CN106709507B - A kind of parallel coordinate system view cluster data binding method of power guiding segmentation bone - Google Patents
A kind of parallel coordinate system view cluster data binding method of power guiding segmentation bone Download PDFInfo
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Abstract
A kind of parallel coordinate system view cluster data binding method of power guiding segmentation bone, pass through binding method innovative design, line style layout after improving binding solves the problems, such as that visual cognition deviation may be caused to the distribution characteristics of data in existing parallel coordinate system cluster binding method.
Description
Technical field
The present invention relates to high dimensional datas to visualize field of drawing, particularly relates to the parallel seat that segmentation bone is oriented to based on power
Mark system view cluster data binding method.
Background technique
1) big data visualizes: data visualization is the important component of field of Computer Graphics, passes through visualization
Method design, data are drawn and are presented in the form of two dimension or 3-D graphic, help user to complete by visual cognition channel
Understanding and analysis to information.
2) parallel coordinate system view: (Parallel Coordinates Plot, PCP) is that the visualization of higher-dimension big data is drawn
One of major way of system.Multiattribute high dimensional data can be mapped on multiple reference axis two-dimensional surface arranged in parallel,
User is helped to carry out data analysis.The basic problem of PCP view first is that the vision how solved between mass data line is mixed and disorderly
Interference.
3) cluster (cluster): be based on a certain standard, allow computer automatically by data acquisition system gather for several mutually it is only
Vertical cluster (classification).Clustering method is applied to the Preprocessing that PCP view can assist user to complete data.
4) it binds (Bundling): by binding method, similar data line being gathered, the harness separation between cluster
It opens, the vision that can effectively reduce PCP view is mixed and disorderly, promotes the identification between cluster.
The binding technology status of cluster data: PCP view cluster data visualization method mainly has binding and the field of force to make
With the methods of .Luo propose by data line by multistage broken line be changed to Cubic kolmogorov's differential system draw, solve broken line visually
The PCP view curve binding method that incoherent problem .Luo is proposed, by adding gravitational field for harness in cluster inner curve
Portion is bound, and each cluster harness is divided equally arrangement in reference axis altitude range to increase distance between cluster, is obviously improved
Cluster curve is drawn in the propositions such as visual recognition the degree .Johansson and Ljung of cluster data with high-precision texture, and is passed through
Transforming function transformation function is converted to the colored ribbon of color coding by harness is clustered, to help user to identify cluster data in addition, Hong Zhou
The clustering method of view-based access control model (geometric attribute) is proposed with Xiaoru Yuan etc., by the minimum of curvature of curve and adjacent
The maximization of sides aligned parallel degree carrys out Optimal Curve, is then devised with realizing that cluster harness gathers .Peihong Guo and HeXiao etc.
It is a kind of for local data in PCP view interact formula vision cluster method user by the view setting gravitation and
Repulsion operator generates the curve of close region and gathers or disperse in real time, and then the vision for generating stratification clusters Liu Fang
It is proposed with the triumphant equal theoretical basis based on Peihong Guo and HeXiao in field and adds repulsion field to the harness of cluster, to pull open
The space length between harness is clustered, identification .Gregorio Palmas and Myroslav Bachynskyi etc. is promoted and proposes
A kind of cluster method for visualizing of new side binding layout, its density based on data distribution in reference axis interact formula layer
Secondary cluster, and cluster data is expressed with layout type that polygon colors in, facilitate the user to carry out the general view of cluster data
The above research improves the effect of visualization of cluster data in PCP view from different angles, but there are still some
Problem: 1) existing binding method is bound in the middle part of cluster harness, closes on the region of reference axis at harness both ends, curve it
Between mixed and disorderly crossover phenomenon still have .2) existing cluster binding method lacks when separating layout between carrying out cluster to cluster
Included data volume difference consider cluster biggish for data volume for, the curve that largely stretches is instead when separating between cluster
It will increase the vision interference of entire view.
Fund project: Luoyang City's development in science and technology planning item (1401064A)；Science and Technology in Henan Room soft science research
Project (142400410036).
