CN113177583B - An air target clustering method - Google Patents

Abstract

The invention discloses an aerial target clustering and grouping method, comprising the following steps: S1: based on a comprehensive weighting theory, combining subjective and objective weights of attributes to generate a comprehensive weight of attributes that affects the result of target grouping; S2: considering different attributes for clustering The difference of influence, the comprehensive weight is introduced into the calculation of similarity, the similarity measure is optimized, the SWBWP indicator used to determine the optimal number of clusters for the target grouping is constructed, and the model used to determine the optimal number of clusters c _opt ; S3: The semi-division method is used to roughly search the value interval [P _min , P _max ] of the bias parameter P, if all P(i) corresponding to the number of clusters [2, c _max ] are searched, i=1, 2, .. .,c _max -1, then calculate the corresponding SWBWP index of different cluster numbers, and use the SWBWP index to determine the optimal cluster number c _opt ; S4: take the SWBWP value of the clustering result as the fitness function value, and adopt the ABC algorithm to finely search for the bias. The parameter subspace [P _n , P _x ], determines the optimal bias parameter P _b . Aiming at the problem of target grouping in which the number of target groups is unknown, the present invention can achieve the purpose of efficient and accurate target grouping in a high air confrontation environment.

Description

An air target clustering method

technical field

The invention relates to the technical field of auxiliary decision-making, in particular to a method for clustering and grouping of aerial targets.

Background technique

In recent years, with the increasing complexity and mutation of air confrontation, swarm confrontation will become an important form of future air confrontation. The targets in the same confrontation cluster have a common overall goal. To achieve this goal, the opposing commander will divide the air targets in the cluster into multiple groups of different sizes, and each group achieves one of the overall goals. Sub-targets; each group is composed of multiple cooperative formations, and each formation performs specific combat tasks; the formation consists of more than one air target, and the targets in the formation need to maintain a certain height and distance difference when flying , therefore, the targets of the same formation have similar maneuvering states.

According to the maneuvering state of the air targets, such as distance, azimuth, heading angle, speed, altitude, etc., the targets can be grouped, and the division of the opponent's target formation can be obtained. The commander of the other side established a cooperative relationship between the targets in the process of forming the target, and concealed the formation's action intention. Target grouping is the inverse process of establishing a formation, which can obtain the cooperative relationship between targets and is the basis for identifying the action intention of the opponent's formation.

The grouping problem is essentially a clustering problem under the condition that the number of classes is unknown. It is a process of dividing the targets with high similarity of feature attributes into the same class, and we cannot obtain the exact target group number information of the other party before the grouping. The current research assumes that the target group number of the other party has been known. For example, Yuan Deping proposed a target grouping method under multiple formations, that is, according to the geometric situation of the opponent's target, the chameleon algorithm based on certain constraints is used to achieve target clustering, and then according to the geometric situation of the opponent's group, the opponent's offensive advantage function is calculated, and Through the derivation of subjective and objective weights, the attack matrix is calculated and then the target groups are divided. Liu Jijun et al. proposed an improved ISODATA algorithm, which optimizes the selection of the initial centroids based on the argument distribution, reduces the amount of clustering computation, and improves the clustering effect. Wu Wenlong et al. used the k-dist descending graph to achieve the division of different density targets, realized the grouping of different density targets, and improved the applicability of the ISODATA algorithm. Zhang Xuliang et al improved the k-means algorithm by introducing modularity, and used this method to realize the grouping of land battlefield targets.

The above methods are all based on the clustering idea to study the air target grouping method under confrontation conditions, and transform the target grouping problem into a clustering problem for problem modeling and optimization. Applicability of the method is insufficient.

SUMMARY OF THE INVENTION

In view of the above existing problems, the present invention aims to provide an aerial target clustering and grouping method, which can achieve the purpose of efficient and accurate target grouping in a high-anti-air environment for the problem of target grouping with unknown target groups.

In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

A kind of aerial target clustering grouping method, is characterized in that, comprises the following steps,

S1: Based on the comprehensive weighting theory, combining the subjective and objective weights of each attribute during the movement of the air target, generate a comprehensive weight of attributes that affects the target grouping result;

S2: Based on the difference in the impact of different attributes on the clustering during the movement of the aerial target, the comprehensive weight is introduced into the calculation of the similarity, the similarity measure is optimized, and the SWBWP indicator used to determine the optimal number of clusters for the target grouping is constructed, and the model used to determine the optimal number of clusters c _opt ;

S3: The semi-division method is used to roughly search the value interval [P _min , P _max ] of the bias parameter P, if all P(i) corresponding to the number of clusters [2, c _max ] are searched, i=1, 2, .. ., c _max -1, then calculate the SWBWP index corresponding to different cluster numbers, and use the SWBWP index to determine the optimal cluster number c _opt ;

S4: Using the SWBWP value of the clustering result as the fitness function value, the ABC algorithm is used to perform a precise search on the bias parameter subspace [P _n , P _x ] to determine the optimal bias parameter P _b .

