CN107219510A

CN107219510A - Radar target identification method based on unlimited largest interval linear discriminant projection model

Info

Publication number: CN107219510A
Application number: CN201710351886.8A
Authority: CN
Inventors: 陈渤; 刘宁; 文伟; 刘宏伟
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2017-05-18
Filing date: 2017-05-18
Publication date: 2017-09-29
Anticipated expiration: 2037-05-18
Also published as: CN107219510B

Abstract

The present invention proposes a kind of radar target identification method based on unlimited largest interval linear discriminant projection model, the technical problem low for solving discrimination present in existing radar target identification method.Realize that step is：Obtain power spectrum characteristic training sample set X category label collection ys corresponding with its；Build unlimited largest interval linear discriminant projection model；Define the expression formula of the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint；Set the initial value of parameters in the expression formula of the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint；Represent the Condition Posterior Distribution of parameters in the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint；The Condition Posterior Distribution of parameters to representing is sampled；Obtain power spectrum characteristic test sample collectionCategory of test label set corresponding with itsObtain the discrimination of radar target.The present invention can be used for carrying out detection identification to Radar High Range Resolution.

Description

Radar target identification method based on unlimited largest interval linear discriminant projection model

Technical field

The invention belongs to Radar Technology field, it is related to a kind of radar target identification method, and in particular to a kind of unlimited maximum Spaced linear differentiates the target identification method of the radar of projection model, and detection knowledge is carried out available for Radar High Range Resolution Not.

Background technology

Radar target recognition is a kind of technological means that radar is used, for recognizing that it is searched in volume it has been found that mesh Mark, its principle is exactly the radar echo signal using target, realizes the judgement to target type.Wideband radar is usually operated at light School district, now radar target can be regarded as being made up of the different scattering point of a large amount of intensity, High Range Resolution HRRP be with width The vector of each scattering point echo-signal on objective body is obtained with radar signal.It reflects scattering point on objective body and regarded along radar The distribution situation of line, contains the important structural information of target, such as target size, scattering point structure etc..Therefore in 20 generation Ji Mo, some scholars propose the technology that radar target automatic identification is completed using HRRP, see [S.P.Jacobs.Automatic target recognition using high-resolution radar range profiles.PhD Dissertation, Washington Univ., St.Louis, MO, 1999] enter 21st century after, this technology is in thunder The extensive concern of people is caused up to field.

In high frequency region, scattering center model describes electromagnetic characteristic of scattering.According to the model, when targeted attitude has During large change, it may occur that scattering center Range cell migration MTRC, i.e. partial dispersion center can be from a range cell movements To another range cell, cause target HRRP acute variation；And during posture generation small change, that is, occur without MTRC. As described above, HRRP is sensitive to targeted attitude, and the HRRP of same target has multimode distribution character, and this often makes data exist Distribution in HRRP spaces has nonlinear separability, this effect that have impact on conventional target identification method and application.HRRP is certainly Dynamic recognition methods is divided into three classes：Method based on template matches, the method based on compressed sensing and the side based on sorter model Method.Method based on template matches is to build a series of reference pictures i.e. template from marked training image, by test image Matched, be grouped into classification where most close template therewith, due to the template number and dimension one of storage respectively with template As it is larger, this method complexity is higher；Method based on compressed sensing built complete storehouse, calculated test sample in training sample Rarefaction representation in sheet, carries out Image Reconstruction and carries out Classification and Identification, but the discrimination of this method by reconstructed error minimum criteria It can largely decline due to the influence of noise in HRRP or shelter；Method based on sorter model is first to target Region section carries out feature extraction and obtains training sample set and test sample collection, is classified by being built with labelled training sample Device model simultaneously carries out parameter calculating, and then unlabeled test sample is input in sorter model and calculates category label, complete Into target identification, the target identification method based on sorter model has preferable robustness and higher discrimination.

