CN102148706A - Evolution mode mining method in dynamic complex network - Google Patents
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Abstract
The invention discloses an evolution mode mining method in a dynamic complex network, which is used for solving analysis on evolution characteristics of local topological structures in a large-scale dynamic complex network, and is convenient for users to predict the behaviors and development tendencies of a complex system. In the invention, the network data at different times in the dynamic complex network is constructed into a summery graph, and the sides of the summery graph is provided with tags under the premise of keeping useful information; on the summery graph, rule sides are searched through character string matching, and each rule is recorded; then a weighing graph is constructed according to the rule sides to complete the searching of the evolution mode. The definition on the mode in the invention has commonality, can process noise data, and discover approximated modes and conservative sub-structures; the mode mining method is simple and flexible, avoids complex calculation on candidate subsets and subgraph isomorphism generated in conventional and frequent mode mining method, and has very high efficiency.
Description
Technical field
The present invention relates to the evolution modelling method for digging in data mining and the Complex Networks Analysis field, particularly DYNAMIC COMPLEX network.
Background technology
Along with computer science and development of internet technology, be exponential growth from the network data of every field.In the correlative study of network data analysis, figure is a kind of very important modeling tool, and individuality is abstracted into node, the contact between the individuality is abstracted into the limit has just constituted graph structure.Figure can carry out modeling to a lot of complication systems, comprises biosystem, physical system, software systems and social system etc.Utilization figure mining algorithm is analyzed complex network, can strengthen understanding and the understanding of people to large scale network, helps association area to make correct decision-making and the expert carries out more deep research to association area.Yet because the complexity of the huge and figure excavation of problem scale itself, extracting useful knowledge and information from mass data becomes the great difficult problem of pendulum in face of people.
Frequent Pattern Mining is that a kind of figure that typically has very high computational complexity excavates problem, and it can be divided into, and set of graphs is excavated (Graph dataset mining) and big figure excavates (large graph mining).It is from the set of a picture group that set of graphs is excavated, the frequent subgraph that occurs of search, and the number of times that these subgraphs occur in the set of this picture group is no less than certain threshold value.It is the frequent subgraph that occurs of search from single big figure that big figure excavates.Frequent Pattern Mining can be widely used in fields such as Web excavation, network invasion monitoring, drug discovery, compound be synthetic.Cluster is excavated problem as the very important figure of another kind, is the process that the set of physics or abstract object is divided into a plurality of corporations (community) structure of being made up of similar object.Belong between the inside member of same corporations and connect closely, the member between the different corporations connects loose.By network is carried out cluster analysis, can obtain identical working group of the functional module of network or interest etc., be convenient for people to make a strategic decision, significant.For example, in commercial affairs, cluster can help the Market Analyst to find different customers from the basic storehouse of client, and portrays the feature of different customers with purchasing model.Biologically, cluster can be used to the to derive classification of plant and animal is classified to gene, obtains the understanding to inherent structure in the population.
Network data in the real world has the feature that slowly changes in time mostly, and such network data is referred to as the DYNAMIC COMPLEX network.Yet current figure method for digging mainly concentrates on the analysis to static network, and these static networks are simple integrated or DYNAMIC COMPLEX network snapshots at a time of the data in a plurality of moment in the DYNAMIC COMPLEX network.Simple analyzes static network, ignores the characteristic that the DYNAMIC COMPLEX network constantly develops, and these analyses have limitation so.Along with the DYNAMIC COMPLEX network data is more and more abundanter, many scholars begin the problem in the static network is expanded to dynamic network, and in researchs such as numerous mode excavation of the enterprising line frequency of dynamic network and clusters.Some methods that are used for static network also have been extended to dynamic network, for example, people such as Wackersreuther have proposed a framework that solves the Frequent Pattern Mining problem in the dynamic network with the figure digging technology on the static map, at first the data with a plurality of moment in the dynamic network are integrated into a big figure, with the frequent subgraph of search on big figure of the classical way in the static network, from these frequent subgraphs, search for the frequent mode of dynamic network at last with suffix tree then.People such as Chakrabarti have proposed the framework of evolution clustering for the first time: this framework is when carrying out cluster to each network data constantly, both require cluster result to meet the network topology characteristic of current time, and required the cluster result of cluster result and previous moment to be consistent again as far as possible.Two targets are combined, seek the balance point an of the best, this meets the DYNAMIC COMPLEX network is slowly to change this essential characteristic.Based on this framework, scholars have proposed some again and have used traditional clustering algorithm to solve the strategy of dynamic network clustering problem.
