CN113177583A - Aerial target clustering method - Google Patents

Aerial target clustering method Download PDF

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CN113177583A
CN113177583A CN202110413139.9A CN202110413139A CN113177583A CN 113177583 A CN113177583 A CN 113177583A CN 202110413139 A CN202110413139 A CN 202110413139A CN 113177583 A CN113177583 A CN 113177583A
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CN113177583B (en
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周旺旺
张杰勇
姚佩阳
马腾
钟贇
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Air Force Engineering University of PLA
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Abstract

The invention discloses an aerial target clustering method, which comprises the following steps of S1: based on the comprehensive weighting theory, combining subjective and objective weights of the attributes to generate attribute comprehensive weights which influence the target grouping result; s2: considering the difference of different attributes on clustering influence, introducing comprehensive weight into similarity calculation, optimizing similarity measurement, constructing SWBWP index for determining optimal clustering number of target grouping, and determining optimal clustering number coptThe model of (2); s3: roughly searching a value interval [ P ] of a deviation parameter P by adopting a half-division methodmin,Pmax]If the cluster number [2, c ] is searchedmax]All corresponding p (i), i ═ 1,2max-1, calculating SWBWP indexes corresponding to different cluster numbers, and determining the optimal cluster number c by using the SWBWP indexesopt(ii) a S4: using the SWBWP value of the clustering result as a fitness function value, and adopting an ABC algorithm to precisely search a deviation parameter subspace [ Pn,Px]Determining an optimum bias parameter Pb. The present invention can solve the problem of target grouping in which the number of target groups is unknownThe purpose of high-efficiency and accurate target grouping in the air high-confrontation environment is achieved.

Description

Aerial target clustering method
Technical Field
The invention relates to the technical field of assistant decision-making, in particular to an aerial target clustering method.
Background
In recent years, with the increasing complexity and mutability of the air countermeasure, the cluster countermeasure mode will become an important mode of the air countermeasure in the future. The targets in the same confrontation cluster have a common overall target, in order to realize the target, an opponent commander divides the aerial target in the cluster into a plurality of groups with different scales, and each group realizes one sub-target in the overall target; each group consists of a plurality of teams which are mutually cooperated, and each team executes a specific combat task; formation is composed of more than 1 aerial target, and the targets in the formation need to keep a certain height and distance difference when flying, so that the targets in the same formation have similar maneuvering states.
The targets are grouped according to the maneuvering state of the aerial targets, such as distance, azimuth angle, course angle, speed, height and the like, and the grouping division condition of the targets of the other party can be obtained. The opposite director establishes the cooperative relationship among the targets in the process of forming the belonged targets, and hides the action intention of the formation. The target grouping is the reverse process of establishing the formation, can obtain the cooperation relation among targets, and is the basis for identifying the action intention of the formation of the other party.
The clustering problem is essentially a clustering problem under the condition of unknown class number, and is a process of dividing targets with high similarity of characteristic attributes into the same class, and one party cannot acquire accurate target cluster number information of the other party before clustering. In the current research, the number of target groups of the opposite party is assumed to be known. The method comprises the steps of adopting a chameleon algorithm based on certain constraint to realize target clustering according to the target geometrical situation of an opposite party, calculating an attack advantage function of the opposite party according to the geometrical situation of a group of the opposite party, and calculating an attack matrix through subjective and objective weight derivation to further divide a target group. The Liuji army and the like propose an improved ISODATA algorithm which optimizes the selection of the initial class centers based on argument distribution, reduces the clustering computation amount and improves the clustering effect. Wu Wen Long et al adopts k-dist descending order diagram to realize the division of different density targets, realize the grouping of different density targets, and improve the applicability of ISODATA algorithm. The Zhang-Chang-Ling method improves the k-means algorithm by introducing modularity, and the method realizes the grouping of the land battlefield targets.
The method is based on a clustering idea to research an aerial target clustering method under a countermeasure condition, and converts a target clustering problem into a clustering problem to perform problem modeling and optimization solution, but the methods assume that the number of target clusters of the opposite side is constant, and the applicability of the method is insufficient.