In existing machine Learning Theory, principal component analysis (PCA), independent component analysis (ICA) factorial analysis (FA) Deng being all unsupervised feature extracting method, the feature extracted with these technologies is not necessarily adapted to the classification task of rear end；In order to Classification information is made full use of, the feature extracting method of a large amount of supervision classes is contemplated, representative method is linear to be differentiated Analyze (LDA), LDA maximizes between class distance of the sample after projection, while minimizing inter- object distance, can effectively carry The separability of high data.But, LDA highly relies on the distribution of data, which limits LDA application, for this problem, greatly Amount scholar proposes different solutions, wherein more representational have subclass discriminant analysis (SDA) method, this method will Initial data is divided into some subclasses, covariance matrix is modified in class, class, improves the scope of application of LDA methods, Although this kind of method obtains good effect on some data sets, this kind of method is two benches feature extraction side Method, is closely linked without the classification task with rear end, may result in classification loss of energy, is damaged in order to avoid this Lose [B.Chen, H.Zhang, X.Zhang et.al., Max-margin discriminant projection via data augmentation[J].IEEE Transactions on Knowledge and Data Engineering.2015,27 (7):1964-1976] article proposes MMLDP models, model joint Bayesian SVM, regard projection properties as hidden variable The input of SVM classifier, under the framework of Bayesian models, carries out combination learning, effectively to projector space and SVM classifier The performance loss that learning tape comes stage by stage is avoided, the discrimination of target is improved.

In the above method, either learn stage by stage or combination learning, the problem of they all have one jointly：It is this kind of Method belongs to global category feature extracting method, that is, is expected that by a global projection matrix, sample is realized in projector space It can divide.But this kind of method is for the data of Nonlinear separability, the especially data to multimode distributed architecture, because it have ignored Implicit structural information inside data, global projecting method may bring classification loss of energy, cause discrimination low.

The content of the invention

It is an object of the invention to overcome the shortcomings of that prior art is present, it is proposed that one kind is linear based on unlimited largest interval Differentiate the target identification method of the radar of projection model, it is low for solving discrimination present in existing radar target identification method Technical problem.

The present invention technical thought be：The data being distributed for multimode, MMLDP is incorporated into by the thought of Mixture of expert model A kind of unlimited maximum boundary linear discriminant projection model (infinite max-margin linear are proposed in model discriminant projection,iMMLDP).Specifically, IMMLDP is mixed by DP (Dirichlet Process) Data set is divided into ' unlimited ' individual subset by model, is learnt the MMLDP graders of a part in each subset, is combined each Local classifiers realize non-linear projection and the classification of the overall situation.In addition, IMMLDP by the division of data set, project subspace Practise and the study of grader be unified under the framework of Bayesian models, by error in classification come the division of guide data collection with The study of subspace is projected, the linear separability of each regional area is preferably ensure that.

According to above-mentioned technical thought, realize that the technical scheme that the object of the invention is taken comprises the following steps：

(1) power spectrum characteristic training sample set X category label collection ys corresponding with its is obtained：

(1a) radar receives N number of C classifications target High Range Resolution, obtains N number of High Range Resolution；

(1b) extracts the power spectrum characteristic of each High Range Resolution in N number of High Range Resolution, obtains power spectrum characteristic Training sample set X={ x₁,x₂,…,x_n,…,x_N, and the corresponding category labels of power spectrum characteristic training sample set X are passed through into class Other label set y is represented：Y={ y₁,y₂,…,y_n,…,y_N, N represents the total number of training sample, x_nRepresent n-th of sample, y_nTable Show the category label y of the n-th class sample_n∈{1,2,…,C}；

(2) unlimited largest interval linear discriminant projection model is built：By Di Li Cray process DP mixed models, projection model It is unified in hidden variable SVM classifier under Bayesian model frameworks, obtains unlimited largest interval linear discriminant projection model；

(3) the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint is defined, its expression formula is：

