CN104143009B - Competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box - Google Patents
Competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box Download PDFInfo
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Abstract
The invention discloses a kind of competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box, the method for proposing the acquisition initial seed point using the maximal clearance cutting of dynamic encompassing box, first fall into a trap the bounding box of evidence of counting in multidimensional feature space, and the data point in the bounding box is projected to most major axis, find out adjacent projections point maximum spacing position to be divided into two the bounding box, such recurrence, until whole space is cut into enough subspaces, the center of subspace is finally calculated as initial seed point；Present invention is alternatively directed to same cluster is broken into the phenomenon of multiple classes, propose to merge operation using distance radius analytic approach to cluster, can adaptive each class group by broken point build up a complete cluster.The present invention can avoid the omission phenomenon that randomization seed point is caused, and can avoid clustering fragmentation phenomenon, be conducive to quickly obtaining real cluster result.
Description
Technical field
The present invention relates to a kind of competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box, belongs to data and digs
Pick technical field.
Background technology
Cluster (Clustering) is the process that a collection of real or abstract data object is grouped into multiple classes or cluster,
It is people's understanding and the effective means for exploring inner link between things.The clustering method for generally adopting have K-means,
ISODATA and fuzzy clustering etc..K-means is a kind of clustering method for minimizing criterion based on mean square error (MSE), but such
There are two major defects in algorithm：1) K-means needs to be determined in advance definite classification number, but in actual applications, it is difficult to really
This parameter fixed；2) so-called " bad element " (dead unit) phenomenon is easily produced.If certain initial cluster center is given not
Properly, will cause to belong to the initial center without any input data, the initial center becomes one " bad element ".In order to gram
These defects are taken, researcher proposes competition learning (Competitive Learning, CL) clustering algorithm, for example:Frequency is quick
Sense Competitive Learning Algorithm (Frequency sensitive competitive algorithm, FSCL) is frequently obtained using minimizing
The mechanism of the victory seed average of wins is solving the problems, such as bad element；Secondary victor is punished competition learning (Rival Penalizing
Competitive Learning, RPCL) redundancy seed point pushes away input using to the Rejection mechanism of suboptimum seed point by algorithm
Sample space, so as to realize automatically determining for class number；Constraint competition learning (the Rival penalized that secondary victor is punished
Controlled competitive learning, RPCCL) be RPCL improvement, it is achieved that the automatically determining of Uulearning rate,
Avoid the defect problem that RPCL is sensitive to Uulearning rate；Distance sensitive (Distance based on cost function minimization criterion
Sensitive DSRPL) algorithm.Although these improved Competitive Learning Algorithms improve some performances, but still there is convergence
Sex chromosome mosaicism, causes cluster centre deviations additionally, due to the Rejection mechanism in algorithm.The algorithm of competition and cooperation study
(Competitive and cooperative learning, CCL) then introduces cooperative mechanism, it is to avoid redundancy seed point is ostracised
Go out input sample space, while ensure being accurately positioned for cluster centre again；While CCL algorithm it also avoid RPCCL clustering algorithm
Not convergence problem.But CCL algorithm yet suffers from some inevitable problems：1) with initial seed point tender subject.
Common clustering algorithm obtains initial seed point using method of randomization, causes the shakiness of algorithm iteration number of times and cluster result
Fixed；2) the unbalanced isomeric data of distribution cannot be applied to, the rare cluster of some data points correctly cannot be recognized；3) cluster knot
Fruit fragmentation problem.CCL algorithm sometimes results in and belongs to originally the data of same cluster and be decomposed into multiple subclasses.From directly perceived
On from the point of view of, these data should belong to same classification.
The presence of problems above, affects using effect and the practical value of CCL clustering algorithm, it is necessary to which CCL is calculated
These defects of method are improved.
Content of the invention
It is an object of the invention to provide a kind of competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box,
Original CCL clustering algorithm is targetedly improved, is more quickly obtained real cluster result.