Disclosure of Invention
Aiming at the existing problems, the invention aims to provide an aerial target clustering and clustering method, which can realize the purpose of high-efficiency and accurate target clustering in an aerial high-confrontation environment aiming at the problem of target clustering with unknown target cluster number.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an aerial target clustering method is characterized by comprising the following steps,
s1: based on a comprehensive weighting theory, combining subjective and objective weights of all attributes in the moving process of the aerial target to generate an attribute comprehensive weight influencing a target grouping result;
s2: based on the difference of cluster influence caused by different attributes in the air target motion process, the comprehensive weight is introduced into the similarity calculation, the similarity measurement is optimized, an SWBWP index for determining the optimal cluster number of the target grouping is constructed, and the optimal cluster number c is determinedoptThe model of (2);
s3: roughly searching a value interval [ P ] of a deviation parameter P by adopting a half-division methodmin，Pmax]If the cluster number [2, c ] is searchedmax]All corresponding p (i), i ═ 1,2max1, calculating SWBWP indexes corresponding to different cluster numbers, and determining the optimal cluster number c by using the SWBWP indexesopt；
S4: using SWBWP value of clustering result as fitness function value, adopting ABC algorithm to bias parameter subspace [ Pn，Px]Performing a fine search to determine the best biasTo parameter Pb。
Further, the specific operation of step S1 includes the following steps,
s101: let the subjective weight of jth attribute in the moving process of aerial target be TjAnd if the subjective weight T of the motion attribute of the aerial target is equal to (T)1，T2，...，Tm) Wherein, in the step (A),
Figure BDA0003024856530000021
m is the number of the target motion attributes; when the domain expert does not evaluate the attribute, T ═ 1/m, 1/m.
S102: for attribute set B ═ Bij)n*mRegularizing it to D ═ D (D)ij)n*mThen the entropy of the jth attribute is
Figure BDA0003024856530000031
Wherein n is the total number of the targets in the air,
Figure BDA0003024856530000032
when d isijWhen' is0, dijln dij′＝0；
S103: let the objective weight of jth attribute be UjIf the attribute set B is (B)ij)n*mHas an objective weight of
Figure BDA0003024856530000033
Wherein the content of the first and second substances,
Figure BDA0003024856530000034
k represents the kth attribute, and k ≠ j;
s104: let the composite weight of jth attribute be wjIf the subjective weight and the objective weight of the attribute are considered in combination and the integrated weight of the attribute is obtained by weighting, the attribute set B is (B)ij)n*mThe composite weight of the j th attribute is wj＝(1-α)Tj+αUjWherein, in the step (A),
Figure BDA0003024856530000035
alpha is a preference coefficient and is the proportion of the objective weight to the comprehensive weight.
Further, the specific operation of step S2 includes the following steps,
s201: optimizing similarity measurement; if the integrated weight generated in step S1 is introduced into the calculation of the similarity matrix S and the similarity metric is optimized, S (i, j) — (d)i-dj)TW(di-dj) (i ≠ j), where W is an attribute weight Wj(j ═ 1, 2.. said, m) is a diagonal matrix of diagonal elements;
s202: calculating weighted minimum inter-class distance swbd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining the weighted minimum inter-class distance swbd (j, i) of the ith sample of the jth class as the minimum value of the average weighted distances from the sample to the samples in other classes, then
Figure BDA0003024856530000036
Where k and j are the class of the sample, di (j)Is the ith sample of the jth class, dp (k)For the p sample of the k class, nkThe number of samples contained in the kth class is W, and the W is an attribute weight diagonal matrix;
s203: calculating weighted minimum intra-class distance swwd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted minimum intra-class distance swwd (j, i) of ith sample of jth class as an average weighted distance value from the sample to other samples of jth class
Figure BDA0003024856530000041
In the formula (d)q (j)For the qth sample of class j, q ≠ i, njThe number of samples of the jth class;
s204: calculating weighted clustering distance swbawd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnSuppose all samples are aggregatedThe class is c, and the weighted clustering distance swbawd (j, i) of the ith sample of the jth class is defined as the sum of the weighted minimum inter-class distance and the intra-class distance of the sample
Figure BDA0003024856530000042
S205: calculating a weighted clustering dispersion distance swbswd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted cluster dispersion distance swbswd (j, i) of ith sample of jth class as the difference between weighted minimum inter-class distance and intra-class distance of the samples, then
Figure BDA0003024856530000043
S206: calculating weighted inter-cluster intra-class division indexes SWBWP (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted inter-cluster inter-class partition index SWBWP (j, i) of ith sample of jth class as the ratio of weighted cluster dispersion distance to cluster distance, then
Figure BDA0003024856530000044
The SWBWP index can reflect the clustering condition of a single sample, and the larger the SWBWP index value is, the better the clustering effect of the sample is; for the attribute set, the larger the average SWBWP value of all samples is, the better the clustering effect of the attribute set is;
s207: construction of the optimal clustering number coptModel (2)
Figure BDA0003024856530000051
Wherein the content of the first and second substances,
Figure BDA0003024856530000052
further, the specific operation of step S3 includes the following steps,
s301: searching a value interval [ P ] of a deviation parameter P by adopting a half-division methodmin,Pmax]Obtaining the clustering number [2, c ]max]Corresponding p (i), i ═ 1,2max-1; wherein, cmaxGet
Figure BDA0003024856530000053
Pmin＝min s(i，j)，i≠j，j＝1，2，...，n，Pmax＝max s(i，j)，i≠j，j＝1，2，...，n；