Wherein, ω_cC class classifier parameters are represented, N (0, β is obeyed in distribution_c ^-1I), grader hyper parameter β_c~Ga (a₀, b₀), c ∈ { 1,2 ..., D }, D represents initial total cluster number；A_c=[a_c1,a_c2,…,a_ck..., a_cK] represent c class samples Projection matrix, c ∈ { 1,2 ..., D }, a_ckRepresent A_cKth rowκ_k~Ga (c₀,d₀), K represents A_cIt is total Columns；Z=[z₁,z₂,…,z_n,…,z_N] the feature samples collection that sample set X is obtained after projection is represented, while being also hidden change Measure the input of SVM classifier, z_nRepresent n-th of sample x_nThe feature samples obtained after projection, z_nInitial distribution be N (A^Τ x_n,Ι)；{μ_c, ∑_cRepresent c class samples distributed constant, μ_cRepresent the average of c class samples, ∑_cRepresent c class samples Covariance matrix, c classes cluster distributed constant { μ_c,Σ_cInitial distribution be Normal-Wishart distribution, i.e. { μ_c,Σ_c} ~NW ({ μ_c,Σ_c}|μ₀,W₀,ν₀,β₀), wherein μ₀,W₀,ν₀,β₀For initial distribution parameter；H=[h₁,h₂,…,h_n,…,h_N] table Show cluster indicator variable collection, h_nRepresent training sample x_nWhich kind of belongs to, h_n∈{1,2,…,D}；υ=[υ₁,υ₂,…,υ_c,…, υ_C] represent based on Stick-breaking construct Di Li Cray process DP mixed models parameter, υ be distributed as Beta (1, α), α is distributed as Ga (e₀,f₀)；X represents training sample, and y represents the corresponding category label of training sample；N () represents Gauss Distribution, Ga () represent that Gamma distributions, NW () represent Normal-Wishart distributions, ()^TRepresent transposition operation；

(4) parameters in the expression formula of the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint are set Initial value：

Set c class classifier parameters ω_cInitial value for one obey N (0,1) distribution K+1 dimension random matrix, C class classifier parameters ω_cCovariance precision β initial value is obedience Ga (10³, 1) distribution random vector, c classes sample throw Shadow matrix A_cInitial value be the corresponding characteristic vectors of characteristic value big K before training sample set X covariance matrix, feature sample This collection Z initial value is the random matrix of a K × N-dimensional for obeying N (0,1) distributions, c class distributed constants { μ_c,Σ_cJust Initial value is one and obeys Normal-Wishart distribution NW ({ μ_c,Σ_c}|μ₀,W₀,ν₀,β₀) random matrix, wherein μ₀=0, W₀ =10^-5I,ν₀=K+1, β₀=10^-3, the parameter υ of Di Li Cray process DP mixed models initial distribution is that Beta (1,1) sets poly- It is an obedience Ga (1,10 to collect the initial value of parameter alpha^-10) distribution random number；

(5) the unlimited pseudo- Posterior distrbutionp expression formula of largest interval linear discriminant projection model joint is representedThe Condition Posterior Distribution of parameters：C class classifier parameters ω_cCondition after Test distribution p (ω_c| -), c class sample projection matrixes A_cKth row a_c,kCondition Posterior Distribution p (a_c,k| -), feature samples collection Z N-th of sample row k z_k,nCondition Posterior Distribution p (z_k,n| -), c class distributed constants { μ_c,Σ_cCondition Posterior Distribution p ({μ_c,Σ_c| -), cluster indicator variable h Condition Posterior Distribution p (h | -), the parameter υ of Di Li Cray process DP mixed models Condition Posterior Distribution p (υ | -)；

(6) Condition Posterior Distribution of the parameters represented to step (5) is sampled：According to the Gibbs method of samplings, The pseudo- Posterior distrbutionp expression formula of unlimited largest interval linear discriminant projection model joint represented to step (5)The Condition Posterior Distribution of parameters, carries out I successively₀Secondary circulating sampling, wherein I₀ For natural number, from I₀+ 1 beginning is at interval of S_PParameter ω in the secondary each projection subspace of preservation_c,A_c, distributed constantSampled result, and preserve T₀The sampled result of subparameter；

(7) power spectrum characteristic test sample collection is obtainedCategory of test label set corresponding with its

(7a) radar is receivedIndividual C classifications target High Range Resolution, is obtainedIndividual High Range Resolution；

(7b) is extractedThe power spectrum characteristic of each High Range Resolution, obtains power spectrum characteristic in individual High Range Resolution Test sample collectionAnd by test sample collectionCorresponding category label passes through category of test mark Number collectionRepresent：Wherein,The total number of test sample is represented,N-th of sample is represented,Table Show the category label of the n-th class sample

(8) discrimination of radar target is obtained：

(8a) is using cluster indicator variable h_nTo test sample collectionClustered, and cluster result is passed through into c class samples This projection matrix A_cIn the projection subspace for projecting to unlimited largest interval linear discriminant projection model, test feature sample is obtained CollectionWherein, test feature sample setIn include multiple subsets；

The c class classifier parameters ω that (8b) passes through preservation_cSampled result, to test feature sample setClassified, Obtain test sample collectionCategory label collection

(8c) is by category of test label setWith test sample collectionCategory label collectionIt is compared, obtains radar mesh Target discrimination.

