CN110334758A - The similarity calculating method of graph topological structure based on topological characteristic - Google Patents
The similarity calculating method of graph topological structure based on topological characteristic Download PDFInfo
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Abstract
The invention discloses a kind of similarity calculating methods of graph topological structure based on topological characteristic, first definition figure GaWith figure GbIt is made of the vertex of different number and side, from figure GaWith figure GbThe middle Global Topological feature for extracting figure constructs Global Topological feature vector using feature vector construction method, then uses the distance metric method of vector, obtain the distance value of global characteristics vector；From figure GaWith figure GbThe middle vertex topological characteristic for extracting figure constructs apex feature vector using the numerical characteristics of feature Distribution value, then uses the distance metric method of vector, obtain the distance value of apex feature vector；Pass through distance and similarity conversion formula, global and vertex topological characteristic similarity is converted by the distance value of the distance value of global characteristics vector and apex feature vector, it is final that summation is weighted to two kinds of similarities using the method for weighted sum, figure similarity is obtained, the present invention solves the problems, such as that measuring similarity existing in the prior art calculates the excessively high problem of cost.
Description
Technical field
The invention belongs to Large Scale Graphs similarity measure technical fields, and in particular to a kind of figure topology knot based on topological characteristic
The similarity calculating method of structure.
Background technique
With the development of science and technology, the scale of the fields generation such as biology, chemistry, internet and communications and transportation diagram data is in
Explosive growth.Large-scale diagram data is effectively analyzed and excavated, and obtaining contained important information is very
Significant research direction.Wherein, how to compare the similarity of figure is research branch important in figure research field.Between two figures
The accurate and effective of similarity measures the evolution to timing diagram, the application fields such as comparison of the abnormality detection of WWW and bio-networks
Research has significant impact.If the figure of required measurement similarity includes millions of vertex and side, the calculating of measuring similarity problem
Cost will increase dramatically.How while strictly comparing topological structure similarity in figure, reduces and calculate cost as extensive
The key of figure similarity research.
Summary of the invention
The object of the present invention is to provide a kind of similarity calculating methods of graph topological structure based on topological characteristic, solve
Measuring similarity problem existing in the prior art calculates the excessively high problem of cost.
The technical scheme adopted by the invention is that the similarity calculating method of the graph topological structure based on topological characteristic, tool
Body follows the steps below to implement:
Step 1, definition figure GaWith figure GbIt is made of the vertex of different number and side, from figure GaWith figure GbMiddle extraction figure
Global Topological feature is indicated using the vector of feature vector construction method building Global Topological feature, then uses feature vector
Distance metric method, obtain the distance value of Global Topological feature vector；
Step 2: from figure GaWith figure GbThe middle vertex topological characteristic for extracting figure constructs top using the numerical characteristics of variable distribution
Point topological characteristic vector indicate, then use feature vector distance metric method, obtain vertex topological characteristic vector away from
From value；
Step 3: by distance and similarity conversion formula, the distance value for the Global Topological feature vector that step 1 is obtained
It is converted into Global Topological characteristic similarity, converts vertex topology for the distance value for the vertex topological characteristic vector that step 2 obtains
Characteristic similarity, the final method using weighted sum carry out Global Topological characteristic similarity and vertex topological characteristic similarity
Weighted sum obtains figure GaWith figure GbTopological characteristic similarity.
The features of the present invention also characterized in that
Step 1 is specifically implemented according to the following steps:
Step 1.1, extract Global Topological feature include number of vertex V, number of edges E, degree related coefficient A, global clustering coefficient GC,
It is connected to component count CO, totally 6 kinds of density S；
Step 1.2: being consolidated using number of vertex, number of edges, degree related coefficient, global clustering coefficient, connection component count, density
Fixed sequence carries out feature vector building, and feature vector is [V, E, A, GC, CO, S]；
Step 1.3: using the distance of 1.2 gained feature vector of lance distance calculation method metrology step, obtaining global spy
Levy the distance value of vector.
