CN109684520A - Large-scale time sequence diagram vertex similarity calculation method - Google Patents
Large-scale time sequence diagram vertex similarity calculation method Download PDFInfo
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Abstract
The invention relates to a method for calculating the similarity of vertexes of a large-scale time sequence diagram, which comprises the following steps of S1, abstracting data of each vertex of a social network into the time sequence diagram; s2, establishing a tree index through a random walk method and a path fusion method, estimating the expectation of time difference of each layer of nodes in the index tree by using a Bootstrap sampling method, and calculating the similarity between a target vertex and other vertices by using a Monte Coral method; and S3, finding out k vertexes most similar to the target fixed point according to the similarity between the target fixed point and other vertexes calculated in the step S2. The technical method of the invention enables the calculation of the vertex similarity to be more accurate, and the method can be used for recommending the user more accurately in a recommending system.
Description
Technical field
The present invention relates to a kind of extensive timing diagram vertex similarity calculating methods, belong to database technical field.
Background technique
Real-life many scenes can be abstracted into graph model, to carry out the processing and analysis of data.In recent years
With the fast development of data science, accurate with higher requirement of the people for data analysis result, however currently for
The research of graph model has focused largely on static map.Static graph model has ignored the time factor in real scene, this makes
Data analysis result inaccuracy in static map.
Vertex Similarity measures are the basic problems in graph theory, are widely used in the reality such as social networks, recommender system and answer
With.By taking social networks as an example, graph structure can be used to indicate the topological structure of social networks, vertex representation social networks in figure
In user, the side in figure can indicate the connection in social networks between user, can be according between user in social networks
Similitude carry out the activities such as friend recommendation, therefore vertex similitude is a particularly significant problem in calculating figure.Current
Research mostly models reality scene using static map, has ignored the time factor in reality scene, makes to analysis result
At very big influence.In response to this, timing diagram should be used to model reality scene, retention time factor is to real field
The influence of scape.Therefore how efficiently to handle vertex Similarity measures in timing diagram is a urgent problem to be solved.
Summary of the invention
(1) technical problems to be solved
In order to solve the above problem of the prior art, the present invention provides a kind of extensive timing diagram vertex similarity calculation side
Method.
(2) technical solution
In order to achieve the above object, the main technical schemes that the present invention uses include:
A kind of extensive timing diagram vertex similarity calculating method, includes the following steps:
S1, by the data abstraction on each vertex of social networks be timing diagram；
S2, tree index is established by random walk method and path fusion method, is estimated using the Bootstrap methods of sampling
The expectation for counting every node layer time difference in index tree calculates the phase of representative points and other vertex using Monte Coral method
Like degree；
S3, according to the calculated representative points of step S2 and other vertex similarities, find out the k most like with pinpoint
A vertex.
Calculation method as described above, it is preferable that in step sl, the slip chart is shown as GT=(V, E, T), wherein
V indicates the vertex set in social networks, and what E was indicated is the set on timing side in network, and each vertex that T is indicated contacts the moment
Set.
Calculation method as described above, it is preferable that in step s 2, the foundation of the tree index includes:
S20101, to the timing diagram GTAny vertex u ∈ V in=(V, E, T) creates one using u as the list of leaf node
Node tree, and remember level (u)=0；
S20102, reversed random walk is carried out to each leaf node, i.e., reversed random walk is carried out to leaf node u, is obtained
Timing path pu=(u, v), wherein v ∈ Γin(u,G)；Remember level (v)=level (u)+1, and node u reach node v when
Between be denoted as tv(u)；
Whether S20103, the timing path for judging that any two leaf node generates meet path fusion conditions, if meeting
Carry out path fusion；
Otherwise continue reversed random walk；Until the neighbors collection that enters of node enters neighbors to be empty or node
Set does not meet timing path condition, stops generating index at this time；
S20104, step S20101-S20103 is repeated until generation index quantity reaches anticipated number.
Calculation method as described above, it is preferable that in step s 2, estimate index tree using the Bootstrap methods of sampling
In the expectation of every node layer time difference be exactly to estimate that the expectation of the time difference of difference level interior joint in index tree is estimated；
T is denoted as to the expectation of level=i node layer time difference in index treei。
Calculation method as described above, it is preferable that in step s 2, described to calculate target using Monte Coral method
The similarity on vertex and other vertex includes: for Goal time order figure GT=(V, E, T) establishes r index；For giving mesh
Vertex x is marked, that is, needs to calculate the similarity of vertex x Yu other all vertex.Section is found in the leaf segment point set of each index
Point x, other leaf nodes that record is set with node x at same later, and record the node and reached recently with destination node
The path length of public ancestor node.