The present invention compared with prior art, with advantages below：

1) HRRP Radar High Range Resolution data sets are divided into ' unlimited ' individual subset by the present invention by DP processes, every One MMLDP model of study inside individual subset, due to clustering and classification is combination learning, thus can effective mining data In hide linear structure.Compared with the target identification technology of existing radar, the discrimination of radar target, especially target are improved In the case of with multimode distribution character, effect is more obvious.

2) study of the division of data set, projection subspace and SVM classifier is unified in Bayesian frame by the present invention Under frame, combination learning is carried out, it is to avoid the classification performance loss that two phase classification method is brought.Simultaneously subset in each respectively Learn simple projection model and grader, individually one projection model of training and the classification on whole data set with prior art Device is compared, and reduces the complexity of model.

Brief description of the drawings

Fig. 1 is implementation process figure of the invention；

Represent the flow entirely tested.

Fig. 2 is cluster posteriority quantity result in measured data experiment.

Embodiment (technical scheme is explained and illustrated)

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail：

Reference picture 1, based on the radar target identification method of unlimited largest interval linear discriminant projection model, including following step Suddenly：

Step (1) obtains power spectrum characteristic training sample set X category label collection ys corresponding with its：

(1a) radar receives 600 3 classification target High Range Resolutions, obtains 600 High Range Resolutions.

(1b) extracts the power spectrum characteristic of each High Range Resolution in 600 High Range Resolutions, obtains power spectrum special Levy training sample set X={ x₁,x₂,…,x_n,…,x_N, and the corresponding category labels of power spectrum characteristic training sample set X are passed through Category label collection y is represented：Y={ y₁,y₂,…,y_n,…,y_N, x_nRepresent n-th of sample, y_nRepresent the classification mark of the n-th class sample Number y_n∈{1,2,3}。

Step (2) builds unlimited largest interval linear discriminant projection model, realizes that step is：

(2a) represents the Di Li Cray process DP mixed models constructed based on Stick-breaking：

υ_c| α~Beta (1, α), θ_c|G₀~G₀, c=1,2 ..., ∞

h_n| π (υ)~Mult (π (υ)), x_n|h_n=c；θ_c~p (x | θ_c), n=1 ..., N

Wherein, υ_cTo cut rod scale parameter,Represent to cut rod length every time, α is υ_cPriori Profile parameter~Ga (e₀,f₀)；θ_cRepresent x_nDistributed constant, θ_cBe distributed as G₀, G₀Base distribution is represented, if base is distributed as Normal-Wishart is distributed, i.e. G₀~NW ({ μ_c,Σ_c}|μ₀,W₀,ν₀,β₀)；h_nIt is x_nIndicator, work as h_nRepresented during=c x_nBelong to c classes i.e. x_n~p (x | θ_c)。

(2b) represents the projection model in each cluster：

Projection model based on MMLDP models can be expressed as：z_n~N (A^Τx_n,I),κ_k~Ga (c₀, d₀), wherein, A represents global projection matrix A=[a₁,a₂,…,a_k], a_kRepresent A kth row, x_nRepresent n-th of sample, κ_kFor a_k Prior distribution parameter, c₀And d₀For κ_kThe hyper parameter of parameter.

Then the projection model in each cluster can be expressed as：

z_n|h_n=c, A_c~N (A_c ^Τx_n,I_p),A_c=[a_c1,a_c2..., a_ck..., a_cK]

Wherein, as cluster indicator variable h_nWhen equal to c, z_nIt is A just to obey average_c ^Τx_n, covariance matrix is I_pJust State is distributed, and p represents unit matrix I dimension.

(2c) represents the model of hidden variable SVM classifier in each cluster：

Set c-th hidden variable SVM classifier parameter obey prior distribution asWill be each hidden The prior distribution of variable SVM classifier is brought into each hidden variable SVM classifier respectively, obtains hidden variable point in each cluster The model of class device, can be expressed as：

Wherein, λ=[λ₁,λ₂,…,λ_c..., λ_C] represent hidden variable SVM classifier in hidden variable, λ_cRepresent c-th it is hidden Hidden variable in variable SVM classifier.