Above-mentioned Frequent Pattern Mining and clustering method based on the DYNAMIC COMPLEX network can help us understand complication system, yet, the evolution rule of DYNAMIC COMPLEX network and the excavation of conservative minor structure are also had great importance.These evolution rules comprise the development trend (Development trendof the evolving systems) of evolution modelling (evolving patterns) and evolutionary system etc.People such as Lahiri use the method for frequent subgraph and scheme-tree to excavate to have periodic pattern.You and Cook utilization figure rewriting rule (graph-rewriting rules) is portrayed network situation over time, is illustrated in time series pattern (temporal patterns) in the structural change with description rule (description rules).Method of the present invention will solve the problem similar with them, but also exists different:
(1) the definition difference of pattern.The pattern that defines among the present invention is more general, and the pattern of people such as Lahiri definition is the special case of the pattern that defines among the present invention.
(2) the evolution rule of having considered the real world complication system has uncertainty to a certain degree, and the network data of collecting has the characteristics of noise, so the present invention also finds approximate mode, has more realistic meaning.
(3) method among the present invention can also be searched for conservative (conserved) minor structure in the DYNAMIC COMPLEX network.Conservative minor structure is a more stable part in the DYNAMIC COMPLEX network change process, has different implications in different application.For example the conservative minor structure in the protein interaction network is being represented the unit with certain function, and the conservative minor structure in scientist's cooperative network is being represented more stable research institution.
The method of (4) dealing with problems is different fully.Method among the present invention has avoided producing in the conventional Frequent Pattern Mining method complicated calculations of candidate subset and subgraph isomorphism, greatly reduce the time and the space complexity of method, have very high efficient, can solve the problem analysis of local topology evolution feature in the extensive DYNAMIC COMPLEX network.
Summary of the invention
In view of above-mentioned analysis, the present invention has defined a kind of pattern more common in the DYNAMIC COMPLEX network, and a kind of method that is used to excavate this pattern proposed, by this quasi-mode is excavated, obtain the localized variation feature in the DYNAMIC COMPLEX network evolution process, be used for predicting the change and progress trend of network.
Key of the present invention is the definition of evolution modelling.So-called evolution modelling, pattern frequent appearance, that have certain appearance rule in DYNAMIC COMPLEX network evolution process exactly.
Technical problem underlying of the present invention is how to finish the screening on regular limit (regular edge) and the search of evolution modelling efficiently.To the figure in a plurality of moment in the DYNAMIC COMPLEX network, under the prerequisite of obliterated data effective information not, be configured to sum graph, the mode excavation problem on a plurality of figure is transformed on the single figure, thereby greatly reduces the time and the space complexity of method.Use a kind of strategy to judge and be marked in the dynamic network change procedure and have the limit that rule occurs, just regular limit obtains a subgraph of the sum graph that is made of regular limit., only the regular limit in this subgraph is carried out during evolution modelling in search, thereby further reduced the computational complexity of algorithm.
One, the concrete steps of the evolution modelling method for digging of standard of the present invention are expressed as follows:
The first step, input DYNAMIC COMPLEX network G=＜G
1, G
2..., G
TAnd threshold value S, structure sum graph G
sGive G
sIn each bar limit e add that length is " 0 " " 1 " character string of T, the label as e is designated as l
e, at the position of label t, if character is " 0 ", expression limit e does not occur in t figure; If character is " 1 ", expression limit e occurs in t figure.Delete not frequent limit, just in the label of limit the number of character " 1 " less than the limit of threshold value S.