Further, it is assumed that node v and destination node x has public ancestors, and reaches the path length of public ancestors
For i, then illustrate that vertex u and v be i in path length is to meet for the first time, is denoted as first (px,pv)=i, according to formula (1) approximation
Calculate vertex similarity, wherein px=(x1,x2,…,xt), pv=(v1,v2,…,vt), 1≤i≤k,
(3) beneficial effect
The beneficial effects of the present invention are:
Extensive timing diagram vertex similarity calculating method provided by the invention, compared with traditional phase knowledge and magnanimity, this method is examined
Consider influence of the time factor for vertex similarity calculation, makes the more accurate of vertex similarity calculation.In real life
It has a wide range of applications, such as is calculating the similarity between user in point-to-point communication network and recommended accordingly,
More accurate data mining can be carried out in social networks according to time factor, connect prediction during can according to when
Between factor more accurately predicted.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of the timing diagram of the specific embodiment of the invention；
Fig. 2 is index establishment process schematic diagram in the present invention；
Fig. 3 is the method flow diagram that the present invention is embodied；
Fig. 4 is the approximation accuracy curve graph of present invention specific implementation result；
When Fig. 5 is the method for the present invention TaSimRank-R and the inquiry of art methods TaSimRank-base similarity
Between scheme.
Specific embodiment
In order to preferably explain the present invention, in order to understand, with reference to the accompanying drawing, by specific embodiment, to this hair
It is bright to be described in detail.
Symbol and its meaning used in the present invention are shown in Table 1.
1 symbol of table and meaning
Define 1 timing diagram: given timing diagram GT=(V, E, T), wherein V indicates the set on vertex in figure, and E indicates side in figure
Set, T indicate figure in the time set.For a line e ∈ E any in figure, it can be expressed as (u, v, t), wherein u, v ∈
V, t ∈ T.
It defines 2 timing paths: for timing diagram G=(V, E, T), there is vertex sequence p=(v1,v2,…,vk,vk+1) wherein
Condition (v is met for any 1≤i≤ki,vi+1,ti) ∈ E and ti< ti+1.Then p is referred to as the paths in timing diagram G.
Define 3 vertex to meet: in timing diagram G=(V, E, T), for any vertex u, v ∈ V, there are the paths that length is t
pu=(u1,u2,…,ut) and pv=(v1,v2,…,vt) for 1≤i≤k, there is ui=viThen illustrate vertex u and v in path length
It is to meet for the first time for i, is denoted as first (pu,pv)=i.
It defines 4 vertex similarities: in timing diagram G=(V, E, T), vertex u, v can be calculated for vertex u, v, x ∈ V
Similarity s (u, v):
Wherein tjPoor at the time of for current time vertex, C is attenuation coefficient.
Embodiment 1
A kind of vertex similarity calculating method towards extensive timing diagram, includes the following steps:
Step 1: using timing diagram GT=(V, E, T) come indicate by the data abstraction on each vertex of social networks be timing
Figure, wherein V indicates the vertex set in social networks, and what E was indicated is the set on timing side in network, each vertex that T is indicated
Contact the set at moment.The data structure of timing diagram is only needed in the weight on side using the data structure as adjacency list
Save all connected moment between node and the probability of spreading between node.
Step 2: the similarity of representative points and other vertex in timing diagram is calculated, the specific method is as follows:
Step 2.1: tree index is established by random walk method；This method combination random walk method and path fusion
Method establishes tree index, comes approximate calculation representative points and other tops in conjunction with Bootstrap and Monte Coral method later
The similarity of point.This method is approximation method, and runing time is very fast, but has error, and the size of error is usually indexed with foundation
Quantity it is related.Simply introduce path fusion: to any vertex u, v ∈ V, opposite vertexes u, v carry out reversed random walk and are grown
Degree is the timing path p of tu=(u0,u1,…,ut) and pv=(v0,v1,…,vt).For 1≤i≤t if there is ui=vi, then exist
uiIt is merged against two timing paths, continues reversed random walk along same paths after fusion.
The method for establishing index is broadly divided into following steps: to timing diagram GTAny vertex u ∈ V in=(V, E, T),
Creation one remembers level (u)=0 using u as the single node tree of leaf node.
Reversed random walk is carried out to each leaf node, i.e., reversed random walk is carried out to leaf node u, obtains timing path
pu=(u, v), wherein v ∈ Γin(u,G).Remember level (v)=level (u)+1, and the time of node u arrival node v is denoted as tv
(u)。
Whether the timing path for judging that any two leaf node generates meets path fusion conditions, and path is carried out if meeting
Fusion.Otherwise continue reversed random walk.Until the neighbors collection that enters of node enters neighbors set to be empty or node
Timing path condition is not met, stops generating index at this time.