Di Li Cray process DP mixed models, projection model and hidden variable SVM classifier are unified in Bayesian by (2d) Under model framework, unlimited largest interval linear discriminant projection model is obtained, its hierarchical structure formula is：

h_n| π (υ)~Disc (π (υ))

x_n|h_n=c, { μ_c,Σ_c}~p (x_n|{μ_c,Σ_c), n=1 ..., N.

y_n,{λ_n}_c|{z_n,h_n=c }, ω_c~φ (y_n,λ_n|ω_c,z_n), c=1 ..., ∞

{μ_c,Σ_c}~NW (μ₀,W₀,ν₀,β₀)

Wherein, according to the stratification expression formula of above formula, n-th of sample x is obtained_nLikelihood distribution function：

Step (3) defines the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint, its specific manifestation form For：

Each in the expression formula of the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint of step (4) setting is joined Several initial values：

Set c class classifier parameters ω_cInitial value for one obey N (0,1) distribution K+1 dimension random matrix, C class classifier parameters ω_cCovariance precision β initial value is obedience Ga (10³, 1) distribution random vector, c classes sample throw Shadow matrix A_cInitial value be the corresponding characteristic vectors of characteristic value big K before training sample set X covariance matrix, feature sample This collection Z initial value is the random matrix of a K × N-dimensional for obeying N (0,1) distributions, c class distributed constants { μ_c,Σ_cJust Initial value is one and obeys Normal-Wishart distribution NW ({ μ_c,Σ_c}|μ₀,W₀,ν₀,β₀) random matrix, wherein μ₀=0, W₀ =10^-5I,ν₀=K+1, β₀=10^-3, the parameter υ of Di Li Cray process DP mixed models initial distribution is that Beta (1,1) sets poly- It is an obedience Ga (1,10 to collect the initial value of parameter alpha^-10) distribution random number.

Step (5) represents the unlimited pseudo- Posterior distrbutionp expression formula of largest interval linear discriminant projection model jointThe Condition Posterior Distribution of parameters, realizes that step is：

(5a) represents c class classifier parameters ω_cCondition Posterior Distribution, its form of expression is：

Wherein：

β_cFor the hyper parameter of c class graders.

(5b) represents c class sample projection matrixes A_cKth row a_c,kCondition Posterior Distribution, its form of expression

For：

Wherein：

x_nRefer to c class samples, κ_c,kRepresent a_c,kParameter inside prior distribution, κ_ck~Ga (c₀,d₀)。

(5c) represents the row k z of feature samples collection Z n-th of sample_k,nCondition Posterior Distribution, its form of expression is：

Wherein：

Wherein WithThe average and covariance matrix of difference respective conditions Posterior distrbutionp.

(5d) represents the distributed constant { μ of c class samples_c,Σ_cCondition Posterior Distribution, its form of expression is：

Wherein：

υ'_c=υ₀+N_c

β_c'=β₀+N_c

N_cThe quantity of c class samples is represented,The average of c class samples is represented,Represent the covariance square of c class samples The average of battle array.

(5e) represents the Condition Posterior Distribution of cluster indicator variable, and its form of expression is：

P (h | -)=Disc (h；π)

And π_cSubmit to restraint for

(5f) represents υ Condition Posterior Distribution, and its form of expression is：

p(υ_c|-)∝p(h|υ)Beta(υ_c；1, α)~Beta (υ_c；ρ_a,ρ_b)

Wherein ρ_a=1+N_c,N_kRepresent the quantity of kth class sample.

(5g) represents the hidden variable λ of hidden variable SVM classifier_nCondition Posterior Distribution, its form of expression is：

Wherein IG () represents dead wind area.

(5h) represents β_cCondition Posterior Distribution, its form of expression is：

Wherein

(5i) represents κ_c,kCondition Posterior Distribution, its form of expression is：

Wherein

(5j) represents α Condition Posterior Distribution, and its form of expression is：

Wherein e'₀=e₀+ D-1,

(6) Condition Posterior Distribution of the parameters represented to step (5) is sampled：According to the Gibbs method of samplings, The pseudo- Posterior distrbutionp expression formula of unlimited largest interval linear discriminant projection model joint represented to step (5)The Condition Posterior Distribution of parameters, carries out 400 circulating samplings successively, from the 401 beginnings preserve each parameter ω projected in subspace at interval of 10 times_c,A_c, distributed constantSampled result, And preserve the sampled result of 10 subparameters.