Further, the specific operation of step S1 includes the following steps:

m为目标运动属性的个数；当领域专家未对属性进行评估时，T＝(1/m，1/m，...，1/m)；S101: Let the subjective weight of the j-th attribute in the air target motion process be T _j , then the subjective weight of the air target motion attribute T=(T ₁ , T ₂ , . . . , T _m ), where,

m is the number of target motion attributes; when the attribute is not evaluated by domain experts, T=(1/m, 1/m, . . . , 1/m);

其中，n为空中目标总数，

当d_ij′＝0时，d_ijln d_ij′＝0；S102: For the attribute set B=(b _ij ) _n*m , normalize it to D=(d _ij ) _n*m , then the entropy value of the jth attribute is

Among them, n is the total number of air targets,

When d _ij '=0, d _ij ln d _ij '=0;

其中，

k表示第k个属性，且k≠j；S103: Let the objective weight of the j-th attribute be U _j , then the objective weight of the j-th attribute of the attribute set B=(bi _ij ) _n*m is:

in,

k represents the kth attribute, and k≠j;

α为偏好系数，是客观权重占综合权重的比例。S104: Let the comprehensive weight of the j-th attribute be w _j , comprehensively consider the subjective weight and objective weight of the attribute, and obtain the comprehensive weight of the attribute by weighting, then the j-th attribute comprehensive weight in the attribute set B=(b _ij ) _n*m The weight is w _j =(1-α)T _j +αU _j , where,

α is the preference coefficient, which is the ratio of the objective weight to the comprehensive weight.

Further, the specific operation of step S2 includes the following steps:

S201: similarity measure optimization; introduce the comprehensive weight generated in step S1 into the calculation of the similarity matrix S, and optimize the similarity measure, then s(i,j)=-(d _i -d _j ) ^T W (d _i -d _j ), (i≠j), where W is a diagonal matrix with attribute weights w _j (j=1,2,...,m) as diagonal elements;

式中，k和j为样本所在类别，d_i ^(j)为第j类的第i个样本，d_p ^(k)为第k类的第p个样本，n_k为第k类中所含样本个数，W为属性权重对角矩阵；S202: Calculate the weighted minimum inter-class distance swbd(j, i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered The class is class c, and the weighted minimum inter-class distance swbd(j,i) of the ith sample of the jth class is defined as the minimum value of the average weighted distance from this sample to the samples in other classes, then

In the formula, k and j are the categories of the samples, d _i ^(j) is the i-th sample of the j-th category, d _p ^(k) is the p-th sample of the k-th category, and n _k is the content of the k-th category. The number of samples, W is the attribute weight diagonal matrix;

式中，d_q ^(j)为第j类的第q个样本，q≠i，n_j为第j类的样本个数；S203: Calculate the weighted minimum intra-class distance swwd(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered The class is class c, and the weighted minimum intra-class distance swwd(j,i) of the i-th sample of the j-th class is defined as the average weighted distance value from this sample to other samples of the j-th class, then

In the formula, d _q ^(j) is the qth sample of the jth class, q≠i, and _nj is the number of samples of the jth class;

S204: Calculate the weighted clustering distance swbawd(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered For class c, define the weighted clustering distance swbawd(j,i) of the ith sample of the jth class as the sum of the weighted minimum inter-class distance and the intra-class distance of the sample

S205: Calculate the weighted clustering dispersion distance swbswd(j, i); let K={D} be the clustering space, where D={d ₁ , d ₂ ,...,d _n }, assuming that all samples are The clustering is class c, and the weighted clustering dispersion distance swbswd(j,i) of the ith sample of the jth class is defined as the difference between the weighted minimum inter-class distance and the intra-class distance of the sample, then

SWBWP指标可以反映单个样本的聚类情况，SWBWP指标值越大，说明该样本聚类效果越好；对于属性集来说，所有样本的平均SWBWP值越大，说明属性集聚类效果越好；S206: Calculate the weighted intra-cluster partition index SWBWP(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all The samples are clustered into class c, and the weighted intra-cluster division index SWBWP(j,i) of the ith sample of the jth class is defined as the ratio of the weighted cluster dispersion distance to the cluster distance, then

The SWBWP index can reflect the clustering situation of a single sample. The larger the SWBWP index value, the better the clustering effect of the sample; for the attribute set, the larger the average SWBWP value of all samples, the better the clustering effect of the attribute set;

其中，

S207: Build a model for determining the optimal number of clusters c _opt

in,

Further, the specific operation of step S3 includes the following steps:

P_min＝min s(i，j)，i≠j，j＝1，2，...，n，P_max＝max s(i，j)，i≠j，j＝1，2，...，n；S301: Use the semi-division method to search the value interval [P _min , P _max ] of the bias parameter P, and obtain P(i) corresponding to the number of clusters [2, c _max ], i=1, 2, . . . , c _max -1; among them, c _max is taken as

P _min =min s(i,j),i≠j,j=1,2,...,n,P _max =max s(i,j),i≠j,j=1,2,... ., n;

_S302 : Calculate the _SWBWP value of the clustering result corresponding to P(i), i=1, 2, .