Random limit is deleted on second step, judgement and marking convention limit.To G
sIn each bar limit e, if l
eAll characters be entirely the individual character of " 1 " or preceding t (user-defined numerical value) entirely for " 0 ", then e is non-regular limit, t=T/2 or t=3T/4 here can certainly be provided with the value of t according to priori.Otherwise, suppose that the length of regular r is d, be expressed as l
e(1..d), get d and equal 2 to T/2, relatively r and remaining T/d section character string if each section is all identical with r, think that then e is regular limit, otherwise e are non-regular limit.Non-regular limit is deleted on the marking convention limit, is only comprised the underlined figure G on regular limit
1
The 3rd step, the rule on regular limit is mapped as weight, obtains weighted graph.(wherein d is the length of rule for d, rule) delegate rules sequence, and rule is corresponding rule with two tuples among the present invention.Suppose that a tag characters string is " 001101001101001101 ", then rule is " 001101 ", and d is 6, represents with two tuples (6, " 001101 ").Like this, just two tuples can be mapped as 6 integers.Method is as follows: highest order is d, and other 5 is the decimal representation of rule.(6, " 001101 ") are mapped as integer 600013.
The 4th goes on foot, goes on foot on the weighted graph that obtains the 3rd and search for evolution modelling.Search procedure is from any regular limit, and the adjacent side that search equates with its weight obtains a connected subgraph with regular limit formation of equal weight, as evolution modelling.Repeat said process, all visited, then obtained whole evolution modellings up to the strictly all rules limit.
By above step, just can be with the evolution modelling in less time and the space complexity acquisition DYNAMIC COMPLEX network.
Two, one of potential application of method is the evolution behavior of prediction DYNAMIC COMPLEX network among the present invention.Because a lot of evolution modellings in the DYNAMIC COMPLEX network are not just to occur in preceding several moment.In order to find the new evolution modelling that produces in the network change process, the present invention has expanded the evolution modelling method for digging of standard.When judging whether a limit is regular limit, ignore leading " 0 ", begin from first " 1 " of label to check rule to occur.In addition, because the evolution rule has certain uncertainty, and there is noise, evolution modelling in the live network is also imperfect, the present invention introduced the notion of shake (jitter), when judging whether a limit is regular limit, defined the scope that a threshold value limits shake.The label 1 of limit e for example
eBeing " 0111001110111101 ", is 1 if set the threshold value of shake, can judge that then e is a regular limit with rule " 11101 ".Another kind of situation is that a subgraph is an evolution modelling, and does not require that all limits of this subgraph all are regular limits.It is considered herein that if a subgraph is an evolution modelling, then there is a regular limit at least in this subgraph.In order to search for the approximate mode in the reality, the present invention has expanded the evolution modelling method for digging of standard.Concrete steps are as follows:
The first step, structure sum graph are consistent with the evolution modelling method for digging of standard.
Second step, judgement and marking convention limit, but keep frequent non-regular limit.
The 3rd step, the rule on regular limit is mapped as weight.
The 4th step, search evolution modelling.Select a regular limit of not visiting at random, expand the adjacent side on this limit.If this adjacent side is regular limit, then compare their weight; Otherwise, with in the label on this limit for the position of " 1 " and the correspondence position of its adjacent side compare, if be " 1 " entirely, then this adjacent side is put into the result, and the mark of having visited on the regular limit that all-access is crossed remembered.Repeat such expansion, up to there not being new adjacent side to add to come in.Like this, an evolution modelling has just formed.Up to having searched for all regular limits, just obtained the whole approximate evolution modelling of this DYNAMIC COMPLEX network.
Three, conservative minor structure is the special case of above-mentioned evolution modelling, is meant the connected subgraph that always exists in the evolutionary process of DYNAMIC COMPLEX network.To the excavation of this pattern, can find highly stable part in the DYNAMIC COMPLEX network change process, be convenient for people to according to practical application, make relevant analysis and decision.The concrete steps of conservative minor structure method for digging are as follows among the present invention:
The first step, structure sum graph are consistent with the evolution modelling method for digging of standard.
Second step, deletion label are not the limit of " 1 " entirely.
The 3rd goes on foot, defines certain rule, goes on foot from second and searches for legal connected subgraph the figure that obtains, and promptly obtains the conservative minor structure in the DYNAMIC COMPLEX network.
Advantage and good effect
Use the method among the present invention to realize that the excavation of evolution modelling has following advantage:
(1) evolution modelling that finds of the method among the present invention has better generality.