S302: calculating p (i), i ═ 1,2max-1 SWBWP value of clustering result corresponding to the maximum value, finding out the clustering number corresponding to the maximum value as the optimal clustering number copt；
S303: partial parameter subspace [ p (c) is searched by adopting a half-division methodopt-1)，p(copt)]Determining the optimal cluster number coptCorresponding lower bound p of the bias parameter subspacen(ii) a Search for a biased parameter subspace [ p (c) ] by a bisection methodopt)，p(copt+1)]Determining the optimal cluster number coptCorresponding upper bound p of the deviation parameter subspacex。
Further, in step S301, an improved AP algorithm is used for clustering, all samples are regarded as potential class representations, and the probability of being selected as the class representations is the same, i.e. S (i, i) are both biased parameters P, and S (i, i) is the median of the corresponding row in the similarity matrix S; in order to select a suitable class representation in a sample, it is necessary to continuously search for an attraction degree r and an attribution degree a, where r (i, j) represents a sample djIs suitable for makingiClass (ii) represents the degree of a point, a (i, j) represents diIs suitable for makingjDegree of class representation point of (1);
for sample diCalculating the sum of the attraction degree r (i, j) and the attribution degree a (i, j) of other samples, and selecting the sample d with the maximum sumjAs diThe update process of the attraction degree r (i, j) and the attribution degree a (i, j) is as follows:
Figure BDA0003024856530000054
Figure BDA0003024856530000061
else,
Figure BDA0003024856530000062
in the formula, t is iteration times; lambda is damping factor, lambda is more than 0.5 and less than 1.
Further, the specific operation of step S4 includes the following steps,
s401: an initialization stage; initial honey sources are all randomly generated in a feasible interval, and the number of rows of the matrix is the number N of the honey sourcesfsThe column of the matrix is a deviation parameter value, and the ith row and the jth column of the element x in the matrixijIs calculated by the formula
Figure BDA0003024856530000063
In the formula (I), the compound is shown in the specification,
Figure BDA0003024856530000064
and
Figure BDA0003024856530000065
respectively representing the upper and lower bounds of j-th column variables in the matrix, and rand representing a random number with the value in a (0,1) interval;
s402: a bee hiring stage; after the initial honey source position is generated, the hiring bee searches for a better honey source nearby the honey source according to the honey source position in the memory, and the update formula is as follows
Figure BDA0003024856530000066
In the formula, xij' is an element for newly generating a honey source,
Figure BDA0003024856530000067
for randomly selecting the corresponding position element, x, of the honey sourcei'jCorresponding position elements of other honey sources, and RAND is an updating threshold value which is generally 0.5;
if xij' exceed
Figure BDA0003024856530000068
In the range of (1), then take xij' is the nearest boundary value, i.e. having
Figure BDA0003024856530000069
S403: a bee observation stage; after all hired bees finish searching, honey source position information is exchanged with the observation bees, and the observation bees adopt a returned tournament selection operator to perform selection operation; at random in NfsSelecting 2 honey sources from the honey sources, calculating SWBWP values which are F respectively1And F2If F is1Is superior to F2I.e. satisfy F1＞F2If so, selecting the 1 st honey source for updating, otherwise, selecting the 2 nd honey source for updating;
s404: a bee scouting stage; after iter _ limit iterations are carried out, if the solution quality of the honey source is not improved, the hiring bee corresponding to the honey source becomes a scout bee, the original honey source is abandoned, and the formula is adopted
Figure BDA00030248565300000610
Generating a new honey source position;
s405: repeating the steps S402-S404 until reaching the maximum iteration number maxcycle, thereby carrying out deviation on the parameter subspace [ P ]n,Px]Performing a fine search to determine an optimal bias parameter Pb。
The invention has the beneficial effects that:
compared with the prior art, the aerial clustering method for generating the attribute comprehensive weight influencing the target grouping result can effectively combine subjective and objective information in the aerial confrontation opposite target grouping process, and the attribute comprehensive weight is more scientific and reasonable to determine; the improved AP algorithm is divided into a coarse search part and a fine search part for clustering, so that the clustering efficiency and the time cost are integrated; the ABC algorithm carries out fine search on the P subspace, so that the problem solving space is reduced to a certain extent, and the searching efficiency is improved. In a word, the method can realize the rapid and accurate grouping of the targets of the other side, thereby ensuring better situation perception effect.
Drawings
FIG. 1 is a flow chart of an aerial target clustering method of the present invention;
FIG. 2 is a relation diagram of cluster number-BWP/SWBWP index value of an attribute set Pid in SWBWP index feasibility verification experiments;
FIG. 3 is a graph showing the relationship between the Data attribute aggregation class number at the coarse search stage and the SWBWP index value in the clustering effect comparison experiment of the present invention;
FIG. 4 is a diagram of a process of fitness change when searching for an optimal bias parameter by the APBMABC (affinity amplification Based on selection Method and Artificial Bee colony algorithm) algorithm obtained by combining two optimization methods, namely a half-divide Method and an Artificial Bee colony algorithm, with an AP algorithm in a clustering effect comparison experiment of the present invention;
FIG. 5(a) is the result of APBWMMP algorithm clustering in the comparison experiment of clustering effect of the present invention;
FIG. 5(b) is a clustering result of the adAP algorithm in the clustering effect comparison experiment of the present invention;
FIG. 5(c) is the result of APBMABC algorithm clustering in the comparison experiment of the clustering effect of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.