S303: Use the semi-division method to search the bias parameter subspace [p(c _opt -1), p(c _opt )], and determine the lower bound p _n of the bias parameter subspace corresponding to the optimal number of clusters c _opt ; use the semi-division method to search for the bias parameters Subspace [p(c _opt ), p(c _opt +1)], determine the upper bound p _x of the bias parameter subspace corresponding to the optimal number of clusters c _opt .

Further, in step S301, the improved AP algorithm is used for clustering, and all samples are regarded as potential class representatives, and the possibility of being selected as class representatives is the same, that is, s(i, i) are all bias 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 representative in the sample, it is necessary to continuously search for the degree of attraction r and the degree of attribution a, where r(i,j) represents The degree to which the sample d _j is suitable to be the class representative point of d _i , a(i, j) represents the degree to which d _i is suitable to be the class representative point of d _j ;

else,

式中，t为迭代次数；λ为阻尼因子，0.5＜λ＜1。For the sample d _i , calculate the sum of the attractiveness r(i,j) and the attribution a(i, _j ) of other samples, select the sample dj with the largest sum as the class representative of d _i , and the attractiveness r(i,j ) and the update process of the attribution a(i,j) is:

else,

In the formula, t is the number of iterations; λ is the damping factor, 0.5<λ<1.

Further, the specific operation of step S4 includes the following steps:

式中，

和

分别表示矩阵中第j列变量的上下界，rand表示取值在(0,1)区间的随机数；S401: Initialization stage; the initial nectar sources are randomly generated within the feasible interval, the number of rows of the matrix is the number of nectar sources N _fs , the columns of the matrix take the values of the bias parameters, and the calculation formula of the element x _ij in the i-th row and the j-th column of the matrix is:

In the formula,

and

Represent the upper and lower bounds of the variables in the jth column of the matrix, respectively, and rand represents a random number with a value in the (0,1) interval;

式中，x_ij'为新生成蜜源的元素，

为随机选取蜜源对应位置元素，x_i'j为其他蜜源对应位置元素，RAND为更新阈值，一般取值为0.5；S402: hired bee stage; after the initial nectar source location is generated, the hired bee searches for a better nectar source near the nectar source according to the nectar source location in memory, and the update formula is

In the formula, x _ij ' is the element of the newly generated nectar source,

In order to randomly select the position elements corresponding to the nectar sources, x _i'j is the position elements corresponding to other nectar sources, and RAND is the update threshold, which is generally 0.5;

的范围，则取x_ij'为最近边界值，即有

If x _ij ' exceeds

, then take x _ij ' as the nearest boundary value, that is, we have

S403: Observer bee stage; after all hired bees complete the search, they exchange nectar source location information with the observer bees, and the observer bees use the tournament selection operator with replacement for selection operation; randomly select 2 nectar sources from N _fs nectar sources, and calculate SWBWP The values are F ₁ and F ₂ respectively. If F ₁ is better than F ₂ , that is, when F ₁ > F ₂ , the first nectar source is selected for updating, otherwise, the second nectar source is selected for updating;

生成新蜜源位置；S404: scout bee stage; after iter_limit iterations are performed, if the solution quality of the nectar source does not improve, the hired bee corresponding to the nectar source becomes a scout bee, and the original nectar source is abandoned. According to the formula

Generate a new nectar location;

S405: Repeat steps S402 to S404 until the maximum number of iterations maxcycle is reached, so as to perform a precise search on the bias parameter subspace [P _n , P _x ] to determine the optimal bias parameter P _b .

The beneficial effects of the present invention are:

Compared with the prior art, the method for generating the comprehensive weight of attributes that affects the result of target grouping can effectively combine the subjective and objective information, and the determination of the comprehensive weight of attributes is more scientific and reasonable; The improved AP algorithm divides the clustering into two parts: rough search and fine search, which realizes the integration of clustering efficiency and time cost; the ABC algorithm performs fine search on the P subspace, which reduces the problem solving space to a certain extent and improves the search efficiency. In a word, the method of the present invention can realize the rapid and accurate grouping of the opponent's target, thereby ensuring a better situational awareness effect.