Summary of the invention
To solve in data visualizations such as 3-D Moulding Design, data mining, business decision, market survey, user studies
Field, the cluster data analysis of parallel coordinate system are widely used binding method and solve the problems, such as that data line interferes in a jumble.It is existing
Binding method major defect is the harness after binding, and there are apparent bending deformation and overall offsets, cause data distribution attribute
Information (dispersion of such as cluster data, the value at cluster data center, cluster data Location distribution) visual expression go out
Existing deviation.The invention patent proposes a kind of parallel coordinate system view cluster data binding side that segmentation bone is oriented to based on power
Method, by binding method innovative design, the line style after improving binding is laid out, and solves existing parallel coordinate system cluster binding side
The problem of may causing visual cognition deviation to the distribution characteristics of data in method.
To realize the above-mentioned technical purpose, the technical solution adopted by the present invention is that: based on power be oriented to segmentation bone parallel seat
Mark system view cluster data binding method, it is characterised in that: include the following steps,
Step 1: acquiring multiple data samples, data sample is gathered using K Mean Method or Self-organizing Maps method
Alanysis, and category label is carried out to data according to cluster result, the classification number scale of obtained cluster is N, is wrapped in each cluster
The quantity of the sample data contained is denoted as ni；
Step 2: the center of each cluster is calculated according to the sample data for including of each cluster, as the cluster
The benchmark that harness is gathered, i.e., the initial position of each cluster centre, also referred to as bone；
Step 3: the equilibrium distance K between cluster is calculated according to the quantity N of the height Height of reference axis and cluster,
Computation model are as follows: K=t × Height/N
Wherein, t is the regulatory factor for controlling the scale of distance between cluster；
Step 4: being based on improved power guidance algorithm, the layout calculation of each cluster centre is carried out, if there are two cluster P
And Q, the distance of two cluster centres are denoted as dist (P, Q),
If 1) existing distance dist (P, Q) > equilibrium distance K between two clusters, then no longer applied force field-effect；
If 2) existing distance dist (P, Q) < equilibrium distance K between two clusters, then repulsion field is added for cluster centre and calculated
Method, the repulsion between two cluster centre of P, Q are denoted as Fr (P, Q), and distance is inversely proportional between repulsion effect and two centers, and distance is got over
Closely, repulsive force is bigger；
Repulsion computation model: Fr (P, Q)=K2/dist(P,Q)
3) gravitational field algorithm is added for cluster centre, simulates gravitation constraint effect of each cluster centre by itself initial position
It answers, will constrain between the cluster centre and the initial position of its own that gravitation is arranged in after offset, cluster centre is by the beginning of itself
The constraint gravitation of beginning position is denoted as Fa, and gravitational effect and center deviation itself initial position distance △ are directly proportional, deviation distance
△ is bigger, and gravitation Fa is bigger, if offset of the center of cluster P and Q under repulsion effect is respectively △ P and △ Q, reaches balanced
Mobile balanced distance is respectively K when positionpAnd KQ, the cluster center P and Q is Fa (P) by the constraint gravitation of itself initial position
With Fa (Q)；
Then cluster the constraint gravitation that the center of P is subject to are as follows:
Fa (P)=Δ P2/KP
Similarly, the constraint gravitation that the center of Q is subject to is clustered are as follows:
Fa (Q)=Δ Q2/KQ
4) according to the sample size n of each intra-clusteri, the gravitation for calculating each cluster adjusts operator d, to offset distance progress
Adjustment, is transferred to lesser cluster for offset；If the sample size that cluster P and Q is included is respectively npAnd nq, then
Cluster offset Δ P=(K-dist (P, Q)) × d of PP
The gravitation for wherein clustering P adjusts operator dP=nQ/(nP+nQ)
Cluster offset Δ Q=(K-dist (P, Q)) × d of QQ
The gravitation for wherein clustering P adjusts operator dQ=nP/(nP+nQ)
5) loop iteration calculates repulsion suffered by each cluster centre and gravitation；
For clustering the center of P, effect by gravitation Fa (P) and repulsion Fr (P, Q):
If Fa (P) > Fr (P, Q), then cluster centre P is mobile along the direction (P) gravitation Fa；
If Fa (P) < Fr (P, Q), then cluster centre P is mobile along the direction (P, Q) repulsion Fr；
If Fa (P)=Fr (P, Q), illustrates that cluster centre P has been in dynamic balance state, enters step five, otherwise recycle
Step 4 is executed, similarly, the other cluster centres of loop iteration, until all cluster centres reach stress balance, then in each cluster