Step (7) obtains power spectrum characteristic test sample collectionCategory of test label set corresponding with its

(7a) radar receives 2400 3 classification target High Range Resolutions, obtains 2400 High Range Resolutions.

(7b) extracts the power spectrum characteristic of each High Range Resolution in 2400 High Range Resolutions, obtains power spectrum special Levy test sample collectionAnd by test sample collectionCorresponding category label passes through category of test Label setRepresent：Wherein,N-th of sample is represented,Represent the classification mark of the n-th class sample Number

(8) discrimination of radar target is obtained：

(8a) is using cluster indicator variable h_nTo test sample collectionClustered, and cluster result is passed through into c class samples Projection matrix A_cIn the projection subspace for projecting to unlimited largest interval linear discriminant projection model, test feature sample set is obtainedWherein, test feature sample setIn include multiple subsets；Cluster indicator variable h_nDetermineSub-set size and quantity, h_n Expression formula is as follows：

p(h_n| -)=Disc (h_n；π) and

The c class classifier parameters ω that step (8b) passes through preservation_cSampled result, to test feature sample setCarry out Classification, obtains test sample collectionCategory label collectionRealize that step is：

ρ=[ρ₁,ρ₂,...,ρ_c,...,ρ_D]

Wherein,Represent the weight coefficient of hidden variable SVM classifier in c-th of cluster of the t times sampling, m=1,2,3, t =1,2 ..., 10, ρ_cThe average output of c-th of hidden variable SVM classifier is represented,Represent to solve maximum correspondence M values.

(8c) is by category of test label setWith test sample collectionCategory label collectionIt is compared, obtains radar target Discrimination.

Tested below in conjunction with emulation experiment and measured data, the technique effect of the present invention is elaborated：

1. emulation experiment

(1) experiment condition

The data set that this experiment is used is the Benchmark data from UCI Machine Learning Repository Collection, therefrom have chosen tri- more complicated data sets of Heart, Splice, Twonorm.

(2) experiment content and interpretation of result

This experiment using input of the initial data as model, using LDA+SVM, MMLDP, k-mean+MMLDP and Tetra- methods of IMMLDP are classified, recognized that this experiment is repeated 10 times per class method, and each method is randomly selected to data set 50% as training sample, remaining to do test sample.The average recognition performance of 10 times is taken to make under different latent space dimensions For final discrimination, by each method, optimal identification rate is listed in table 1 under different latent space dimensions.

Table 1, discrimination of the distinct methods in different pieces of information

It may be seen that classification performances of the IMMLDP on different pieces of information collection is better than other method from table 1. IMMLDP models show compared with MMLDP Model Identification rates, and data are first clustered, and learn a projection model in each cluster It is better than global projection model method.IMMLDP models show that IMMLDP will be clustered, divided compared with Km+MMLDP Model Identification rates Class device and projection carry out combination learning, disclose the implicit structure of data, thus obtain being obviously improved for recognition performance.

2 measured datas are tested

(1) experiment condition

The present invention is handled the actual measurement HRRP data of three class Aircraft Targets using wave band c radar.Returned using the norm of mould 2 One method eliminates HRRP amplitude sensitive, and extracts its power spectrum characteristic and eliminate its and translate sensitiveness, i.e., we obtain Sample data set is HRRP power spectrum characteristic, in experiment, and section rod upper limit that we take is set to 10.

(2) experiment content and interpretation of result

600 power spectrum characteristics are chosen as training sample, 2400 power spectrum characteristics are hidden in 3-dimensional as test sample Under the dimension in space, result is identified as shown in table 2.

Table 2, IMMLDP is clustered and performance evaluation in Radar High Range Resolution

The cluster posteriority quantity that IMMLDP is obtained is as shown in Figure 2, it can be seen that effective number of clusters is three classes, from table 2 We can see that each intra-cluster obtains preferable nicety of grading, this, which has benefited from us, will cluster subspace and classification Device carries out combination learning, it is ensured that good classification performance in each cluster, so as to realize the lifting of global classification performance, improves To the discrimination of radar target.