Description of drawings

Fig. 1 is the flow chart of the air target clustering and grouping method of the present invention;

Fig. 2 is the cluster number-BWP/SWBWP index value relation diagram of attribute set Pid in the SWBWP index feasibility verification experiment of the present invention;

3 is a diagram showing the relationship between the number of clusters of the Data attribute set-SWBWP index value in the rough search stage in the clustering effect comparison experiment of the present invention;

Fig. 4 shows the fitness change process of the APBMABC (Affinity Propagation Based on Bisection Method and ArtificialBee Colony Algorithm) algorithm when searching for the best bias parameter in the clustering effect comparison experiment of the present invention by combining the two optimization methods of the semi-division method and the artificial bee colony algorithm with the AP algorithm. picture;

Fig. 5 (a) is the clustering result of APBWMMP algorithm in the clustering effect comparison experiment of the present invention;

Fig. 5 (b) is the clustering result of adAP algorithm in the clustering effect comparison experiment of the present invention;

Figure 5(c) is the clustering result of the APBMABC algorithm in the clustering effect comparison experiment of the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention are further described below with reference to the accompanying drawings and embodiments.

An aerial target clustering method, as shown in accompanying drawing 1, comprises the following steps,

S1: Based on the comprehensive weighting theory, combining the subjective and objective weights of each attribute during the movement of the air target, generate a comprehensive weight of attributes that affects the target grouping result;

m为属性的个数；当领域专家未对属性进行评估时，T＝(1/m,1/m,...,1/m)；Specifically, S101: Let the subjective weight of the j-th attribute in the air target movement process be T _j , the domain expert evaluates the cluster attribute according to the specific characteristics of the attribute in the attribute domain and combined with their own experience, and assigns the air target movement attribute Subjective weight T=(T ₁ ,T ₂ ,...,T _m ), where,

m is the number of attributes; when domain experts do not evaluate attributes, T=(1/m,1/m,...,1/m);

其中，n为空中目标总数，

当d_ij′＝0时，d_ijlnd_ij′＝0；S102: For the attribute set B=(b _ij ) _n*m , normalize it to D=(d _ij ) _n*m , then the entropy value of the jth attribute is

Among them, n is the total number of air targets,

When d _ij '=0, d _ij lnd _ij '=0;

其中，

k表示第k个属性，且k≠j；当样本某属性差别越大，该属性的熵值越小，所获得的权重就越高；S103: Let the objective weight of the j-th attribute be U _j , then the objective weight of the j-th attribute of the attribute set B=(bi _ij ) _n*m is:

in,

k represents the kth attribute, and k≠j; when the difference of a certain attribute of the sample is larger, the entropy value of the attribute is smaller, and the obtained weight is higher;

α为偏好系数，是客观权重占综合权重的比例。S104: Let the comprehensive weight of the j-th attribute be w _j , comprehensively consider the subjective weight and objective weight of the attribute, and obtain the comprehensive weight of the attribute by weighting, then the j-th attribute comprehensive weight in the attribute set B=(b _ij ) _n*m The weight is w _j =(1-α)T _j +αU _j , where,

α is the preference coefficient, which is the ratio of the objective weight to the comprehensive weight.

Further, step S2: based on the difference in the influence of different attributes on the clustering in the movement of the aerial target, the comprehensive weight is introduced into the calculation of the similarity, the similarity measure is optimized, and a method for determining the optimal number of clusters for the target grouping is constructed. The SWBWP metric, and the model used to determine the optimal number of clusters, c _opt ;

Specifically, S201: Optimization of similarity measure; most clustering algorithms use the Euclidean distance between samples as their similarity measure. By default, all attributes have the same weight, and the difference in the impact of different attributes on clustering is not considered, that is, s(i,j )=-||d _i -d _j || ² , (i≠j);

In the present invention, the difference in the influence of attributes on clustering is considered, and the similarity measure is optimized; the comprehensive weight generated in step S1 is introduced into the calculation of the similarity matrix S, and the similarity measure is optimized, then s(i,j)= -(d _i -d _j ) ^T W(d _i -d _j ),(i≠j), where W is the diagonal element of attribute weight w _j (j=1,2,...,m) The diagonal matrix of ;

式中，k和j为样本所在类别，d_i ^(j)为第j类的第i个样本，d_p ^(k)为第k类的第p个样本，n_k为第k类中所含样本个数，W为属性权重对角矩阵；S202: Calculate the weighted minimum inter-class distance swbd(j, i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered The class is class c, and the weighted minimum inter-class distance swbd(j,i) of the ith sample of the jth class is defined as the minimum value of the average weighted distance from this sample to the samples in other classes, then

In the formula, k and j are the categories of the samples, d _i ^(j) is the i-th sample of the j-th category, d _p ^(k) is the p-th sample of the k-th category, and n _k is the content of the k-th category. The number of samples, W is the attribute weight diagonal matrix;

式中，d_q ^(j)为第j类的第q个样本，q≠i，n_j为第j类的样本个数；S203: Calculate the weighted minimum intra-class distance swwd(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered The class is class c, and the weighted minimum intra-class distance swwd(j,i) of the i-th sample of the j-th class is defined as the average weighted distance value from this sample to other samples of the j-th class, then

In the formula, d _q ^(j) is the qth sample of the jth class, q≠i, and _nj is the number of samples of the jth class;