For reaching above-mentioned purpose, the technical solution used in the present invention is as follows：
Based on the competition and cooperation clustering method of dynamic encompassing box maximal clearance cutting, comprise the following steps：
1) initial clustering classification number K is set；
2) N number of input data is analyzed, K seed is initialized using dynamic encompassing box maximal clearance segmentation algorithm
Point, comprises the following steps that：
2-1) using input data as the point of hyperspace, the minimum outsourcing rectangle that can include all input datas is calculated；
2-2) the length in minimum each dimension of outsourcing rectangle of comparison, it is cutting axle to select the maximum corresponding dimension of length；
2-3) by all input data spot projections to the cutting axle, then subpoint is carried out according to ascending order
Arrangement；
Former and later two adjacent projections points the distance between 2-4) are calculated, two maximum adjacent projections point conducts of chosen distance
Dicing position, input data is divided into two subsets along the cutting axle；
That subset for 2-5) selecting bounding box volume in all subsets maximum execution step 2-1 again) 2-4), to this
Subset is divided into two；
2-6) repeat step 2-5), till obtaining K subset；
The geometric center of obtained K subset 2-7) is calculated, as initial seed point；
3) the wins n of each initial seed point is madek=1, k=1 ..., K；
4) for present input data xi, parameter function I (j | xi)：
Wherein, cpRepresent p-th seed point, rpRepresent the relative average of wins of p-th seed point,
npFor the wins of p-th seed point,
Find out meet target function I (j | xiThe seed point of)=1, is designated as triumph seed point cw；
5) search with seed point c of winningwCentered on, with | | cw-xi| | for all seed points in the circle of radius, formed and close
Make colony；
6) it is updated to cooperating intragroup all seed points as follows：
Wherein,Represent the seed point before updating,Represent the seed point after updating, η is Study rate parameter；
7) triumph seed point c is updated as the following formulawWins,
Wherein,For triumph seed point c before updatingwWins,For triumph seed point c after renewalwTriumph time
Number；
8) repeat step 4) step 7), until seed point no longer changes；
9) reject and repeat seed point；
10) Cluster merging operation is carried out, forms final cluster result：
After assuming to complete iteration and repeat seed point deletion, M seed point is finally given, referred to as cluster centre, is designated as
dm, m=1 ... M, M≤K, then each input data is labeled as affiliated cluster centre, the concrete operations of Cluster merging are such as
Under：
10-1) label information Lab (the x of the cluster centre according to belonging to input datai), calculate each cluster centre institute energy
The radius R of coveringm, m=1 ... M；
10-2) two cluster centre d are taken outqAnd dt, q ∈ [1, M], t ∈ [1, M], and meet q ＜ t, calculate between them
Euclidean distance DqtIf meeting following condition:
Dqt≤RqOr Dqt≤Rt
Then by label information Lab (x in input datai) all re-flag as q for the input data of t, will t class be merged into
Q class；
10-3) step 10-2 is carried out to all of two cluster centres) operation, until without annexable cluster
Till；
The cluster centre of each class after merging 10-4) is recalculated, obtains final H (H≤M) cluster centre.
Aforementioned step 1) described in initial clustering classification number K be much larger than concrete class number K*.
Aforementioned step 6) learning rate parameter η value be 0.001.
Aforementioned step 9) in reject repeat seed point refer to be deleted the multiple seed points for converging to identical position
Remove, only retain one of those.
Aforementioned step 10) in, each input data is labeled as affiliated cluster centre and is referred to all of input number
According to xi, calculate it nearest with which cluster centre, it is assumed that xiWith s-th cluster centre recently, then by xiLabel L ab (xi) put
For s, represent that the input data belongs to s-th cluster centre：
Lab(xi)=s.
Aforementioned step 10-1) in, radius RmComputational methods be：Obtain m-th cluster centre and belong in the cluster
Distance value between all input datas of the heart, takes maximum therein as radius Rm.
It is an advantage of the current invention that：
The present invention can be according to the regularity of distribution of input data itself certainly using dynamic encompassing box maximal clearance cutting method
Dynamic selection obtains initial seed point, accelerates cluster speed, improves the stability of algorithm, and it is pockety to can be suitably used for class
Isomeric data.In addition, the initial seed point that this method is obtained is closer to real cluster centre, it is thus possible to accelerate algorithm
Convergence rate.