It repeats step 1-3 and reaches anticipated number until generating index quantity.
Step 2.2: using the expectation of every node layer time difference in Bootstrap methods of sampling estimation index tree；
Since the time on side each in figure is not necessarily identical, in order to more accurate after carrying out random walk
The similarity between vertex is calculated, the time difference on every layer of vertex in the index to foundation is needed to calculate expectation.It is established due to index
Process is the process being sampled to timing diagram, and in order to use part sample to estimate population sample, the present invention is used
Bootstrap method estimates the expectation of the time difference of difference level interior joint in index tree.To level in index tree
The expectation of=i node layer time difference is denoted as ti。
Step 2.3: using the similarity of Monte Coral method estimation representative points and other vertex；
Assuming that before carrying out vertex similarity calculation, for Goal time order figure GT=(V, E, T), this method establishes r
A index.For giving representative points u, this method finds node u on the leaf node of each index, later record and node u
Other leaf nodes on same tree, and record the path length of the public ancestor node of the node and destination node arrival recently
Degree.Assuming that node v and destination node u has public ancestors, and the path length for reaching public ancestors is i.According to fixed before
Justice, the situation can be denoted as first (pu,pv)=i.Formula (1) approximate calculation top can be used according to Monte Coral method
Point similarity.
Step 3: according to the calculated representative points of step 2 and other vertex similarities, finding out most like with pinpoint
K vertex.
Embodiment 2
The present embodiment combines Fig. 1 to be illustrated timing diagram and related notion.Fig. 1 is timing diagram, and number of vertices is
7, i.e. V={ a, b, c, d, e, f, g } have 9, static side, 10, timing side in figure.
It is related at the time of connection in timing diagram between vertex is on side, by taking side (a, b, 1) as an example, indicate vertex a and top
Point b exists at the moment 1 to be contacted.Time factor has very big influence to the structure of figure in timing diagram.Do not considering time factor
In the case where, there is path p in Fig. 1static=(a, c, f) exists.Consider time factor, in timing diagram there are side (a, c, 3) and
(c, f, 1), the i.e. connection of vertex c and vertex f exist at the moment 1, and the connection of vertex a and vertex c exist at the moment 3, path p=
(a, c, f) is not present in timing diagram.
Exist in Fig. 1 using vertex e and vertex f as the reverse path p of starting pointe=(e, b, a) and pf=(f, b can a) be seen
This two paths meets in vertex b out, and path length is 1 at this time, is denoted as first (pe,pf)=1.
The similarity of vertex b and vertex c can be calculated by the following method in Fig. 1.It include vertex b and vertex c in Fig. 1
Side have (a, b, 1) respectively, (a, b, 5) and (a, c, 3).It is the reverse path of starting point in vertex a using vertex b and vertex c
It meets, according to shown in the similarity calculating method such as formula (2) for defining 3 vertex b and vertex c.
Specific embodiment is proposed by the present invention towards extensive timing diagram vertex similarity calculation side by experiment test
Method.In an experiment, TaSimRank-R represents method of the invention, and TaSimRank-base indicates to accurately calculate figure according to definition
The method of middle vertex similarity.
Experimental data is using the data on the sequential network on storehouse exchange website Ask Ubuntu, including 159316 tops
Point, 964437 timing sides, 596933 static sides, time span 2613 days.In TaSimRank-R model, 100 are established
Tree index, attenuation coefficient c value is 0.8 during calculating vertex similarity, since this object of experiment is to obtain k and mesh
The most like vertex of calibration point, in order to verify the accuracy that k value is not tested simultaneously, taking k value respectively is 200,400,600,800,
1000.In this experiment, pass through the approximation accuracy of formula (3) confirmatory experiment, wherein precision indicates approximate exact
Degree, approximated_set indicate the set of approximate calculation, and exact_set indicates the set accurately calculated；
Method for running present embodiment on extensive timing diagram, process are as shown in Figure 3, comprising the following steps:
Step 1: the use in vertex representation network by the sequential network data abstraction on website at timing diagram, in timing diagram
Family, the side in timing diagram indicate the connection between user；
Step 2: calculating the similarity of representative points and other vertex in timing diagram；
Given representative points, in conjunction with random walk and Monte Coral method approximate calculation representative points and other vertex
Similarity.The k vertex most like with representative points before finding.