(2) method among the present invention can be found approximate mode, and pattern can occur in DYNAMIC COMPLEX networks development process, and not necessarily will just occur constantly at first, and such pattern more meets the rule of development of real world things.
(3) method among the present invention can be searched for conservative minor structure in the DYNAMIC COMPLEX network.
(4) efficient of the method among the present invention is very high, is applicable to the excavation of evolution modelling in the extensive DYNAMIC COMPLEX network.
Description of drawings
Fig. 1 is the flow chart of the evolution modelling method for digging of standard.
Fig. 2 is the flow chart of the evolution modelling method for digging of expansion.
The main distinction of Fig. 2 and Fig. 1 is: judge that the method among Fig. 2 was at first removed leading " 0 " when whether a limit was regular limit; To the processing difference on frequent non-regular limit, the method among Fig. 2 keeps non-regular limit, and the method among Fig. 1 is directly deleted non-regular limit; According to the method difference of weighted graph search evolution modelling, the method among Fig. 2 is searched for according to weight and label, and the method among Fig. 1 is only searched for according to weight.
Fig. 3 is that rule is the evolution modelling of " 1100 " in the Football data.
Fig. 4 is that rule is the evolution modelling of " 0011 " in the Football data.
Fig. 5 is that rule is the approximate evolution modelling of " 1111110 " in the Enron E-mail data.
Fig. 6 is that rule is the approximate evolution modelling of " 11110 " in the Enron E-mail data.
Fig. 7 is the conservative minor structure that has 4 nodes in the DBLP cooperative network data.
Embodiment
The present invention will be further described below in conjunction with drawings and Examples.
Embodiment 1
The evolution modelling that utilizes the evolution modelling method for digging of standard among the present invention to finish the Football data excavates.The Football data are schedule tables of American college athletic association football match, and wherein each node is represented a football team, and every limit is represented between two football teams bout.What use among the present invention is data from 2000 to 2009, is unit per year, constitutes the dynamic network with 10 moment.
The implementation step following (workflow is seen accompanying drawing 1) of utilizing the evolution modelling method for digging of standard that the Football data are carried out mode excavation:
The first step, input dynamic network G=＜G1, G2 ..., G10 〉, structure sum graph Gs adds label for each the bar limit e among the Gs, is designated as le.Delete not frequent limit, this moment, threshold value S was made as 2.
Non-regular limit is deleted on second step, judgement and marking convention limit.To G
sIn each bar limit e, according to the label of e, judge whether e is regular limit.To regular limit, its rule is preserved with two tuples; To non-regular limit, directly from G
sMiddle deletion.
The 3rd step, the rule on regular limit is mapped as weight.At first obtain representing the sequence of rules on every regular limit two tuples (d, rule).The mapping ruler of the evolution modelling method for digging of the standard of pressing is mapped as the integer weight with each two tuple.
The 4th goes on foot, goes on foot on the weighted graph that obtains the 3rd and search for evolution modelling.Begin expansion from any regular limit, for example (Colorado) begins search to this edge of Texas (Texas) from the state of Colorado, expands the limit that equates with its weight, obtains an evolution modelling.The all accessed mistake up to whole regular limits has just found whole evolution modellings of Football data.
By above step, the standard evolution modelling of just having finished the Football data excavates.Fig. 3 shows be one have 12 nodes, 16 limits, since the 1st moment, rule evolution modelling for " 1100 "; Fig. 4 shows be one have 12 nodes, 15 limits, since the 1st moment, rule evolution modelling for " 0011 ".
Embodiment 2
The approximate evolution modelling that utilizes the evolution modelling method for digging of expanding among the present invention to finish Enron E-mail data excavates.Enron E-mail data are records that the employee of Enron intra-company receives and dispatches E-mail, and the E-mail contact was arranged between two employees, and then directly there is a limit in both.What use among the present invention is data from year March in December, 1999 to 2002, monthly is unit, constitutes the dynamic network with 28 moment.
The implementation step following (workflow is seen accompanying drawing 2) that the approximate evolution modelling that utilizes the present invention to finish Enron E-mail data excavates:
The first step, input dynamic network G=＜G1, G2 ..., G28 〉, structure sum graph Gs adds label for each the bar limit e among the Gs, is designated as le.Delete not frequent limit, this moment, threshold value S was made as 2.