Present invention employs dynamic encompassing box maximal clearance cutting method and seed point is obtained, gather for some data are rare
Class is also obtained in that initial seed point, so as to the omission phenomenon for avoiding randomization seed point from causing.
The present invention merges operation using distance radius analytic approach to cluster, can avoid clustering fragmentation phenomenon, favorably
In the real cluster result of acquisition.
Description of the drawings
Fig. 1 is the schematic diagram that all input datas are cut into 2 subsets using the inventive method；
Fig. 2 is that cutting is the schematic diagram of 3 subsets on the basis of Fig. 1；
Fig. 3 is the initialization seed point schematic diagram obtained using method of randomization；
Fig. 4 is the cluster result schematic diagram on the basis of Fig. 3 using original CCL clustering method gained；
Fig. 5 is the initialization seed point schematic diagram for being obtained using method of randomization again；
Fig. 6 is cluster result schematic diagram again using original CCL clustering method gained；
Fig. 7 is the initialization seed point schematic diagram obtained using dynamic cutting method in the present invention；
Fig. 8 is the cluster result schematic diagram obtained using the inventive method；
Fig. 9 is a cluster result schematic diagram using original CCL algorithm gained；
Figure 10 is a cluster result schematic diagram using the inventive method gained.
Specific embodiment
The present invention is described in further detail in conjunction with the drawings and specific embodiments.
The present invention is had found its weak point, is targetedly carried out by experiment and analysis to original CCL clustering algorithm
Improve.Concept according to the present invention and symbol definition as follows：
Input sample：That is input data, each input data is a multi-C vector, is designated as xi, i represents i-th input
Data；
Seed point：Cluster centre is also referred to as in the present invention, and input data is designated as c with the vector of dimensioni, i represents i-th
Individual seed point；
Winner：For present input data xi, apart from xiNearest seed point is referred to as winner, is designated as cw, here away from
Euclidean distance is adopted from tolerance；
Cooperative cluster：To present input data xi, with winner cwCentered on, | | cw-xi| | for other seeds in radius circle
Point and cwTogether, referred to as cooperative cluster；
The competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box of the present invention, comprises the following steps：
For N number of input data x1,x2,...,xN,
1) initial clustering classification number K is set so as to much larger than concrete class number K*.
2) N number of input data is analyzed, K seed is initialized using dynamic encompassing box maximal clearance segmentation algorithm
Point, comprises the following steps that：
2-1) by input data as the point of hyperspace, the minimum outsourcing rectangle that can include all input datas is calculated,
If 2 dimension data are then planar rectangular, if 3-dimensional data are then 3-dimensional cuboid, by that analogy.
2-2) the length in minimum each dimension of outsourcing rectangle of comparison, it is cutting axle to select the maximum corresponding dimension of length.
2-3) by all input data spot projections to the cutting axle, now, subpoint is actual is changed into 1 dimension data.Then will
Subpoint is arranged according to ascending order.
Former and later two adjacent projections points the distance between 2-4) are calculated, two maximum adjacent projections point conducts of chosen distance
Dicing position, using input data also less than the point to less input data in the two subpoints and subpoint as a son
Collection, using input data also bigger than which to the input data of another subpoint and subpoint as another subset, so will be defeated
Enter data and be divided into two subsets along the cutting axle.As Fig. 1, it is the result that input data is cut into two subsets along x-axis, figure
In, an inframe is a subset.
2-5) and then, select in subset that maximum subset of bounding box volume execution step 2-1 again) 2-4), right
The subset is divided into two as shown in Fig. 2 in figure, an inframe is a subset.Then concentrate from this 3 sons, select bag
Enclose the maximum cutting for proceeding to be divided into two of box body product.The process is gone on always, till obtaining K subset.
The geometric center of obtained K subset 2-6) is calculated, as initial seed point.Thus obtain needed for cluster
K initial seed point.
3) the wins n of each initial seed point is madek=1, k=1 ..., K.
4) for present input data xi, parameter function I (j | xi)：
Wherein, cpRepresent p-th seed point, rpRepresent the relative average of wins of p-th seed point,
npWins for p-th seed point.