An aerial target clustering method, as shown in figure 1, comprises the following steps,
s1: based on a comprehensive weighting theory, combining subjective and objective weights of all attributes in the moving process of the aerial target to generate an attribute comprehensive weight influencing a target grouping result;
specifically, S101: let the subjective weight of jth attribute in the moving process of aerial target be TjThe domain expert evaluates the clustering attributes according to the specific characteristics of the attributes in the attribute domain and by combining self experience, and gives subjective weight T ═ T (T) to the aerial target motion attributes1,T2,...,Tm) Wherein, in the step (A),
Figure BDA0003024856530000081
m is the number of attributes; when the domain expert does not evaluate the attribute, T ═ 1/m, 1/m.
S102: for attribute set B ═ Bij)n*mRegularizing it to D ═ D (D)ij)n*mThen the entropy of the jth attribute is
Figure BDA0003024856530000082
Wherein n is the total number of the targets in the air,
Figure BDA0003024856530000083
when d isijWhen' is0, dijlndij′＝0；
S103: let the objective weight of jth attribute be UjIf the attribute set B is (B)ij)n*mHas an objective weight of
Figure BDA0003024856530000084
Wherein the content of the first and second substances,
Figure BDA0003024856530000085
k represents the kth attribute, and k ≠ j; when the difference of certain attribute of the sample is larger, the entropy value of the attribute is smaller, and the obtained weight is higher;
s104: let the composite weight of jth attribute be wjIf the subjective weight and the objective weight of the attribute are considered in combination and the integrated weight of the attribute is obtained by weighting, the attribute set B is (B)ij)n*mThe composite weight of the j th attribute is wj＝(1-α)Tj+αUjWherein, in the step (A),
Figure BDA0003024856530000086
alpha is a preference coefficient and is the proportion of the objective weight to the comprehensive weight.
Further, step S2: based on the difference of cluster influence caused by different attributes in the air target motion process, the comprehensive weight is introduced into the similarity calculation, the similarity measurement is optimized, an SWBWP index for determining the optimal cluster number of the target grouping is constructed, and the optimal cluster number c is determinedoptThe model of (2);
specifically, S201: optimizing similarity measurement; most clustering algorithms take the Euclidean distance between samples as the similarity measurement, default weights of all attributes are the same, and the difference of the influence of different attributes on clustering is not considered, namely s (i, j) ═ i di-dj||2,(i≠j)；
In the invention, the difference of the influence of the attributes on clustering is considered, and the similarity measurement is optimized; if the integrated weight generated in step S1 is introduced into the calculation of the similarity matrix S and the similarity metric is optimized, S (i, j) — (d)i-dj)TW(di-dj) (i ≠ j), where W is an attribute weight Wj(j ═ 1, 2.. said, m) is a diagonal matrix of diagonal elements;
s202: calculating weighted minimum inter-class distance swbd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining the weighted minimum inter-class distance swbd (j, i) of the ith sample of the jth class as the minimum value of the average weighted distances from the sample to the samples in other classes, then
Figure BDA0003024856530000091
Where k and j are the class of the sample, di (j)Is the ith sample of the jth class, dp (k)For the p sample of the k class, nkThe number of samples contained in the kth class is W, and the W is an attribute weight diagonal matrix;
s203: calculating weighted minimum intra-class distance swwd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted minimum intra-class distance swwd (j, i) of ith sample of jth class as an average weighted distance value from the sample to other samples of jth class
Figure BDA0003024856530000092
In the formula (d)q (j)For the qth sample of class j, q ≠ i, njThe number of samples of the jth class;
s204: calculating weighted clustering distance swbawd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd defining weighted clustering distance swbawd (j, i) of the ith sample of the jth class as weighted minimum inter-class distance of the samples under the condition that all the samples are clustered into c classesSum of distance and intra-class distance
Figure BDA0003024856530000101
S205: calculating a weighted clustering dispersion distance swbswd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted cluster dispersion distance swbswd (j, i) of ith sample of jth class as the difference between weighted minimum inter-class distance and intra-class distance of the samples, then
Figure BDA0003024856530000102
S206: calculating weighted inter-cluster intra-class division indexes SWBWP (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted inter-cluster inter-class partition index SWBWP (j, i) of ith sample of jth class as the ratio of weighted cluster dispersion distance to cluster distance, then
Figure BDA0003024856530000103
The SWBWP index can reflect the clustering condition of a single sample, and the larger the SWBWP index value is, the better the clustering effect of the sample is; for the attribute set, the larger the average SWBWP value of all samples is, the better the clustering effect of the attribute set is. (ii) a
S207: construction of the optimal clustering number coptModel (2)