The heart completes layout calculation, obtains new equilbrium position；
Step 5: carry out the calculating of segmented bone based on cluster centre, in conjunction with the initial position of each cluster centre and new
Equilbrium position obtains a plurality of three-stage cluster bone by interpolation method；
Step 6: harness adds gravitational field algorithm, the left and right two based on the three-stage bone in each cluster in each cluster
The gravitation characteristic point of section, the graviational interaction point at both ends on every data line is close to bone, if data line itself initial position
Energy initial value be Ecurvature, the energy by bone constraint graviational interaction is Eattraction-constrain.Then in bone graviational interaction
The energy value of new position down are as follows:
E=αcEcurvature+(1-αc)Eattraction-constrain
Wherein α c is the regulatory factor of gravitation in cluster, and α c value is bigger, then data line more draws close bone；
Step 7: the graviational interaction point based on data point and data line both ends on adjacent coordinates axis, it is bent to draw B-spline
Line, obtains both ends fast convergence, and middle part is in band-like line style；
Step 8: the transparency of data line is calculated and is arranged by transmission function according to the packing density in reference axis, it is complete
It clusters and binds at parallel coordinate system view.
The medicine have the advantages that
1, method of the invention proposes the binding method of the guiding segmented bone layout of the power based on optimization, and power is oriented to
Model separates layout calculation between introducing cluster；The negative incidence for establishing data volume and repulsion in cluster, the shifting that will be separated between cluster when binding
Momentum is transferred to lesser cluster；Benchmark using segmented bone as cluster interior lines beam convergence obtains both ends fast convergence, in
Between be in band-like harness form, with improve parallel coordinate system cluster data drafting visual cognition effect.
2, three-stage bone: it is to gather center that existing binding method, which is with linear type mean value line, is only arranged one at midpoint
A gravitation characteristic point, the curve of drafting lose directional information, and small in both ends degree of convergence, and the overlapping staggered case of lines is bright
It is aobvious.The present invention uses three-stage bone design philosophy, and advantage is 1) the two gravitation characteristic points in left and right, so that curve is fast at both ends
Speed is gathered, and the overlapping that further reduced lines compared to conventional method interlocks.2) line style middle part is in band-like, remains line orientations
Information facilitates the properties of distributions of user cognition data.
3, method introduces in gravitation calculating and adjusts operator d: traditional binding mainly has the processing separated between cluster
Two methods: 1) each cluster is divided equally in reference axis short transverse arranges, 2) repulsion field is arranged between each cluster, but repulsion between cluster and partially
Shifting amount is reciprocity.These methods all do not consider the factor of included sample data volume cluster Nei.This method establishes sample in cluster
The reverse correlation relationship of this quantity and gravitation and offset reduces the offset of the harness of main cluster (more containing data),
To improve the cognition accuracy of data subject.
4, the bone that power guidance algorithm introduces PCP view is laid out, and is improved: in traditional power guidance algorithm, two
Gravitation and repulsion are existed simultaneously between two nodes, repulsion is present between bone two-by-two in this method, and gravitation is arranged in bone
Between bone and the initial position of itself, the design philosophy for reducing cluster harness offset is embodied.This problem is tied up in traditional
Determine rare in method be related to.
Detailed description of the invention
Fig. 1 is flow diagram of the invention；
Fig. 2 is that the comparison diagram of effect picture is drawn in the cluster binding of the PCP view and this method of the invention without binding；
Fig. 3 draws for the cluster binding of the PCP view of the invention without binding, traditional binding method and this method imitates
Fruit comparison diagram；
Fig. 4 gravitation that repulsion field and bone are subject between cluster of the present invention constrains schematic diagram；
Fig. 5 is that the present invention is based on gravitational field schematic diagrames in the cluster of three-stage bone；
Fig. 6 is that packing density of the present invention and the adjustment of curve transparency are schemed；
Fig. 7 is the original parallel coordinate system view, traditional binding method and binding method pair of the present invention of present example 1
It than figure, is drawn as can be seen from Figure by this method, the barycentre offset of the cluster more than sample size is smaller, realizes and preferably draws
Effect processed.