Find out meet target function I (j | xiThe seed point of)=1 is designated as triumph seed point c as triumph seed pointw.
5) search with seed point c of winningwCentered on, with | | cw-xi| | for all seed points in the circle of radius, formed and close
Make colony.
6) it is updated to cooperating intragroup all seed points as follows：
Wherein,Represent the seed point before updating,Represent the seed point after updating, η is Study rate parameter, typically takes
It is worth for 0.001.
7) triumph seed point c is updatedwWins, keep the wins of other seed points constant.
Wherein,For triumph seed point c before updatingwWins,For triumph seed point c after renewalwTriumph
Number of times.
8) repeat step 4) step 7), until seed point no longer changes.
9) reject and repeat seed point.As the cooperative group mechanism in iterative process may cause different multiple seed points
Identical position is converged to, only need to retain one of those.
10) based on poly- between class distance radius analysis, Cluster merging operation is carried out, forms final cluster result.
Carry out the analysis of poly- between class distance and the effect of Cluster merging is cluster fragmentation problem is eliminated, true in order to obtain
Cluster result.After assuming the iteration for completing above and repeating seed point deletion, M seed point is finally given, is referred to as clustered
Center, is designated as dm, m=1 ... M, M≤K.Then to all of input data xi, calculate it nearest with which cluster centre.Assume
xiWith s-th cluster centre recently, then by xiLabel L ab (xi) s is set to, represent that the input data belongs in s-th cluster
The heart：
Lab(xi)=s.
The concrete operations of Cluster merging are as follows：
10-1) label information Lab (the x of the cluster centre according to belonging to input datai), calculate each cluster centre institute energy
The radius R of coveringm, m=1 ... M, radius RmBe calculated as follows：Obtain m-th cluster centre and belong to all of the cluster centre
Distance value between input data, takes maximum therein as radius Rm.
10-2) two cluster centre d are taken outqAnd dt, q ∈ [1, M], t ∈ [1, M], and meet q ＜ t, calculate between them
Euclidean distance DqtIf meeting following condition:
Dqt≤RqOr Dqt≤Rt
Then by label information Lab (x in input datai) all re-flag as q for the input data of t, will t class be merged into
Q class.
10-3) step 10-2 is carried out to all of two cluster centres) operation, until not having the cluster that can merge to be
Only.
The cluster centre of each class after merging 10-4) is recalculated, obtains final H (H≤M) cluster centre.
Fig. 3 is the initialization seed point schematic diagram obtained using the 1st randomization of method of randomization, in figure, and small circle is
Initial seed point, Fig. 4 be on the basis of Fig. 3, using the cluster result schematic diagram of original CCL clustering method gained, cluster numbers
For 6, iterations is 553, takes 1.2 seconds.Fig. 5 is the initialization seed point schematic diagram for being obtained using method of randomization again,
In figure, small circle are initial seed point, different from the seed point in Fig. 3；Fig. 6 is to adopt original CCL on the basis of Fig. 5 again
The cluster result schematic diagram of clustering method gained, cluster numbers are 6, and iterations is 568, takes 1.24 seconds, tie with the cluster of Fig. 4
Fruit is also different.Fig. 7 is the initialization seed point schematic diagram obtained using dynamic cutting method in the present invention, the seed for obtaining every time
Point is all；Fig. 8 is the cluster result schematic diagram obtained using the inventive method, cluster numbers 6, iterations 323 time-consuming 0.72
Second；From figure 7 it can be seen that the initial seed point more adjunction obtained using the dynamic encompassing box maximal clearance cutting method of the present invention
It is bordering on real cluster centre, it is thus possible to accelerate convergence of algorithm speed；And the rare cluster of some data also can
Enough initial seed point is obtained, so as to the omission phenomenon for avoiding randomization seed point from causing.Fig. 9 is gathering using original CCL algorithm
Class result schematic diagram, Figure 10 are the cluster result schematic diagrames using the inventive method, iris out part it can be seen that existing from Fig. 9
Fragmentation phenomenon, and Figure 10 avoids clustering fragmentation phenomenon, is conducive to obtaining real cluster result.