Figure BDA0003024856530000104
Wherein the content of the first and second substances,
Figure BDA0003024856530000105
further, step S3: roughly searching a value interval [ P ] of a deviation parameter P by adopting a half-division methodmin，Pmax]If the cluster number [2, c ] is searchedmax]All corresponding p (i), i ═ 1,2max1, calculating SWBWP indexes corresponding to different cluster numbers, and determining the optimal cluster number c by using the SWBWP indexesopt；
Specifically, S301: searching a value interval [ P ] of a deviation parameter P by adopting a half-division methodmin,Pmax]Obtaining the clustering number [2, c ]max]Corresponding p (i), i ═ 1,2max-1; wherein, cmaxGet
Figure BDA0003024856530000111
Pmin＝mins(i，j)，i≠j，j＝1，2，...，n，Pmax＝max s(i，j)，i≠j，j＝1，2，...，n；
Clustering by adopting an improved AP algorithm, regarding all samples as potential class representatives, and selecting the samples as the class representatives with the same possibility, namely S (i, i) are all deviation parameters P, and S (i, i) are median of corresponding rows in a similarity matrix S; in order to select a suitable class representation in a sample, it is necessary to continuously search for an attraction degree r and an attribution degree a, where r (i, j) represents a sample djIs suitable for makingiClass (ii) represents the degree of a point, a (i, j) represents diIs suitable for makingjDegree of class representation point of (1);
for sample diCalculating the sum of the attraction degree r (i, j) and the attribution degree a (i, j) of other samples, and selecting the sample d with the maximum sumjAs diThe update process of the attraction degree r (i, j) and the attribution degree a (i, j) is as follows:
Figure BDA0003024856530000112
Figure BDA0003024856530000113
else,
Figure BDA0003024856530000114
in the formula, t is iteration times; lambda is damping factor, lambda is more than 0.5 and less than 1.
S302: calculating p (i), i ═ 1,2max-1 SWBWP value of clustering result corresponding to the maximum value, finding out the clustering number corresponding to the maximum value as the optimal clustering number copt；
S303: searching deviation parameters by adopting half-division methodSubspace [ p (c)opt-1)，p(copt)]Determining the optimal cluster number coptCorresponding lower bound p of the bias parameter subspacen(ii) a Search for a biased parameter subspace [ p (c) ] by a bisection methodopt)，p(copt+1)]Determining the optimal cluster number coptCorresponding upper bound p of the deviation parameter subspacex。
Further, step S4: using SWBWP value of clustering result as fitness function value, adopting ABC algorithm to bias parameter subspace [ Pn，Px]Performing a fine search to determine an optimal bias parameter Pb。
Specifically, S401: an initialization stage; initial honey sources are all randomly generated in a feasible interval, and the number of rows of the matrix is the number N of the honey sourcesfsThe column of the matrix is a deviation parameter value, and the ith row and the jth column of the element x in the matrixijIs calculated by the formula
Figure BDA0003024856530000121
In the formula (I), the compound is shown in the specification,
Figure BDA0003024856530000122
and
Figure BDA0003024856530000123
respectively representing the upper and lower bounds of j-th column variables in the matrix, and rand representing a random number with the value in a (0,1) interval;
s402: a bee hiring stage; after the initial honey source position is generated, the hiring bee searches for a better honey source nearby the honey source according to the honey source position in the memory, and the update formula is as follows
Figure BDA0003024856530000124
In the formula, xij' is an element for newly generating a honey source,
Figure BDA0003024856530000125
for randomly selecting the corresponding position element, x, of the honey sourcei'jCorresponding position elements of other honey sources, and RAND is an updating threshold value which is generally 0.5;
if xij' exceed
Figure BDA0003024856530000126
In the range of (1), then take xij' is the nearest boundary value, i.e. having
Figure BDA0003024856530000127
S403: a bee observation stage; after all hired bees finish searching, honey source position information is exchanged with the observation bees, and the observation bees adopt a returned tournament selection operator to perform selection operation; at random in NfsSelecting 2 honey sources from the honey sources, calculating SWBWP values which are F respectively1And F2If F is1Is superior to F2I.e. satisfy F1＞F2If so, selecting the 1 st honey source for updating, otherwise, selecting the 2 nd honey source for updating;
s404: a bee scouting stage; after iter _ limit iterations are carried out, if the solution quality of the honey source is not improved, the hiring bee corresponding to the honey source becomes a scout bee, the original honey source is abandoned, and the formula is adopted
Figure BDA0003024856530000128
Generating a new honey source position;
s405: repeating the steps S402-S404 until reaching the maximum iteration number maxcycle, thereby carrying out deviation on the parameter subspace [ P ]n,Px]Performing a fine search to determine an optimal bias parameter Pb。
In summary, in the method for clustering aerial targets of the present invention, the preference coefficient α and the total number of honey sources N may be set firstfsThe maximum iteration times maxcycle and the maximum honey source staying times iter _ limit, and then the aerial target clustering can be carried out.