Step 2 is specifically implemented according to the following steps:
Step 2.1, extraction vertex topological characteristic include degree, Local Clustering coefficient, eigencenter degree, page rank, are averaged
Totally 5 kinds of arest neighbors degree；
Step 2.2: feature vector uses the arithmetic mean number of every kind of apex featureMedian Me, variances sigma2, it is average exhausted
To deviation MAE, minimum value MIN and maximum value MAX, kurtosis β, degree of bias α, totally 8 kinds of numerical characteristics, and according to the degree D on vertex, part
Cluster coefficients LT, eigenvector centrality degree E, page rank P, average arest neighbors degree K permanent order feature vector is constructed are as follows:
Step 2.3: using the distance of lance distance calculation method measures characteristic vector, obtaining the distance of apex feature vector
Value.
Step 3 is specifically implemented according to the following steps:
Step 3.1: pass through distance and similarity conversion formula:
1/(1+d)
Global, vertex topological characteristic the similarity by global, apex feature vector distance value conversion, wherein d indicates step
Rapid 1 and step 2 in calculate resulting feature vector distance value；
Step 3.2: importance weighting being carried out to global, vertex topological characteristic similarity respectively, and acquires phase after weighting
Like the sum of degree, the similarity of figure is obtained.
The invention has the advantages that the similarity calculating method of the graph topological structure based on topological characteristic, passes through extraction
The overall situation and vertex topological characteristic that figure characteristic can be represented, graph topological structure comparison problem complicated in traditional measure method is turned
It turns to and compares the few and simple topological characteristic of data volume, obtain intuitive similarity eventually by the distance between measures characteristic vector
As a result.The present invention has effectively evaded in graph topological structure comparison problem, and relative efficiency is low, calculates problem at high cost, section
About figure measuring similarity cost greatly improves the practicability of figure measuring similarity.
Detailed description of the invention
Fig. 1 is the similarity calculating method flow chart of the graph topological structure the present invention is based on topological characteristic.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The present invention is based on the similarity calculating method of the graph topological structure of topological characteristic, flow chart is as shown in Figure 1, specifically press
Implement according to following steps:
Step 1, definition figure GaWith figure GbIt is made of the vertex of different number and side, from figure GaWith figure GbMiddle extraction figure
Global Topological feature is indicated using the vector of feature vector construction method building Global Topological feature, then uses feature vector
Distance metric method, obtain the distance value of Global Topological feature vector, be specifically implemented according to the following steps:
Step 1.1, extract Global Topological feature include number of vertex V, number of edges E, degree related coefficient A, global clustering coefficient GC,
It is connected to component count CO, totally 6 kinds of density S；
Step 1.2: being consolidated using number of vertex, number of edges, degree related coefficient, global clustering coefficient, connection component count, density
Fixed sequence carries out feature vector building, and feature vector is [V, E, A, GC, CO, S]；
Step 1.3: using the distance of 1.2 gained feature vector of lance distance calculation method metrology step, obtaining global spy
Levy the distance value of vector.
Step 2: from figure GaWith figure GbThe middle vertex topological characteristic for extracting figure constructs top using the numerical characteristics of variable distribution
Point topological characteristic vector indicate, then use feature vector distance metric method, obtain vertex topological characteristic vector away from
From value, it is specifically implemented according to the following steps:
Step 2.1, extraction vertex topological characteristic include degree, Local Clustering coefficient, eigencenter degree, page rank, are averaged
Totally 5 kinds of arest neighbors degree；
Step 2.2: feature vector uses the arithmetic mean number of every kind of apex featureMedian Me, variances sigma2, it is average exhausted
To deviation MAE, minimum value MIN and maximum value MAX, kurtosis β, degree of bias α, totally 8 kinds of numerical characteristics, and according to the degree D on vertex, part
Cluster coefficients LT, eigenvector centrality degree E, page rank P, average arest neighbors degree K permanent order feature vector is constructed are as follows:
Step 2.3: using the distance of lance distance calculation method measures characteristic vector, obtaining the distance of apex feature vector
Value.