Claims (6)
1. the competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box, it is characterised in that comprise the following steps：
1) initial clustering classification number K is set；
2) N number of input data is analyzed, K seed point, tool is initialized using dynamic encompassing box maximal clearance segmentation algorithm
Body step is as follows：
2-1) using input data as the point of hyperspace, the minimum outsourcing rectangle that can include all input datas is calculated；
2-2) the length in minimum each dimension of outsourcing rectangle of comparison, it is cutting axle to select the maximum corresponding dimension of length；
2-3) by all input data spot projections to the cutting axle, then subpoint is arranged according to ascending order
Row；
Former and later two adjacent projections points the distance between 2-4) are calculated, and two maximum adjacent projections points of chosen distance are used as cutting
Position, input data is divided into two subsets along the cutting axle；
That subset for 2-5) selecting bounding box volume in all subsets maximum execution step 2-1 again) 2-4), to the subset
It is divided into two；
2-6) repeat step 2-5), till obtaining K subset；
The geometric center of obtained K subset 2-7) is calculated, as initial seed point；
3) the wins n of each initial seed point is madek=1, k=1 ..., K；
4) for present input data xi, parameter function I (j | xi)：
Wherein, cpRepresent p-th seed point, rpRepresent the relative average of wins of p-th seed point,
npFor the wins of p-th seed point,
Find out meet target function I (j | xiThe seed point of)=1, is designated as triumph seed point cw；
5) search with seed point c of winningwCentered on, with | | cw-xi| | for all seed points in the circle of radius, form cooperative cluster
Body；
6) it is updated to cooperating intragroup all seed points as follows：
Wherein,Represent the seed point before updating,Represent the seed point after updating, η is Study rate parameter；
7) triumph seed point c is updated as the following formulawWins,
Wherein,For triumph seed point c before updatingwWins,For triumph seed point c after renewalwWins；
8) repeat step 4) step 7), until seed point no longer changes；
9) reject and repeat seed point；
10) Cluster merging operation is carried out, forms final cluster result：
After assuming to complete iteration and repeat seed point deletion, M seed point is finally given, referred to as cluster centre, is designated as dm, m=
Then each input data is labeled as affiliated cluster centre by 1 ... M, M≤K, and the concrete operations of Cluster merging are as follows：
10-1) label information Lab (the x of the cluster centre according to belonging to input datai), calculating each cluster centre can cover
Radius Rm, m=1 ... M；
10-2) two cluster centre d are taken outqAnd dt, q ∈ [1, M], t ∈ [1, M], and meet q ＜ t, calculate the Europe between them
Formula is apart from DqtIf meeting following condition:
Dqt≤RqOr Dqt≤Rt
Then by label information Lab (x in input datai) all re-flag as q for the input data of t, will t class be merged into q class；
10-3) step 10-2 is carried out to all of two cluster centres) operation, until without annexable cluster be
Only；
The cluster centre of each class after merging 10-4) is recalculated, obtains final H (H≤M) cluster centre.
2. the competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box according to claim 1, its feature
Be, the step 1) described in initial clustering classification number K much larger than concrete class number K*.
3. the competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box according to claim 1, its feature
It is, the step 6) value of learning rate parameter η is 0.001.
4. the competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box according to claim 1, its feature
Be, the step 9) in reject and repeat seed point and refer to be deleted the multiple seed points for converging to identical position, only
Retain one of those.
5. the competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box according to claim 1, its feature
It is, the step 10) in, each input data is labeled as affiliated cluster centre and is referred to all of input data xi,
Calculate it nearest with which cluster centre, it is assumed that xiWith s-th cluster centre recently, then by xiLabel L ab (xi) it is set to s, table
Show that the input data belongs to s-th cluster centre：
Lab(xi)=s.
6. the competition and cooperation clustering method based on the maximal clearance cutting of dynamic encompassing box according to claim 1, its feature
It is, step 10-1) in, radius RmComputational methods be：The institute for obtaining m-th cluster centre and belonging to the cluster centre
The distance value having between input data, takes maximum therein as radius Rm.
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