Simulation test:
to verify the effectiveness of the method proposed by the present invention, the following computer simulation experiments were performed.
The experimental environment is as follows: the simulation experiment adopts an Intel Core i7-6700HQ quad-Core processor, an 8GB memory and a computer of a Windows7 operating system, and MATLAB2016a is used for realizing simulation of the algorithm. Preference factor alpha is set to 0.5, resistanceThe damping factor lambda is 0.8, and the total number of honey sources NfsThe maximum iteration number maxcycle is 20, the maximum iteration number maxcycle is 80, and the maximum number of honey source stays iter _ limit is 8.
(1) SWBWP index feasibility verification experiment
The experiment used the real property sets Pima-indians-diabetes (pid), break-cancer-wisconsin (bcw) and Wine in the 3 university of california european college (UCI) databases, and two artificial property sets Model1 and Model2 as test property sets. And evaluating the clustering result by respectively using the Between-withProport (BWP) index and the SWBWP index in the invention to determine the optimal clustering number. The following table 1 shows the number of the best clusters evaluated by the above 5 attribute sets, fig. 2 is a relationship diagram of the number of the Pid attribute clusters and BWP and SWBWP index values, and the following table 2 shows BWP and SWBWP index values corresponding to different cluster numbers of the Model2 attribute sets.
TABLE 1 optimal cluster number for attribute set evaluated by BWP and SWBWP metrics
Figure BDA0003024856530000131
TABLE 2 Model2 Cluster index value for the attribute set
Number of clusters BWP SWBWP
2 0.5090 0.6369
3 0.5350 0.7630
4 0.3439 0.5764
5 0.3443 0.5106
6 0.1996 0.5344
7 0.2059 0.4965
8 0.2141 0.5134
9 0.2233 0.5241
10 0.2266 0.5253
As can be seen from Table 1, the SWBWP index provided by the invention can obtain the same cluster number as the actual cluster number on three UCIs and two artificial attribute sets; the BWP index can obtain the same cluster number as the correct cluster number on the attribute sets Pid, Bcw and Model2, but cannot obtain the correct cluster number on the Wine and Model1 attribute sets.
The number of sample classes of the attribute set Pid is 2, and as can be seen from fig. 2, the BWP and SWBWP index values both have the maximum value when the number of clusters is 2, and are the same as the number of true classes.
As can be seen from Table 2, the BWP index takes a maximum value of 0.5350 for the index value when the number of clusters is 3, the SWBWP index takes a maximum value of 0.7630 for the index value when the number of clusters is 3, and both the BWP and SWBWP indices can obtain the optimal number of clusters for the Model2 attribute set.
(2) Clustering effect contrast experiment
Assuming that an enemy sends 300 airplanes together to spread a cluster to fight, the cluster is divided into four functional groups of reconnaissance, attack, penetration, monitoring and the like, the attribute set Data is characteristic values of motion attributes of the 300 airplanes, such as azimuth angle, distance, horizontal speed, course angle, altitude and the like, and part of Data is shown in the following table 3. And the attribute subjective weight value T is (0.35, 0.35, 0.5, 0.65, 0.65). Based on attribute sets Bcw, Wine, Model1 and Data, the clustering method (APBMABC algorithm) in the invention is compared with Adaptive Affinity clustering (ADAP) and Affinity clustering (Affinity based on weighted Mahalanobis Distance and Modified Preference (APBWMMP)) for clustering accuracy.
TABLE 3 object motion Attribute eigenvalues and cluster classes
Figure BDA0003024856530000151
FIG. 3 shows SWBWP index values under different clustering numbers searched in the rough search stage based on the attribute set Data; FIG. 4 is a process diagram of searching for optimal bias parameters by the APBMABC algorithm based on the attribute set Data; as can be seen from fig. 3 and fig. 4, the APBMABC algorithm proposed in the present invention can effectively determine the optimal cluster number of the attribute set through the coarse search process, and determine the search range for the fine search process. The fine search process adopting the ABC algorithm is stable after being iterated for about 40 times, and the optimal clustering result is obtained.
Table 4 below shows the results of clustering by three different algorithms based on the attribute set Data, and fig. 5(a) -fig. 5(c) show the comparison of the results of clustering by three different algorithms based on the attribute set Data. From fig. 5(a) -fig. 5(c) and table 4, the APBWMMP, adAP and APBMABC algorithms all can obtain the same optimal cluster number as the actual cluster number, but the APBMABC algorithm clustering effect based on the two search processes of the coarse search and the fine search is better than the APBWMMP and adAP algorithms as a whole.