S204: Calculate the weighted clustering distance swbawd(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered For class c, define the weighted clustering distance swbawd(j,i) of the ith sample of the jth class as the sum of the weighted minimum inter-class distance and the intra-class distance of the sample

S205: Calculate the weighted clustering dispersion distance swbswd(j, i); let K={D} be the clustering space, where D={d ₁ , d ₂ ,...,d _n }, assuming that all samples are The clustering is class c, and the weighted clustering dispersion distance swbswd(j,i) of the ith sample of the jth class is defined as the difference between the weighted minimum inter-class distance and the intra-class distance of the sample, then

SWBWP指标可以反映单个样本的聚类情况，SWBWP指标值越大，说明该样本聚类效果越好；对于属性集来说，所有样本的平均SWBWP值越大，说明属性集聚类效果越好。；S206: Calculate the weighted intra-cluster partition index SWBWP(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all The samples are clustered into class c, and the weighted intra-cluster division index SWBWP(j,i) of the ith sample of the jth class is defined as the ratio of the weighted cluster dispersion distance to the cluster distance, then

The SWBWP index can reflect the clustering of a single sample. The larger the SWBWP index value, the better the clustering effect of the sample; for the attribute set, the larger the average SWBWP value of all samples, the better the clustering effect of the attribute set. ;

其中，

S207: Build a model for determining the optimal number of clusters c _opt

in,

Further, step S3: using the semi-division method to roughly search the value interval [P _min , P _max ] of the bias parameter P, if all P(i) corresponding to the number of clusters [2, c _max ] are searched, i=1, 2, ..., c _max -1, then calculate the SWBWP index corresponding to different cluster numbers, and use the SWBWP index to determine the optimal cluster number c _opt ;

P_min＝mins(i，j)，i≠j，j＝1，2，...，n，P_max＝max s(i，j)，i≠j，j＝1，2，...，n；Specifically, S301: Use the semi-division method to search the value interval [P _min , P _max ] of the bias parameter P, and obtain P(i) corresponding to the number of clusters [2, c _max ], i=1, 2,  … , c _max -1; where, c _max is taken as

P _min =mins(i,j), i≠j,j=1,2,...,n, _Pmax =max s(i,j),i≠j,j=1,2,... , n;

The improved AP algorithm is used for clustering, and all samples are regarded as potential class representatives, and the possibility of being selected as class representatives is the same, that is, s(i,i) are all bias 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 representative in the sample, it is necessary to continuously search for the degree of attraction r and the degree of attribution a, where r(i, j) indicates that the sample d _j is suitable for d _i The class represents the degree of the point, a(i, j) represents the degree that d _i is suitable for the class of d _j to represent the point;

else,For the sample d _i , calculate the sum of the attractiveness r(i,j) and the attribution a(i, _j ) of other samples, select the sample dj with the largest sum as the class representative of d _i , and the attractiveness r(i,j ) and the update process of the attribution a(i,j) is:

else,

式中，t为迭代次数；λ为阻尼因子，0.5＜λ＜1。

In the formula, t is the number of iterations; λ is the damping factor, 0.5<λ<1.

_S302 : Calculate the _SWBWP value of the clustering result corresponding to P(i), i=1, 2, .

S303: Use the semi-division method to search the bias parameter subspace [p(c _opt -1), p(c _opt )], and determine the lower bound p _n of the bias parameter subspace corresponding to the optimal number of clusters c _opt ; use the semi-division method to search for the bias parameters Subspace [p(c _opt ), p(c _opt +1)], determine the upper bound p _x of the bias parameter subspace corresponding to the optimal number of clusters c _opt .

Further, step S4: using the SWBWP value of the clustering result as the fitness function value, using the ABC algorithm to perform a precise search on the bias parameter subspace [P _n , P _x ] to determine the optimal bias parameter P _b .

式中，

和

分别表示矩阵中第j列变量的上下界，rand表示取值在(0,1)区间的随机数；Specifically, S401: initialization stage; the initial nectar sources are randomly generated within the feasible interval, the number of rows of the matrix is the number of nectar sources N _fs , the columns of the matrix take the values of the bias parameters, and the calculation of the element x _ij in the i-th row and the j-th column in the matrix The formula is

In the formula,

and

Represent the upper and lower bounds of the variables in the jth column of the matrix, respectively, and rand represents a random number with a value in the (0,1) interval;

式中，x_ij'为新生成蜜源的元素，

为随机选取蜜源对应位置元素，x_i'j为其他蜜源对应位置元素，RAND为更新阈值，一般取值为0.5；S402: hired bee stage; after the initial nectar source location is generated, the hired bee searches for a better nectar source near the nectar source according to the nectar source location in memory, and the update formula is

In the formula, x _ij ' is the element of the newly generated nectar source,

In order to randomly select the position elements corresponding to the nectar sources, x _i'j is the position elements corresponding to other nectar sources, and RAND is the update threshold, which is generally 0.5;