Step 3: by distance and similarity conversion formula, the distance value for the Global Topological feature vector that step 1 is obtained
It is converted into Global Topological characteristic similarity, converts vertex topology for the distance value for the vertex topological characteristic vector that step 2 obtains
Characteristic similarity, the final method using weighted sum carry out Global Topological characteristic similarity and vertex topological characteristic similarity
Weighted sum obtains figure GaWith figure GbTopological characteristic similarity, be specifically implemented according to the following steps:
Step 3.1: pass through distance and similarity conversion formula:
1/(1+d)
Global, vertex topological characteristic the similarity by global, apex feature vector distance value conversion, wherein d indicates step
Rapid 1 and step 2 in calculate resulting feature vector distance value；
Step 3.2: importance weighting being carried out to global, vertex topological characteristic similarity respectively, and acquires phase after weighting
Like the sum of degree, the similarity of figure is obtained.
Embodiment
The present invention is based on the similarity calculating method of the graph topological structure of topological characteristic, flow chart is as shown in Figure 1, specifically press
Implement according to following steps:
Step 1 generates the uncalibrated visual servo figure G that optimum selecting intensity is 1 and 0.9 using BA scale-free modelaWith figure Gb。
From figure GaWith figure GbThe middle Global Topological feature for extracting figure, using the vector of feature vector construction method building Global Topological feature
It indicates, then uses the distance metric method of feature vector, the distance value of Global Topological feature vector is obtained, specifically according to following
Step is implemented:
Step 1.1, extract Global Topological feature include number of vertex V, number of edges E, degree related coefficient A, global clustering coefficient GC,
It is connected to component count CO, totally 6 kinds of density S, concrete outcome is as shown in table 1；
Table 1 extracts Global Topological mark sheet
| Global characteristics | Scheme Ga | Scheme Gb |
| Number of vertex V | 10000 | 10000 |
| Number of edges E | 796760 | 796760 |
| Spend related coefficient A | -0.0407 | -0.0563 |
| Global clustering coefficient GC | 0.0417 | 0.0532 |
| It is connected to component count CO | 354 | 368 |
| Density S | 0.00796 | 0.00796 |
Step 1.2: being consolidated using number of vertex, number of edges, degree related coefficient, global clustering coefficient, connection component count, density
Fixed sequence carries out feature vector building, and feature vector is [V, E, A, GC, CO, S]；
Step 1.3: using the distance of 1.2 gained feature vector of lance distance calculation method metrology step, obtaining global spy
The distance value for levying vector is 0.36.
Step 2: from figure GaWith figure GbThe middle vertex topological characteristic for extracting figure constructs top using the numerical characteristics of variable distribution
Point topological characteristic vector indicate, then use feature vector distance metric method, obtain vertex topological characteristic vector away from
From value, it is specifically implemented according to the following steps:
Step 2.1, extraction vertex topological characteristic include degree, Local Clustering coefficient, eigencenter degree, page rank, are averaged
Totally 5 kinds of arest neighbors degree；
Step 2.2: feature vector uses the arithmetic mean number of every kind of apex featureMedian Me, variances sigma2, it is average exhausted
To deviation MAE, minimum value MIN and maximum value MAX, kurtosis β, degree of bias α, totally 8 kinds of numerical characteristics, and according to the degree D on vertex, part
Cluster coefficients LT, eigenvector centrality degree E, page rank P, average arest neighbors degree K permanent order feature vector is constructed are as follows:
Step 2.3: using the distance of lance distance calculation method measures characteristic vector, obtaining the distance of apex feature vector
Value 9.2.
Step 3: by distance and similarity conversion formula, the distance value for the Global Topological feature vector that step 1 is obtained
It is converted into Global Topological characteristic similarity, converts vertex topology for the distance value for the vertex topological characteristic vector that step 2 obtains
Characteristic similarity, the final method using weighted sum carry out Global Topological characteristic similarity and vertex topological characteristic similarity
Weighted sum obtains figure GaWith figure GbTopological characteristic similarity, be specifically implemented according to the following steps:
Step 3.1: pass through distance and similarity conversion formula:
1/(1+d)
By similarity 0.73, the vertex topological characteristic of global, apex feature vector distance value conversion Global Topological feature
Similarity 0.1, wherein d indicates to calculate resulting feature vector distance value in step 1 and step 2；
Step 3.2: importance weighting is carried out respectively to global, vertex topological characteristic similarity, Global Topological feature
Similarity importance is weighted to 0.5, and the similarity importance of vertex topological characteristic is weighted to 1.5, and acquires similarity after weighting
Sum, obtain the similarity 0.51 of figure, i.e., 51%.