Specific embodiment
Method of the invention has been carried out, and the effect of drafting is drawn effect with existing method and is compared, and carries out
Visual cognition measure of merit, it was demonstrated that for the distribution character of data, binding method of the invention has better vision
Expression effect.
Specific steps:
1, clustering is carried out to data sample using the methods of K-MEANS (K mean value) or SOM (Self-organizing Maps),
And category label is carried out to data according to cluster result.The classification number scale of finally obtained cluster is N.Include in each cluster
The quantity of sample data is denoted as ni。
2, according to the sample data for including of each cluster, the center of each cluster is calculated, as the cluster harness
The benchmark gathered, also referred to as bone.
3, according to the quantity N of the height Height of reference axis and cluster, the equilibrium distance K between cluster is calculated.
Computation model are as follows: K=t × Height/N
T is regulatory factor, for controlling the scale of distance between cluster.T value can be set as needed in user.
4, it is based on improved power guidance algorithm (force-directed algorithm), carries out the cloth of each cluster centre
Office calculates.
As shown in figure 4, setting there are two P and Q is clustered, in PCP view, the distance of two cluster centres is denoted as dist (P, Q)
If 1) existing distance dist (P, Q) > equilibrium distance K between two clusters, then no longer applied force field-effect.
If 2) existing distance dist (P, Q) < equilibrium distance K between two clusters, then repulsion field is added for cluster centre and calculated
Method.Repulsion between two cluster centre of P, Q is denoted as Fr (P, Q).Distance is inversely proportional between repulsion effect and two centers, and distance is got over
Closely, repulsive force is bigger.
Repulsion computation model: Fr (P, Q)=K2/dist(P,Q)
3) gravitational field algorithm is added for cluster centre, simulates gravitation constraint effect of each cluster centre by itself initial position
It answers.Gravitation is present between node two-by-two in traditional power guidance algorithm, is used new thinking in the present invention, will be constrained
Gravitation is arranged between the cluster centre after offset and the initial position of its own.This step is innovative part of the invention.It is poly-
Class center is denoted as Fa, gravitational effect and center deviation itself initial position distance △ by the constraint gravitation of itself initial position
Directly proportional, deviation distance △ is bigger, and gravitation Fa is bigger.If clustering offset of the center of P under repulsion effect is △ P, reach
Balanced distance when equilibrium locations is Kp, and cluster centre is Fa (P) by the constraint gravitation of itself initial position.
Then cluster the constraint gravitation that the center of P is subject to are as follows:
Fa (P)=Δ P2/KP
Similarly, the constraint gravitation that the center of Q is subject to is clustered are as follows:
Fa (Q)=Δ Q2/KQ
4) according to the sample size n of each intra-clusteri, the gravitation for calculating each cluster adjusts operator d, to offset distance progress
Adjustment.Offset is transferred to lesser cluster.
Cluster offset Δ P=(K-dist (P, Q)) × d of PP
The gravitation for wherein clustering P adjusts operator dP=nQ/(nP+nQ)
Cluster offset Δ Q=(K-dist (P, Q)) × d of QQ
The gravitation for wherein clustering P adjusts operator dQ=nP/(nP+nQ)
5) loop iteration calculate each cluster centre suffered repulsion and gravitation.
Effect for clustering the center of P, by gravitation Fa (P) and repulsion Fr (P, Q).
If Fa (P) > Fr (P, Q), then cluster centre P is mobile along the direction (P) gravitation Fa.
If Fa (P) < Fr (P, Q), then cluster centre P is mobile along the direction (P, Q) repulsion Fr.
If Fa (P)=Fr (P, Q), illustrates that cluster centre P has been in dynamic balance state.Into step 5.
Effect for clustering the center of Q, by gravitation Fa (Q) and repulsion Fr (P, Q).
If Fa (Q) > Fr (P, Q), then cluster centre Q is mobile along the direction (Q) gravitation Fa.