Second step, judgement and marking convention limit keep non-regular limit simultaneously.When judging whether a limit is regular limit, remove leading " 0 ", to find emerging pattern in DYNAMIC COMPLEX network change process.
The 3rd step, the rule on regular limit is mapped as weight.At first obtain representing the sequence of rules on every regular limit two tuples (d, rule).According to the mapping ruler in the evolution modelling method for digging of standard, each two tuple is mapped as the integer weight.
The 4th goes on foot, goes on foot on the weighted graph that obtains the 3rd and search for evolution modelling, and this seasonal jitter equals 1, with the evolution modelling that obtains being similar to.
By above step, the approximate evolution modelling of just having finished the Enron-E-mail data excavates.Fig. 5 shows be one have 9 nodes, 8 limits, since the 12nd moment, rule evolution modelling for " 1111110 "; Fig. 6 shows be one have 23 nodes, 22 limits, since the 18th moment, rule evolution modelling for " 11110 ".These two evolution modellings all are very sparse, and are star or class star structure.If think that these two patterns are respectively little working groups, can infer that two Centroids are representing the key leader in the working group separately respectively, they regularly and group member separately link up.These information can be used for predicting DYNAMIC COMPLEX the network behavior and the development trend in future.
Embodiment 3
The conservative minor structure of utilizing method among the present invention to finish DBLP cooperative network data is excavated.The DBLP data are the reference list information of the publication of computer science, the present invention from this extracting data in the period of 2000 to 2009 in the cooperative relationship of the paper of 28 important meetings of database, data mining and artificial intelligence field, be unit per year, constitute dynamic network with 10 moment, wherein each node is represented an author, and on behalf of two authors, every limit cooperate to deliver one piece of paper at least.
It is as follows to utilize the present invention to finish the implementation step of conservative minor structure of DBLP cooperative network data:
The first step, input dynamic network G=＜G1, G2 ..., G10 〉, structure sum graph Gs adds label for each the bar limit e among the Gs, is designated as le.
Second step, deletion label are not the limit of " 1 " entirely.
The 3rd goes on foot, goes on foot the figure that obtains from second and search for connected subgraph, promptly obtains the conservative minor structure in the DYNAMIC COMPLEX network.
Fig. 7 shows be one have 4 nodes, 6 limits, since the 1st moment, remain into the conservative minor structure of last moment always.This complete subgraph is represented four corresponding authors, from each year in the period of 2009 in 2000, all cooperates to deliver one piece of paper arbitrarily between the two at least.
Embodiment 4
The present invention has defined the standard of several evaluation evolution modellings and dynamic network.
Because different evolution modellings has different importance in the dynamical system, the present invention has defined the intensity (Strength) of evolution modelling g:
Wherein l and L represent the number of character " 1 " in the rule of evolution modelling g and the length of rule respectively.The density of the subgraph of density (g) expression evolution modelling g correspondence:
The intensity of an evolution modelling is big more, illustrates that this pattern is important more in the dynamical system of correspondence.
Because evolution modelling can be predicted the development trend of dynamic network according to the localized variation characteristic, the present invention has defined a kind of module of verifying its accuracy that predicts the outcome.The predictability of evolution modelling g (Prediction) is:
Timesteps is the moment number of the data that are used for giving a forecast.If in the prediction data, evolution modelling g occurs constantly at i, then real
i(g) equal 1, otherwise equal 0.If predicting evolution modelling g, method occurs constantly, then predicted at i
i(g) equal 1, otherwise equal 0.
The Prediction value of an evolution modelling is big more, and expression is carried out prediction accuracy with this pattern in DYNAMIC COMPLEX network evolution process big more.
The present invention also portrays the DYNAMIC COMPLEX stability of network with conservative rate (ConservedRate).DYNAMIC COMPLEX network G=＜G
1, G
2..., G
TConservative rate be defined as:
Wherein g is conservative minor structure, its scale be defined as size (g)=| V
g|+| E
g|.
The conservative rate of a DYNAMIC COMPLEX network is big more, represents that this stability of network is big more, illustrates that also these conservative minor structures are big more to the effect or the meaning of DYNAMIC COMPLEX system simultaneously.