的范围，则取x_ij'为最近边界值，即有

If x _ij ' exceeds

, then take x _ij ' as the nearest boundary value, that is, we have

S403: Observer bee stage; after all hired bees complete the search, they exchange nectar source location information with the observer bees, and the observer bees use the tournament selection operator with replacement for selection operation; randomly select 2 nectar sources from N _fs nectar sources, and calculate SWBWP The values are F ₁ and F ₂ respectively. If F ₁ is better than F ₂ , that is, when F ₁ > F ₂ , the first nectar source is selected for updating, otherwise, the second nectar source is selected for updating;

生成新蜜源位置；S404: scout bee stage; after iter_limit iterations are performed, if the solution quality of the nectar source does not improve, the hired bee corresponding to the nectar source becomes a scout bee, and the original nectar source is abandoned. According to the formula

Generate a new nectar location;

S405: Repeat steps S402 to S404 until the maximum number of iterations maxcycle is reached, so as to perform a precise search on the bias parameter subspace [P _n , P _x ] to determine the optimal bias parameter P _b .

To sum up, in the aerial target clustering method of the present invention, the preference coefficient α, the total number of nectar sources N _fs , the maximum number of iterations maxcycle and the maximum number of nectar stays iter_limit can be set first, and then aerial target clustering can be performed.

Simulation test:

In order to verify the effectiveness of the method proposed in the present invention, the following computer simulation experiments were carried out.

Experimental environment: The simulation experiment uses a computer with Intel Core i7-6700HQ quad-core processor, 8GB memory, Windows7 operating system, and uses MATLAB2016a to simulate the algorithm. The preference coefficient α is set to 0.5, the damping factor λ is 0.8, the total number of nectar sources N _fs is 20, the maximum number of iterations maxcycle is 80, and the maximum number of nectar stays iter_limit is 8.

(1) SWBWP indicator feasibility verification experiment

The experiments use the real attribute sets Pima-indians-diabetes (Pid), Breast-cancer-wisconsin (Bcw) and Wine from three University of California Irvine (UCI) databases, and two artificial attribute sets Model1 and Model2 as tests property set. The clustering results are evaluated by using the between-within-proportion (BWP) index and the SWBWP index in the present invention, respectively, to determine the optimal number of clusters. The following table 1 is the optimal number of clusters evaluated by the above-mentioned 5 attribute sets, and the accompanying drawing 2 is the relationship diagram between the number of clusters in the Pid attribute set and the BWP, SWBWP index values, and the following table 2 is the number of different clusters in the Model2 attribute set. Corresponding BWP, SWBWP indicator values.

Table 1 The optimal number of clusters for attribute sets evaluated by BWP and SWBWP indicators

Table 2 Clustering index values of Model2 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

It can be seen from Table 1 that the SWBWP index proposed in the present invention can obtain the same number of clusters as the actual number of clusters on three UCIs and two artificial attribute sets; the BWP index can obtain the same number of clusters on the attribute sets Pid, Bcw and Model2. The same number of clusters as the correct number of classes, but cannot get the correct number of clusters on the Wine and Model1 attribute sets.

The number of sample classes in the attribute set Pid is 2. It can be seen from Figure 2 that the index values of BWP and SWBWP both achieve the maximum value when the number of clusters is 2, which is the same as the number of real classes.

It can be seen from Table 2 that when the number of clusters is 3, the BWP index achieves the maximum value of 0.5350, and the SWBWP index achieves the maximum value of 0.7630 when the number of clusters is 3. Both the BWP and SWBWP indicators can obtain the maximum value for the Model2 attribute set. optimal number of clusters.

(2) Comparative experiment of clustering effect

Assume that the enemy dispatches a total of 300 aircrafts to carry out cluster operations against me, which are divided into four functional groups: reconnaissance, attack, penetration, and surveillance. The attribute set Data is the azimuth, distance, horizontal speed, heading angle and The eigenvalues of motion attributes such as height, some data are shown in Table 3 below. Attribute subjective weight value T=(0.35, 0.35, 0.5, 0.65, 0.65). Based on the attribute sets Bcw, Wine, Model1 and Data, the clustering method (APBMABC algorithm) in the present invention is combined with the adaptive affinity propagation clustering (adAP), the weighted Mahalanobis distance and the membership degree. The optimized nearest neighbor propagation clustering algorithm (Affinity Propagation Based on Weighted Mahalanobis Distance and Modified Preference, APBWMMP) compares the clustering accuracy.

Table 3 Target motion attribute eigenvalues and groups

Accompanying drawing 3 is the SWBWP index value under different cluster numbers that the rough search stage based on attribute set Data searches out; It can be seen from FIG. 4 that the APBMABC algorithm proposed in the present invention can effectively determine the optimal number of clusters of the attribute set through the rough search process, and determine the search range for the fine search process. The fine search process using the ABC algorithm has been iterated to about 40 times and has become stable, and the best clustering results have been obtained.