If Fa (Q) < Fr (P, Q), then cluster centre Q is mobile along the direction (P, Q) repulsion Fr.
If Fa (Q)=Fr (P, Q), illustrates that cluster centre P has been in dynamic balance state.Into step 5.
Otherwise circulation executes the 5) step, until all cluster centres reach stress balance, then each cluster centre completes layout
It calculates.
5, the calculating of segmented bone is carried out based on cluster centre P.In conjunction with the initial position Lp-Rp of cluster centre (mean value line)
Three-stage cluster bone P is obtained by interpolation method with new equilbrium position Lp'-Rp'1P3P2, cluster centre Q similarly can be obtained
Three-stage cluster bone.
6, as shown in fig. 6, adding gravitational field algorithm to harness in cluster.Bone P is clustered for three-stage1P3P2Left and right two
The gravitation characteristic point P of section1And P2, by the graviational interaction point f1 at both ends on data line (by taking data line Dl-Dr and Dl'-Dr' as an example),
F2, f1' and f2' are to bone P1P3P2It is close.If the energy initial value of data line itself initial position is Ecurvature, constrained by bone
The energy of graviational interaction is Eattraction-constrain.Then under bone graviational interaction new position energy value are as follows:
E=αcEcurvature+(1-αc)Eattraction-constrain
Wherein α c is the regulatory factor of gravitation in cluster, is set as needed by user.α c value is bigger, then data line is more drawn close
Bone.
7, the graviational interaction point based on data point and data line both ends on adjacent coordinates axis is drawn B-spline curves, is obtained
To both ends fast convergence, middle part is in band-like line style.
8, it as shown in fig. 7, according to the packing density in reference axis, is calculated by transmission function and the transparent of data line is set
Degree.
The gravitation characteristic point is the equal part three parts between vertical reference axis, and data line bit is in left and right is two-part
Heart point is two gravitation characteristic points.
Embodiment 1
As shown in fig. 7, setting the data in parallel coordinate system view, result is obtained after K-MEANS (K mean value) method cluster
For 4 clusters, wherein the sample size for clustering 1 is 7, and the sample size for clustering 2 is 55, and the sample size for clustering 3 is 72, clusters 4
Sample size is 65,.It is drawn respectively with traditional binding method and binding method of the invention, and comparing result.
1) traditional binding method:
Step 1: according to the sample data for including of each cluster, the center of each cluster is calculated, as the cluster
The benchmark that harness is gathered.
Step 2: according to the quantity N of the height Height of reference axis and cluster, calculating the spacing H between cluster.
Computation model are as follows: H=Height/N
Step 3: dividing equally the center (mean value line) of 4 clusters of arrangement within the scope of reference axis height Height according to spacing H
Position.
Step 4: adding gravitational field algorithm to harness in cluster.Method particularly includes: it is arranged at the center of each cluster mean value line
The characteristic point of one gravitation, a graviational interaction point is arranged in the midpoint of every data line in cluster.If graviational interaction point on data line
Initial position energy initial value be Ecurvature, the energy by characteristic point graviational interaction is Eattraction-constrain.Then in feature
The energy value of new position under point graviational interaction are as follows:
E=αcEcurvature+(1-αc)Eattraction-constrain
Wherein α c is the regulatory factor of gravitation in cluster, is set as needed by user.α c value is bigger, then data line is more drawn close
Bone.
Step 5: a graviational interaction point based on the data point on adjacent coordinates axis and in the middle part of data line draws B-spline
Curve obtains the line style (as shown in Figure 7) of middle bent.
2) binding method of the present invention:
Step 1: according to the sample data for including of each cluster, the center of each cluster is calculated, as the cluster
The benchmark that harness is gathered, also referred to as bone.
Step 2: according to the quantity N of the height Height of reference axis and cluster, calculating the equilibrium distance K between cluster.
Computation model are as follows: K=t × Height/N
T is regulatory factor, for controlling the scale of distance between cluster.T value can be set as needed in user.
Step 3: being based on improved power guidance algorithm (force-directedalgorithm), carry out each cluster centre
Layout calculation.
1) the distance dist (P, Q) of 4 cluster centres between any two is calculated, if dist (P, Q) > equilibrium distance K, then not
Applied force field-effect again.