Utilize formula (1) and formula (2) in the evaluation criterion, can in the hope of, the intensity of the evolution modelling among Fig. 5 is 0.19, the intensity of the evolution modelling among Fig. 6 is 0.07.The intensity of these two evolution modellings is all lower, is that topological structure by pattern is very sparse essential characteristic decision.
Should be understood that, for those of ordinary skills, can be improved according to the above description or conversion, and all these improvement and conversion all should belong to the protection range of claims of the present invention.
Claims (3)
1. the evolution modelling method for digging in the DYNAMIC COMPLEX network is characterized in that concrete steps are as follows:
(1) input DYNAMIC COMPLEX network G=＜G
1, G
2..., G
TAnd threshold value S, structure sum graph G
sGive G
sIn each bar limit e add that length is " 0 " " 1 " character string of T, the label as e is designated as l
e, at the position of label t, if character is " 0 ", expression limit e does not occur in t figure; If character is " 1 ", expression limit e occurs in t figure.Delete not frequent limit, just in the label of limit the number of character " 1 " less than the limit of threshold value S;
(2) judge also marking convention limit, delete non-regular limit; To G
sIn each bar limit e, if l
eAll characters be that " 1 " or a preceding t character are " 0 " entirely entirely, then e is non-regular limit, t=T/2 or t=3T/4 here can certainly be provided with the value of t according to priori.Otherwise, suppose that the length of regular r is d, be expressed as l
e(1..d), get d and equal 2 to T/2, relatively r and remaining T/d section character string if each section is all identical with r, think that then limit e is regular limit, otherwise e are non-regular limit; Non-regular limit is deleted on the marking convention limit, is only comprised the underlined figure G on regular limit
1
(3) rule with regular limit is mapped as weight, obtains weighted graph;
(4) on the weighted graph that step (3) obtains, search for evolution modelling.
2. the evolution modelling method for digging in the DYNAMIC COMPLEX network is characterized in that concrete steps are as follows:
(1) input DYNAMIC COMPLEX network G=＜G
1, G
2..., G
TAnd threshold value S, structure sum graph G
sGive G
sIn each bar limit e add that length is " 0 " " 1 " character string of T, the label as e is designated as l
e, at the position of label t, if character is " 0 ", expression limit e does not occur in t figure; If character is " 1 ", expression limit e occurs in t figure.Delete not frequent limit, just in the label of limit the number of character " 1 " less than the limit of threshold value S;
(2) judge also marking convention limit, but keep frequent non-regular limit;
(3) rule with regular limit is mapped as weight;
(4) search evolution modelling; Select a regular limit of not visiting at random, expand the adjacent side on this limit.If this adjacent side is regular limit, then compare their weight; Otherwise, with in the label on this limit for the position of " 1 " and the correspondence position of its adjacent side compare, if be " 1 " entirely, then this adjacent side is put into the result, and the mark of having visited on the regular limit that all-access is crossed remembered.Repeat such expansion, up to there not being new adjacent side to add to come in.Like this, an evolution modelling has just formed.Up to having searched for all regular limits, all approximate evolution modellings of this DYNAMIC COMPLEX network have just been obtained.
3. the evolution modelling method for digging in the DYNAMIC COMPLEX network is characterized in that concrete steps are as follows:
(1) input DYNAMIC COMPLEX network G=＜G
1, G
2..., G
TAnd threshold value S, structure sum graph G
sGive G
sIn each bar limit e add that length is " 0 " " 1 " character string of T, the label as e is designated as l
e, at the position of label t, if character is " 0 ", expression limit e does not occur in t figure; If character is " 1 ", expression limit e occurs in t figure;
(2) the deletion label is not the limit of " 1 " entirely;
(3) define certain rule, go on foot from second and search for legal connected subgraph the figure that obtains, promptly obtain the conservative minor structure in the DYNAMIC COMPLEX network.
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| CN107038215B (en) * | 2017-03-07 | 2020-07-17 | 东方网力科技股份有限公司 | Database searching method for obtaining maximum complete subgraph from m graphs |
| CN108664548A (en) * | 2018-03-27 | 2018-10-16 | 中国科学院软件研究所 | A kind of network under degenerative conditions accesses behavioural characteristic team innovation method for digging and system |
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