Table 4 below shows the clustering results of three different algorithms based on the attribute set Data, and Figure 5(a)-Figure 5(c) is a comparison of the clustering results of the three different algorithms based on the attribute set Data. Available from accompanying drawing 5(a)-accompanying drawing 5(c) and table 4, APBWMMP, adAP and APBMABC algorithm all can obtain the same optimal number of clusters as the actual number of classes, but based on rough search and fine search two The clustering effect of APBMABC algorithm in the search process is better than that of APBWMMP and adAP algorithm on the whole.

Table 4 Comparison of clustering effects of APBWMMP, adAP and APBMABC algorithms

To sum up, the aerial target grouping method based on the combined algorithm of coarse search and fine search proposed by the present invention can provide a better target grouping scheme. Compared with other methods, the grouping accuracy of the method proposed by the present invention is higher. high.

The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments. The above-mentioned embodiments and descriptions only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Various changes and modifications fall within the scope of the claimed invention. The claimed scope of the present invention is defined by the appended claims and their equivalents.

Claims (6)

1. an aerial target clustering and grouping method, is characterized in that, comprises the following steps, S1: Based on the comprehensive weighting theory, combining the subjective and objective weights of each attribute during the movement of the air target, generate a comprehensive weight of attributes that affects the target grouping result; S2: Based on the difference in the impact of different attributes on the clustering during the movement of the aerial target, the comprehensive weight is introduced into the calculation of the similarity, the similarity measure is optimized, and the SWBWP indicator used to determine the optimal number of clusters for the target grouping is constructed, and the model used to determine the optimal number of clusters c _opt ; S3: The semi-division method is used to roughly search the value interval [P _min , P _max ] of the bias parameter P, if all P(i) corresponding to the number of clusters [2, c _max ] are searched, i=1, 2, .. ., c _max -1, then calculate the SWBWP index corresponding to different cluster numbers, and use the SWBWP index to determine the optimal cluster number c _opt ; S4: Using the SWBWP value of the clustering result as the fitness function value, the ABC algorithm is used to perform a precise search on the bias parameter subspace [P _n , P _x ] to determine the optimal bias parameter P _b . 2. a kind of aerial target clustering grouping method according to claim 1, is characterized in that, the concrete operation of step S1 comprises the following steps, S101: Let the subjective weight of the j-th attribute in the air target motion process be T _j , then the subjective weight of the air target motion attribute T=(T ₁ , T ₂ , . . . , T _m ), where,

m is the number of target motion attributes; when the attribute is not evaluated by domain experts, T=(1/m, 1/m, . . . , 1/m); S102: For the attribute set B=(b _ij ) _n*m , normalize it to D=(d _ij ) _n*m , then the entropy value of the jth attribute is

Among them, n is the total number of air targets,

When d _ij '=0, d _ij lnd _ij '=0; S103: Let the objective weight of the j-th attribute be U _j , then the objective weight of the j-th attribute of the attribute set B=(bi _ij ) _n*m is:

in,

k represents the kth attribute, and k≠j; S104: Let the comprehensive weight of the j-th attribute be w _j , comprehensively consider the subjective weight and objective weight of the attribute, and obtain the comprehensive weight of the attribute by weighting, then the j-th attribute comprehensive weight in the attribute set B=(b _ij ) _n*m The weight is w _j =(1-α)T _j +αU _j , where,

α is the preference coefficient, which is the ratio of the objective weight to the comprehensive weight. 3. a kind of aerial target clustering grouping method according to claim 2 is characterized in that, the concrete operation of step S2 comprises the following steps, S201: similarity measure optimization; introduce the comprehensive weight generated in step S1 into the calculation of the similarity matrix S, and optimize the similarity measure, then s(i,j)=-(d _i -d _j ) ^T W (d _i -d _j ), (i≠j), where W is a diagonal matrix with attribute weights w _j (j=1,2,...,m) as diagonal elements; S202: Calculate the weighted minimum inter-class distance swbd(j, i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered The class is class c, and the weighted minimum inter-class distance swbd(j,i) of the ith sample of the jth class is defined as the minimum value of the average weighted distance from this sample to the samples in other classes, then

In the formula, k and j are the categories of the samples, d _i ^(j) is the i-th sample of the j-th category, d _p ^(k) is the p-th sample of the k-th category, and n _k is the content of the k-th category. The number of samples, W is the attribute weight diagonal matrix; S203: Calculate the weighted minimum intra-class distance swwd(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered The class is class c, and the weighted minimum intra-class distance swwd(j,i) of the i-th sample of the j-th class is defined as the average weighted distance value from this sample to other samples of the j-th class, then

In the formula, d _q ^(j) is the qth sample of the jth class, q≠i, and _nj is the number of samples of the jth class; S204: Calculate the weighted clustering distance swbawd(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all samples are clustered For class c, define the weighted clustering distance swbawd(j,i) of the ith sample of the jth class as the sum of the weighted minimum inter-class distance and the intra-class distance of the sample