Step 2.1: r index is established to timing diagram.By taking Fig. 1 as an example, Fig. 2 is an index establishment process.Clock synchronization first
Any vertex u ∈ V creates one using the vertex as the single node tree of leaf node in sequence figure, and remembers level (u)=0, specific as schemed
Shown in 2 (a).Next reversed random walk is carried out to each leaf node in timing diagram, as shown in Fig. 2 (b).It is deposited in Fig. 1
At side (a, c, 3), therefore the ancestor node a of leaf node c can be found, and remember level (a)=1.Above procedure is repeated, until
Establish index tree depth reach prescribed depth or present node enter in timing diagram neighbors concentrate it is not satisfactory
Node.Such as Fig. 2 (b) leaf node a, which does not enter neighbors in timing diagram, therefore in the index without ancestor node.
Fig. 2 (c) is that index generates result.
Step 2.2: using the expectation of every node layer time difference in Bootstrap methods of sampling estimation index tree.In order to
The more accurate similarity calculated between vertex, this method use the Bootstrap methods of sampling, are estimated with sample time difference overall
The expectation of time difference.The method of operation of this method is briefly described below.By taking Fig. 2 as an example in Fig. 2 (c), calculates and pushed up in Level 1
The expectation of point time difference.It can be seen that a total of 6 sides in Level 1, according to Bootstrap method in this 6 Bian Zhongjin
Row has the sampling put back to, extract 3 sides every time in the method and extract 3 available results be extract for the first time side when
Carve is 5,4,6；Second is 2,3,6,；Third time is 5,2,4.The expectation of each sample time difference absolute value can be calculated, the
Once it isIt is for the second timeThird time is 2.Therefore being desired for for estimation overall time difference absolute value can be calculated
Step 2.3: using the similarity of Monte Coral method estimation representative points and other vertex.The step for
In, this method finds destination node in each index, calculates destination node and its other node on same tree later
Nearest ancestor node, and record destination node and reach the path length of public ancestor node with other nodes.By taking Fig. 2 as an example,
Fig. 2 (c) is the index established based on Fig. 1, it is assumed that destination node e then finds node e, discovery section in the index first
Point f, g and node e are on same tree.Therefore the two nodes and node e similarity are not 0, other nodes and section in index
Point e similarity is 0.Node f and node e public ancestor node b again is recorded simultaneously, and node f and node e reaches public ancestors
The path length of node is 1.It is 2 that similarly node g and node e, which reaches the path length of public ancestor node a,.Record similarity meter
Calculation process median SimArray (e, f)=ct1With SimArray (e, g)=c2t1t2.Wherein t1And t2For 1 He of Level
The time difference absolute value of Level 2 it is expected.If establishing index quantity is r, destination node and other are recorded in each index
Median during node similarity calculation, and be added.The similarity of destination node and other nodes can pass through public affairs
Formula (4) is calculated, and * indicates other vertex in figure, in this example because only establishing 1 index, r=1.
Step 3: according to the calculated representative points of step 2 and other vertex similarities, finding out most like with pinpoint
K vertex.Specific method is k result before being ranked up and selecting to calculated similarity.
TaSimRank-R method is a kind of method of approximate calculation vertex similarity, different according to k value, passes through formula
(3) corresponding approximation accuracy is calculated, obtained approximation accuracy is as shown in Figure 4.It is concluded that i.e. when k value is smaller
When, approximation accuracy is lower, and when k value is larger, approximation accuracy is higher.The experiment proves that the method for TaSImRank-R has
Effect property.The runing time of Fig. 5 expression TaSimRank-base algorithm and TaSimRank-R algorithm, the results showed that the side TaSimRank
Method has apparent reduction compared to the TaSimRank-base method for accurately calculating vertex similarity in terms of run time.Simultaneously
TaSimRank-R method calculates vertex similarity by establishing index, and the index that this method is established can be used for multiple times.And it should
Method has preferable scalability, is when timing graph structure changes, and TaSimRank-base method needs recalculate
The similarity on all vertex.And TaSimRank-R method is only needed for be added on the vertex being newly added and be indexed, or by the top of deletion
Point is deleted from index.It is above-mentioned the experimental results showed that the validity of TaSimRank-R algorithm of the invention and can expand
Malleability illustrates that TaSimRank-R algorithm can calculate the similarity on vertex on extensive timing diagram.
The above described is only a preferred embodiment of the present invention, being not the limitation for doing other forms to the present invention, appoint
What those skilled in the art can use the equivalence enforcement that technology contents disclosed above were changed or be modified as equivalent variations
Example.But without departing from the technical solutions of the present invention, according to the technical essence of the invention to the above embodiments
What simple modification, equivalent variations and remodeling, still falls within the protection scope of technical solution of the present invention.