TABLE 4 APBWMMP, adaP and APBMABC algorithm clustering effect contrast
Figure BDA0003024856530000161
In summary, the aerial target clustering method based on the algorithm combining the coarse search and the fine search provided by the invention can provide a better target clustering scheme, and compared with other methods, the method provided by the invention has higher grouping precision.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (6)

1. An aerial target clustering method is characterized by comprising the following steps,
s1: based on a comprehensive weighting theory, combining subjective and objective weights of all attributes in the moving process of the aerial target to generate an attribute comprehensive weight influencing a target grouping result;
s2: based on the difference of cluster influence caused by different attributes in the air target motion process, the comprehensive weight is introduced into the similarity calculation, the similarity measurement is optimized, an SWBWP index for determining the optimal cluster number of the target grouping is constructed, and the optimal cluster number c is determinedoptThe model of (2);
s3: miningRoughly searching a value interval [ P ] of a deviation parameter P by using a half-division methodmin，Pmax]If the cluster number [2, c ] is searchedmax]All corresponding p (i), i ═ 1,2max1, calculating SWBWP indexes corresponding to different cluster numbers, and determining the optimal cluster number c by using the SWBWP indexesopt；
S4: using SWBWP value of clustering result as fitness function value, adopting ABC algorithm to bias parameter subspace [ Pn，Px]Performing a fine search to determine an optimal bias parameter Pb。
2. The aerial target clustering method of claim 1, wherein the specific operation of step S1 includes the following steps,
s101: let the subjective weight of jth attribute in the moving process of aerial target be TjAnd if the subjective weight T of the motion attribute of the aerial target is equal to (T)1，T2，...，Tm) Wherein, in the step (A),
Figure FDA0003024856520000011
m is the number of the target motion attributes; when the domain expert does not evaluate the attribute, T ═ 1/m, 1/m.
S102: for attribute set B ═ Bij)n*mRegularizing it to D ═ D (D)ij)n*mThen the entropy of the jth attribute is
Figure FDA0003024856520000012
Wherein n is the total number of the targets in the air,
Figure FDA0003024856520000013
when d isijWhen' is0, dijlndij′＝0；
S103: let the objective weight of jth attribute be UjIf the attribute set B is (B)ij)n*mHas an objective weight of
Figure FDA0003024856520000021
Wherein the content of the first and second substances,
Figure FDA0003024856520000022
k represents the kth attribute, and k ≠ j;
s104: let the composite weight of jth attribute be wjIf the subjective weight and the objective weight of the attribute are considered in combination and the integrated weight of the attribute is obtained by weighting, the attribute set B is (B)ij)n*mThe composite weight of the j th attribute is wj＝(1-α)Tj+αUjWherein, in the step (A),
Figure FDA0003024856520000023
alpha is a preference coefficient and is the proportion of the objective weight to the comprehensive weight.
3. The aerial target clustering method of claim 2, wherein the specific operation of step S2 comprises the following steps,
s201: optimizing similarity measurement; if the integrated weight generated in step S1 is introduced into the calculation of the similarity matrix S and the similarity metric is optimized, S (i, j) — (d)i-dj)TW(di-dj) (i ≠ j), where W is an attribute weight Wj(j ═ 1, 2.. said, m) is a diagonal matrix of diagonal elements;
s202: calculating weighted minimum inter-class distance swbd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining the weighted minimum inter-class distance swbd (j, i) of the ith sample of the jth class as the minimum value of the average weighted distances from the sample to the samples in other classes, then
Figure FDA0003024856520000024
Where k and j are the class of the sample, di (j)Is the ith sample of the jth class, dp (k)For the p sample of the k class, nkIs the number of samples contained in the kth class, W is an attributeA weight diagonal matrix;
s203: calculating weighted minimum intra-class distance swwd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted minimum intra-class distance swwd (j, i) of ith sample of jth class as an average weighted distance value from the sample to other samples of jth class
Figure FDA0003024856520000031
In the formula (d)q (j)For the qth sample of class j, q ≠ i, njThe number of samples of the jth class;
s204: calculating weighted clustering distance swbawd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted clustering distance swbawd (j, i) of the ith sample of the jth class as the sum of weighted minimum inter-class distance and intra-class distance of the samples
Figure FDA0003024856520000032
S205: calculating a weighted clustering dispersion distance swbswd (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted cluster dispersion distance swbswd (j, i) of ith sample of jth class as the difference between weighted minimum inter-class distance and intra-class distance of the samples, then
Figure FDA0003024856520000033
S206: calculating weighted inter-cluster intra-class division indexes SWBWP (j, i); let K ═ { D } be a clustering space, where D ═ D1,d2,...,dnAnd assuming that all samples are clustered into c classes, defining weighted inter-cluster inter-class partition index SWBWP (j, i) of ith sample of jth class as the ratio of weighted cluster dispersion distance to cluster distance, then
