL network, the EAT network and the SFH network, we can intuitively observe that the distribution obtained by EST _ rw is more similar to the real distribution in shape, and the distance between the two is much smaller than the distance between the distribution estimated by EST _ out and the real distribution. For the AMR network, although the EST _ rw estimate results in a distribution with a shape deviating somewhat from the true distribution in the first half, its overall shape is much closer to the true distribution than the result from EST _ out as a whole.
Then, the results of EST _ rw and EST _ out estimations, i.e., index D, are quantitatively analyzed KS The difference between them and the real distribution is measured, and the specific result is shown in fig. 3. It can be seen that in these four real networks, EST _ rw yields D KS All of which are smaller than the results obtained by EST _ out. Specifically, D obtained from EST _ rw KS The average ratio EST _ out is 0.29 less in the WEL network, 0.60 less in the EAT network, 0.78 less in the SFH network, and 0.85 less in the AMR network. That is, EST _ rw results in an estimation that is more similar to the true distribution than the corresponding EST _ out results.
The above results are very good illustrations of 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. Meanwhile, the distribution estimated by the method has higher similarity with the real distribution no matter in a model network or a real network.
Compared with the method of wandering the whole network (referred to as the global acquisition method for short), although the method provided by the invention cannot obtain accurate entry information after all or most of the exit edges in the network are acquired like the global acquisition method, the efficiency of the method provided by the invention is far higher than that of the global acquisition method. If all outgoing edges of the network are to be obtained, each edge is traversed at least once, that is, at least the number of steps of random walk to be executed is the total number of edges of the whole network; the number of steps of the random walk set by the invention is the same as the number of nodes of the network, namely, only the edges with the same number as the number of the nodes of the network need to be accessed; therefore, the efficiency of the present invention is < k > times of the global acquisition method (< k > is the average degree of the network).
In addition, compared with the method for delivering, the new method does not need to collect extra data such as delivering in the random walk process, and only needs to record the accessed times; the new method is also more efficient than the out-of-date method from a data collection volume perspective, requiring less process data to be stored.
The above are only preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples, and all technical solutions that fall under the spirit of the present invention belong to the 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 (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, for any one of the entries is
Node (a) ofi，Approximately connect the nodeiFor accessed processnModeling by using a secondary Bernoulli experiment:
whereinX i Representative nodeiA random variable of the number of times accessed in a random walk,x i for each nodeiThe number of times the access is repeated is determined,p i is a nodeiThe probability of being likely to be visited in a random walk,X i is expressed as:
E[X i ]=np i ，
in a directed network, arbitrary nodesiProbability of sample entryp i Approximately in line with it
Is proportional, i.e.
<k in >Which represents the average in-degree of the network,Nthe number of nodes of the network;
then theX i Is expressed as:
and step 3: number of steps while walkingnNumber of nodes with networkNWhen they are equal, thenX i Is expressed as:
indicating that the number of times a node is accessed during random walks is approximately equal to its degree of entry
Is in direct proportion;
and 4, step 4: counting each nodeiNumber of times of accessx i According to each node countediAccessed number estimation in-degree informationp d (x i ) And outputting;
whereinm i Is accessed in the random walk processx i The 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 the processor, the memory storing a program of a random walk access frequency based approach information estimation method, the program of the random walk access frequency based approach information estimation method when executed by the processor implementing the steps of the method of claim 1.
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