S205: Calculate the weighted clustering dispersion distance swbswd(j, i); let K={D} be the clustering space, where D={d ₁ , d ₂ ,...,d _n }, assuming that all samples are The clustering is class c, and the weighted clustering dispersion distance swbswd(j,i) of the ith sample of the jth class is defined as the difference between the weighted minimum inter-class distance and the intra-class distance of the sample, then

S206: Calculate the weighted intra-cluster partition index SWBWP(j,i); let K={D} be the clustering space, where D={d ₁ ,d ₂ ,...,d _n }, assuming that all The samples are clustered into class c, and the weighted intra-cluster division index SWBWP(j,i) of the ith sample of the jth class is defined as the ratio of the weighted cluster dispersion distance to the cluster distance, then

The SWBWP index can reflect the clustering situation of a single sample. The larger the SWBWP index value, the better the clustering effect of the sample; for the attribute set, the larger the average SWBWP value of all samples, the better the clustering effect of the attribute set; S207: Build a model for determining the optimal number of clusters c _opt

in,

4. a kind of aerial target clustering grouping method according to claim 3 is characterized in that, the concrete operation of step S3 comprises the following steps, S301: Use the semi-division method to search the value interval [P _min , P _max ] of the bias parameter P, and obtain P(i) corresponding to the number of clusters [2, c _max ], i=1, 2, . . . , c _max -1; among them, c _max is taken as

P _min =min s(i,j),i≠j,j=1,2,...,n,P _max =max s(i,j),i≠j,j=1,2,... ., n; _S302 : Calculate the _SWBWP value of the clustering result corresponding to P(i), i=1, 2, . S303: Use the semi-division method to search the bias parameter subspace [p(c _opt -1), p(c _opt )], and determine the lower bound p _n of the bias parameter subspace corresponding to the optimal number of clusters c _opt ; use the semi-division method to search for the bias parameters Subspace [p(c _opt ), p(c _opt +1)], determine the upper bound p _x of the bias parameter subspace corresponding to the optimal number of clusters c _opt . 5. a kind of aerial target clustering grouping method according to claim 4, is characterized in that, in step S301, adopts improved AP algorithm to carry out clustering, regards all samples as potential class representative, and is selected as class representative The possibility is the same, that is, s(i,i) are all bias 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 representative in the sample, it is necessary to Continuously search for the degree of attraction r and the degree of attribution a, where r(i, j) represents the degree to which the sample d _j is suitable for the class representative point of d _i , and a(i, j) represents the class representative point of d _i suitable for d _j Degree; For the sample d _i , calculate the sum of the attractiveness r(i,j) and the attribution a(i, _j ) of other samples, select the sample dj with the largest sum as the class representative of d _i , and the attractiveness r(i,j ) and the update process of the attribution a(i,j) is:

If i≠j,

else,

In the formula, t is the number of iterations; λ is the damping factor, 0.5<λ<1. 6. a kind of aerial target clustering grouping method according to claim 4 is characterized in that, the concrete operation of step S4 comprises the following steps, S401: Initialization stage; the initial nectar sources are randomly generated within the feasible interval, the number of rows of the matrix is the number of nectar sources N _fs , the columns of the matrix take the values of the bias parameters, and the calculation formula of the element x _ij in the i-th row and the j-th column of the matrix is:

In the formula,

and

Represent the upper and lower bounds of the variables in the jth column of the matrix, respectively, and rand represents a random number with a value in the (0,1) interval; S402: hired bee stage; after the initial nectar source location is generated, the hired bee searches for a better nectar source near the nectar source according to the nectar source location in memory, and the update formula is

In the formula, x _ij ' is the element of the newly generated nectar source,

In order to randomly select the position elements corresponding to the nectar sources, x _i'j is the position elements corresponding to other nectar sources, and RAND is the update threshold, which is generally 0.5; If x _ij ' exceeds

, then take x _ij ' as the nearest boundary value, that is, we have

S403: Observer bee stage; after all hired bees complete the search, they exchange nectar source location information with the observer bees, and the observer bees use the tournament selection operator with replacement for selection operation; randomly select 2 nectar sources from N _fs nectar sources, and calculate SWBWP The values are F ₁ and F ₂ respectively. If F ₁ is better than F ₂ , that is, when F ₁ > F ₂ , the first nectar source is selected for updating, otherwise, the second nectar source is selected for updating; S404: scout bee stage; after iter_limit iterations are performed, if the solution quality of the nectar source does not improve, the hired bee corresponding to the nectar source becomes a scout bee, and the original nectar source is abandoned. According to the formula

Generate a new nectar location; S405: Repeat steps S402 to S404 until the maximum number of iterations maxcycle is reached, so as to perform a precise search on the bias parameter subspace [P _n , P _x ] to determine the optimal bias parameter P _b .

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