Figure FDA0003024856520000041
The SWBWP index can reflect the clustering condition of a single sample, and the larger the SWBWP index value is, the better the clustering effect of the sample is; for the attribute set, the larger the average SWBWP value of all samples is, the better the clustering effect of the attribute set is;
s207: construction of the optimal clustering number coptModel (2)
Figure FDA0003024856520000042
Wherein the content of the first and second substances,
Figure FDA0003024856520000043
4. the aerial target clustering method of claim 3, wherein the specific operation of step S3 comprises the following steps,
s301: searching a value interval [ P ] of a deviation parameter P by adopting a half-division methodmin,Pmax]Obtaining the clustering number [2, c ]max]Corresponding p (i), i ═ 1,2max-1; wherein, cmaxGet
Figure FDA0003024856520000044
Pmin＝min s(i，j)，i≠j，j＝1，2，...，n，Pmax＝max s(i，j)，i≠j，j＝1，2，...，n；
S302: calculating p (i), i ═ 1,2max-1 SWBWP value of clustering result corresponding to the maximum value, finding out the clustering number corresponding to the maximum value as the optimal clustering number copt；
S303: partial parameter subspace [ p (c) is searched by adopting a half-division methodopt-1)，p(copt)]Determining the optimal cluster number coptCorresponding lower bound p of the bias parameter subspacen(ii) a Search for a biased parameter subspace [ p (c) ] by a bisection methodopt)，p(copt+1)]Determining the optimal cluster number coptCorresponding upper bound p of the deviation parameter subspacex。
5. According toThe aerial target clustering method of claim 4, wherein in step S301, clustering is performed by using an improved AP algorithm, all samples are considered as potential class representatives, and the probability of being selected as the class representatives is the same, i.e. S (i, i) are all biased parameters P, and S (i, i) is the median of the corresponding row in the similarity matrix S; in order to select a suitable class representation in a sample, it is necessary to continuously search for an attraction degree r and an attribution degree a, where r (i, j) represents a sample djIs suitable for makingiClass (ii) represents the degree of a point, a (i, j) represents diIs suitable for makingjDegree of class representation point of (1);
for sample diCalculating the sum of the attraction degree r (i, j) and the attribution degree a (i, j) of other samples, and selecting the sample d with the maximum sumjAs diThe update process of the attraction degree r (i, j) and the attribution degree a (i, j) is as follows:
Figure FDA0003024856520000051
If i≠j,
Figure FDA0003024856520000052
else,
Figure FDA0003024856520000053
in the formula, t is iteration times; lambda is damping factor, lambda is more than 0.5 and less than 1.
6. The aerial target clustering method of claim 4, wherein the specific operation of step S4 includes the following steps,
s401: an initialization stage; initial honey sources are all randomly generated in a feasible interval, and the number of rows of the matrix is the number N of the honey sourcesfsThe column of the matrix is a deviation parameter value, and the ith row and the jth column of the element x in the matrixijIs calculated by the formula
Figure FDA0003024856520000054
In the formula (I), the compound is shown in the specification,
Figure FDA0003024856520000055
and
Figure FDA0003024856520000056
respectively representing the upper and lower bounds of j-th column variables in the matrix, and rand representing a random number with the value in a (0,1) interval;
s402: a bee hiring stage; after the initial honey source position is generated, the hiring bee searches for a better honey source nearby the honey source according to the honey source position in the memory, and the update formula is as follows
Figure FDA0003024856520000061
In the formula, xij' is an element for newly generating a honey source,
Figure FDA0003024856520000062
for randomly selecting the corresponding position element, x, of the honey sourcei'jCorresponding position elements of other honey sources, and RAND is an updating threshold value which is generally 0.5;
if xij' exceed
Figure FDA0003024856520000063
In the range of (1), then take xij' is the nearest boundary value, i.e. having
Figure FDA0003024856520000064
S403: a bee observation stage; after all hired bees finish searching, honey source position information is exchanged with the observation bees, and the observation bees adopt a returned tournament selection operator to perform selection operation; at random in NfsSelecting 2 honey sources from the honey sources, calculating SWBWP values which are F respectively1And F2If F is1Is superior to F2I.e. satisfy F1＞F2If so, selecting the 1 st honey source for updating, otherwise, selecting the 2 nd honey source for updating;
s404: a bee scouting stage; after iter _ limit iterations are carried out, if the solution quality of the honey source is not improved, the hiring bee corresponding to the honey source becomes a scout bee, the original honey source is abandoned, and the formula is adopted
Figure FDA0003024856520000065
Generating a new honey source position;
s405: repeating the steps S402-S404 until reaching the maximum iteration number maxcycle, thereby carrying out deviation on the parameter subspace [ P ]n,Px]Performing a fine search to determine an optimal bias parameter Pb。
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