It 2) is then poly- if the distance between certain two cluster center dist (P, Q) < equilibrium distance K in 4 cluster centres
Add repulsion field algorithm in class center.Repulsion between two cluster centre of P, Q is denoted as Fr (P, Q).Between repulsion effect and two centers
Distance is inversely proportional, and distance is closer, and repulsive force is bigger.
Repulsion computation model: Fr (P, Q)=K2/dist(P,Q)
3) gravitational field algorithm is added for cluster centre, simulates gravitation constraint effect of each cluster centre by itself initial position
It answers.Cluster centre is denoted as Fa, gravitational effect and center deviation itself initial position by the constraint gravitation of itself initial position
Distance △ is directly proportional, and deviation distance △ is bigger, and gravitation Fa is bigger.If clustering offset of the center of P under repulsion effect is △
P, balanced distance when reaching equilibrium locations are Kp, and cluster centre is Fa (P) by the constraint gravitation of itself initial position.
Then cluster the constraint gravitation that the center of P is subject to are as follows:
Fa (P)=Δ P2/KP
Similarly, the constraint gravitation that the center of Q is subject to is clustered are as follows:
Fa (Q)=Δ Q2/KQ
4) according to the sample size n of each intra-clusteri, the gravitation for calculating each cluster adjusts operator d, to offset distance progress
Adjustment.Offset is transferred to lesser cluster.
Cluster offset Δ P=(K-dist (P, Q)) × d of PP
The gravitation for wherein clustering P adjusts operator dP=nQ/(nP+nQ)
Cluster offset Δ Q=(K-dist (P, Q)) × d of QQ
The gravitation for wherein clustering P adjusts operator dQ=nP/(nP+nQ)
5) loop iteration calculate each cluster centre suffered repulsion and gravitation.
Effect for clustering the center of P, by gravitation Fa (P) and repulsion Fr (P, Q).
If Fa (P) > Fr (P, Q), then cluster centre P is mobile along the direction (P) gravitation Fa.
If Fa (P) < Fr (P, Q), then cluster centre P is mobile along the direction (P, Q) repulsion Fr.
If Fa (P)=Fr (P, Q), illustrates that cluster centre P has been in dynamic balance state.Into step 5.
Otherwise circulation executes the 5) step, until all cluster centres reach stress balance, then each cluster centre completes layout
It calculates.
Step 4: being based on 4 cluster centres, carry out the calculating of segmented bone respectively.In conjunction with the first of cluster centre (mean value line)
Beginning position and new equilbrium position obtains the three-stage cluster bones of 4 clusters by interpolation method.
Step 5: adding gravitational field algorithm to harness in cluster.The gravitation characteristic point of two sections of the left and right based on three-stage bone,
The graviational interaction point at both ends on data line is close to bone.If the energy initial value of data line itself initial position is Ecurvature,
Energy by bone constraint graviational interaction is Eattraction-constrain.Then under bone graviational interaction new position energy value are as follows:
E=αcEcurvature+(1-αc)Eattraction-constrain
Wherein α c is the regulatory factor of gravitation in cluster, is set as needed by user.α c value is bigger, then data line is more drawn close
Bone.
Step 6: it is bent to draw B-spline for the graviational interaction point based on data point and data line both ends on adjacent coordinates axis
Line, obtains both ends fast convergence, and middle part is in band-like line style.
Step 7: according to the packing density in reference axis, the transparency of data line is calculated and be arranged by transmission function.