Claims (6)
1. a kind of extensive timing diagram vertex similarity calculating method, which is characterized in that it includes the following steps:
S1, by the data abstraction on each vertex of social networks be timing diagram；
S2, tree index is established by random walk method and path fusion method, estimates rope using the Bootstrap methods of sampling
The expectation for drawing every node layer time difference in tree calculates the similarity of representative points and other vertex using Monte Coral method；
S3, according to the calculated representative points of step S2 and other vertex similarities, find out and most like k top of pinpoint
Point.
2. calculation method as described in claim 1, which is characterized in that in step sl, the slip chart is shown as GT=(V,
E, T), wherein V indicates the vertex set in social networks, and what E was indicated is the set on timing side in network, each top that T is indicated
The set at point connection moment.
3. calculation method as described in claim 1, which is characterized in that in step s 2, the foundation of the tree index includes:
S20101, to the timing diagram GTAny vertex u ∈ V in=(V, E, T) creates one using u as the single node of leaf node
Tree, and remember level (u)=0；
S20102, reversed random walk is carried out to each leaf node, i.e., reversed random walk is carried out to leaf node u, obtains timing
Path pu=(u, v), wherein v ∈ Γin(u,G)；Remember level (v)=level (u)+1, and node u reaches the time note of node v
For tv(u)；
Whether S20103, the timing path for judging that any two leaf node generates meet path fusion conditions, carry out if meeting
Path fusion；
Otherwise continue reversed random walk；Until the neighbors collection that enters of node enters neighbors set to be empty or node
Timing path condition is not met, stops generating index at this time；
S20104, step S20101-S20103 is repeated until generation index quantity reaches anticipated number.
4. calculation method as described in claim 1, which is characterized in that in step s 2, estimated using the Bootstrap methods of sampling
In meter index tree the expectation of every node layer time difference be exactly estimate the expectation of the time difference of difference level interior joint in index tree into
Row estimation；T is denoted as to the expectation of level=i node layer time difference in index treei。
5. calculation method as described in claim 1, which is characterized in that in step s 2, described to use Monte Coral method
The similarity for calculating representative points and other vertex includes: for Goal time order figure GT=(V, E, T) establishes r index；It is right
In finding node u on given representative points u, the leaf node of each index, later record with node u same tree on other
Leaf node, and record the path length of the public ancestor node of the node and destination node arrival recently.
6. calculation method as claimed in claim 5, which is characterized in that the path length of the nearest public ancestor node is
It is to meet for the first time that vertex u and v, which is i in path length, is denoted as first (pu,pv)=i, according to formula (1) approximate calculation vertex phase
Like degree, wherein pu=(u1,u2,…,ut), pv=(v1,v2,…,vt), 1≤i≤k,
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| CN110287424A (en) * | 2019-06-28 | 2019-09-27 | 中国人民大学 | Collaborative filtering recommending method based on single source SimRank |
| CN110334758A (en) * | 2019-06-28 | 2019-10-15 | 西安理工大学 | The similarity calculating method of graph topological structure based on topological characteristic |
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| CN113515674A (en) * | 2021-06-10 | 2021-10-19 | 清华大学 | Sampling method and device for random walk of timing diagram |
| CN114385359A (en) * | 2022-01-07 | 2022-04-22 | 重庆邮电大学 | Internet of things cloud side end task timing sequence coordination method |
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| CN110287424A (en) * | 2019-06-28 | 2019-09-27 | 中国人民大学 | Collaborative filtering recommending method based on single source SimRank |
| CN110334758A (en) * | 2019-06-28 | 2019-10-15 | 西安理工大学 | The similarity calculating method of graph topological structure based on topological characteristic |
| CN111898095A (en) * | 2020-07-10 | 2020-11-06 | 佛山科学技术学院 | Deep migration learning intelligent fault diagnosis method and device, storage medium and equipment |
| CN111898095B (en) * | 2020-07-10 | 2024-04-19 | 佛山科学技术学院 | Deep migration learning intelligent fault diagnosis method, device, storage medium and equipment |
| CN113515674A (en) * | 2021-06-10 | 2021-10-19 | 清华大学 | Sampling method and device for random walk of timing diagram |
| CN113515674B (en) * | 2021-06-10 | 2022-10-25 | 清华大学 | Sampling method and device for random walk of timing diagram |
| CN114385359A (en) * | 2022-01-07 | 2022-04-22 | 重庆邮电大学 | Internet of things cloud side end task timing sequence coordination method |
| CN114385359B (en) * | 2022-01-07 | 2024-05-14 | 重庆邮电大学 | Cloud edge task time sequence cooperation method for Internet of things |
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