The present invention is based on the similarity calculating methods of the graph topological structure of topological characteristic, can represent figure characteristic by extracting
The overall situation and vertex topological characteristic, convert graph topological structure comparison problem complicated in traditional measure method to and compare data volume
Simple topological characteristic less obtains intuitive similarity result eventually by the distance between measures characteristic vector.The present invention has
The graph topological structure comparative approach of having evaded of effect calculates problem at high cost, saves figure measuring similarity cost, greatlys improve
The practicabilities of Large Scale Graphs measuring similarities.
Claims (4)
1. the similarity calculating method of the graph topological structure based on topological characteristic, which is characterized in that specifically real according to the following steps
It applies:
Step 1, definition figure GaWith figure GbIt is made of the vertex of different number and side, from figure GaWith figure GbThe overall situation of middle extraction figure is opened up
Feature is flutterred, is indicated using the vector of feature vector construction method building Global Topological feature, then uses the distance of feature vector
Measure obtains the distance value of Global Topological feature vector；
Step 2: from figure GaWith figure GbThe middle vertex topological characteristic for extracting figure is opened up using the numerical characteristics building vertex of variable distribution
The vector for flutterring feature indicates, then uses the distance metric method of feature vector, obtains the distance value of vertex topological characteristic vector；
Step 3: by distance and similarity conversion formula, the distance value for the Global Topological feature vector that step 1 is obtained is converted
For Global Topological characteristic similarity, vertex topological characteristic is converted by the distance value for the vertex topological characteristic vector that step 2 obtains
Similarity, it is final that Global Topological characteristic similarity and vertex topological characteristic similarity are weighted using the method for weighted sum
Summation, obtains figure GaWith figure GbTopological characteristic similarity.
2. the similarity calculating method of the graph topological structure according to claim 1 based on topological characteristic, which is characterized in that
The step 1 is specifically implemented according to the following steps:
Step 1.1, extraction Global Topological feature include number of vertex V, number of edges E, degree related coefficient A, global clustering coefficient GC, connection
Totally 6 kinds of component count CO, density S；
Step 1.2: suitable using number of vertex, number of edges, degree related coefficient, global clustering coefficient, connection component count, the fixation of density
Sequence carries out feature vector building, and feature vector is [V, E, A, GC, CO, S]；
Step 1.3: using the distance of 1.2 gained feature vector of lance distance calculation method metrology step, obtain global characteristics to
The distance value of amount.
3. the similarity calculating method of the graph topological structure according to claim 1 based on topological characteristic, which is characterized in that
The step 2 is specifically implemented according to the following steps:
Step 2.1, extraction vertex topological characteristic include degree, Local Clustering coefficient, eigencenter degree, page rank, are averaged recently
Totally 5 kinds of adjacent degree；
Step 2.2: feature vector uses the arithmetic mean number of every kind of apex featureMedian Me, variances sigma2, mean absolute deviation
MAE, minimum value MIN and maximum value MAX, kurtosis β, degree of bias α, totally 8 kinds of numerical characteristics, and according to the degree D on vertex, Local Clustering system
Number LT, eigenvector centrality degree E, page rank P, average arest neighbors degree K permanent order feature vector is constructed are as follows:
Step 2.3: using the distance of lance distance calculation method measures characteristic vector, obtaining the distance value of apex feature vector.
4. the similarity calculating method of the graph topological structure according to claim 1 based on topological characteristic, which is characterized in that
The step 3 is specifically implemented according to the following steps:
Step 3.1: pass through distance and similarity conversion formula:
1/(1+d)
Global, vertex topological characteristic the similarity by global, apex feature vector distance value conversion, wherein d indicates step 1
With resulting feature vector distance value is calculated in step 2；
Step 3.2: importance weighting being carried out to global, vertex topological characteristic similarity respectively, and acquires similarity after weighting
Sum, obtain the similarity of figure.
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