Claims (1)
1. a kind of parallel coordinate system view cluster data binding method of power guiding segmentation bone, it is characterised in that: including following
Step,
Step 1: acquiring multiple data samples, cluster point is carried out to data sample using K Mean Method or Self-organizing Maps method
Analysis, and category label is carried out to data according to cluster result, the classification number scale of obtained cluster is N, includes in each cluster
The quantity of sample data is denoted as ni；
Step 2: the center of each cluster is calculated according to the sample data for including of each cluster, as the cluster harness
The benchmark gathered, i.e., the initial position of each cluster centre, also referred to as bone；
Step 3: the equilibrium distance K between cluster is calculated according to the quantity N of the height Height of reference axis and cluster,
Computation model are as follows: K=t × Height/N
Wherein, t is the regulatory factor for controlling the scale of distance between cluster；
Step 4: being based on improved power guidance algorithm, the layout calculation of each cluster centre is carried out, if there are two P and Q is clustered,
The distance of two cluster centres is denoted as dist (P, Q),
If 1) existing distance dist (P, Q) > equilibrium distance K between two clusters, then no longer applied force field-effect；
It is then cluster centre addition repulsion field algorithm if 2) existing distance dist (P, Q) < equilibrium distance K between two clusters, P,
Repulsion between two cluster centre of Q is denoted as Fr (P, Q), and distance is inversely proportional between repulsion effect and two centers, and distance is closer, repels
Power is bigger；
Repulsion computation model: Fr (P, Q)=K2/dist(P,Q)
3) gravitational field algorithm is added for cluster centre, simulates gravitation effect of restraint of each cluster centre by itself initial position, it will
Constraint gravitation is arranged between the cluster centre after offset and the initial position of its own, and cluster centre is by itself initial position
Constraint gravitation be denoted as Fa, gravitational effect and center deviation itself initial position distance △ are directly proportional, and deviation distance △ is bigger,
Gravitation Fa is bigger, if offset of the center of cluster P and Q under repulsion effect is respectively △ P and △ Q, when reaching equilibrium locations
Mobile balanced distance is respectively KpAnd KQ, the cluster center P and Q is Fa (P) and Fa by the constraint gravitation of itself initial position
(Q)；
Then cluster the constraint gravitation that the center of P is subject to are as follows:
Fa (P)=Δ P2/KP
Similarly, the constraint gravitation that the center of Q is subject to is clustered are as follows:
Fa (Q)=Δ Q2/KQ
4) according to the sample size n of each intra-clusteri, the gravitation adjusting operator d of each cluster is calculated, offset distance is adjusted,
Offset is transferred to lesser cluster, if the sample size that cluster P and Q is included is respectively nPAnd nQ, then；Cluster the offset of P
Δ P=(K-dist (P, Q)) × dP
The gravitation for wherein clustering P adjusts operator dP=nQ/(nP+nQ)
Cluster offset Δ Q=(K-dist (P, Q)) × d of QQ
The gravitation for wherein clustering P adjusts operator dQ=nP/(nP+nQ)
5) loop iteration calculates repulsion suffered by each cluster centre and gravitation；
For clustering the center of P, effect by gravitation Fa (P) and repulsion Fr (P, Q):
If Fa (P) > Fr (P, Q), then cluster centre P is mobile along the direction (P) gravitation Fa；
If Fa (P) < Fr (P, Q), then cluster centre P is mobile along the direction (P, Q) repulsion Fr；
If Fa (P)=Fr (P, Q), illustrates that cluster centre P has been in dynamic balance state, enter step five, otherwise circulation is executed
Step 4, similarly, the other cluster centres of loop iteration, until all cluster centres reach stress balance, then each cluster centre is complete
At layout calculation, new equilbrium position is obtained；
Step 5: the calculating of segmented bone is carried out based on cluster centre, initial position and new balance in conjunction with each cluster centre
Position obtains a plurality of three-stage cluster bone by interpolation method；
Step 6: harness adds gravitational field algorithm in each cluster, two sections of the left and right based on the three-stage bone in each cluster
Gravitation characteristic point, the graviational interaction point at both ends on every data line is close to bone, if the energy of data line itself initial position
Amount initial value is Ecurvature, the energy by bone constraint graviational interaction is Eattraction-constrain, then new under bone graviational interaction
The energy value of position are as follows:
E=αcEcurvature+(1-αc)Eattraction-constrain
Wherein αcIt is the regulatory factor of gravitation in cluster, αcValue is bigger, then data line more draws close bone；
Step 7: the graviational interaction point based on data point and data line both ends on adjacent coordinates axis, draws B-spline curves, obtains
To both ends fast convergence, middle part is in band-like line style；
Step 8: the transparency of data line is calculated and be arranged by transmission function according to the packing density in reference axis, complete flat
The cluster binding of row coordinate system view.
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