Claims

1. a kind of radar target identification method based on unlimited largest interval linear discriminant projection model, comprises the following steps：

(1b) extracts the power spectrum characteristic of each High Range Resolution in N number of High Range Resolution, obtains power spectrum characteristic training Sample set X={ x₁,x₂,…,x_n,…,x_N, and the corresponding category labels of power spectrum characteristic training sample set X are passed through into classification mark Number collection y represent：Y={ y₁,y₂,…,y_n,…,y_N, N represents the total number of training sample, x_nRepresent n-th of sample, y_nRepresent the The category label y of n class samples_n∈{1,2,…,C}；

(2) unlimited largest interval linear discriminant projection model is built：By Di Li Cray process DP mixed models, projection model and hidden Variable SVM classifier is unified under Bayesian model frameworks, obtains unlimited largest interval linear discriminant projection model；

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Wherein, ω_cC class classifier parameters are represented, distribution is obeyedGrader hyper parameter β_c~Ga (a₀,b₀), c ∈ { 1,2 ..., D }, D represent initial total cluster number；A_c=[a_c1,a_c2,…,a_ck..., a_cK] represent c class samples projection Matrix, c ∈ { 1,2 ..., D }, a_ckRepresent A_cKth rowκ_k~Ga (c₀,d₀), K represents A_cTotal columns； Z=[z₁,z₂,…,z_n,…,z_N] the feature samples collection that sample set X is obtained after projection is represented, while being also hidden variable SVM The input of grader, z_nRepresent n-th of sample x_nThe feature samples obtained after projection, z_nInitial distribution be N (A^Τx_n, Ι)；{μ_c, ∑_cRepresent c class samples distributed constant, μ_cRepresent the average of c class samples, ∑_cRepresent the association of c class samples Variance matrix, c classes cluster distributed constant { μ_c,Σ_cInitial distribution be Normal-Wishart distribution, i.e. { μ_c,Σ_c}~ NW({μ_c,Σ_c}|μ₀,W₀,ν₀,β₀), wherein μ₀,W₀,ν₀,β₀For initial distribution parameter；H=[h₁,h₂,…,h_n,…,h_N] represent Cluster indicator variable collection, h_nRepresent training sample x_nWhich kind of belongs to, h_n∈{1,2,…,D}；υ=[υ₁,υ₂,…,υ_c,…,υ_C] The parameter based on the Stick-breaking Di Li Cray process DP mixed models constructed is represented, υ's is distributed as Beta (1, α), α Be distributed as Ga (e₀,f₀)；X represents training sample, and y represents the corresponding category label of training sample；N () expressions Gaussian Profile, Ga () represents that Gamma distributions, NW () represent Normal-Wishart distributions, ()^TRepresent transposition operation；

(4) the initial of parameters in the expression formula of the pseudo- Posterior distrbutionp of unlimited largest interval linear discriminant projection model joint is set Value：

Set c class classifier parameters ω_cInitial value for one obey N (0,1) distribution K+1 dimension random matrix, c classes Classifier parameters ω_cCovariance precision β initial value is obedience Ga (10³, 1) distribution random vector, c classes sample projection square Battle array A_cInitial value be the corresponding characteristic vectors of characteristic value big K before training sample set X covariance matrix, feature samples collection Z initial value is the random matrix of a K × N-dimensional for obeying N (0,1) distributions, c class distributed constants { μ_c,Σ_cInitial value Normal-Wishart distribution NW ({ μ c, Σ are obeyed for one_c}|μ₀,W₀,ν₀,β₀) random matrix, wherein μ₀=0, W₀=10^-5I,ν₀=K+1, β₀=10^-3, the parameter υ of Di Li Cray process DP mixed models initial distribution sets for Beta (1,1) assembles ginseng Number α initial value is an obedience Ga (1,10^-10) distribution random number；

(6) Condition Posterior Distribution of the parameters represented to step (5) is sampled：According to the Gibbs method of samplings, to step Suddenly the pseudo- Posterior distrbutionp expression formula of unlimited largest interval linear discriminant projection model joint that (5) are representedThe Condition Posterior Distribution of parameters, carries out I successively₀Secondary circulating sampling, wherein I₀ For natural number, from I₀+ 1 beginning is at interval of S_PParameter ω in the secondary each projection subspace of preservation_c,A_c, distributed constantSampled result, and preserve T₀The sampled result of subparameter；

(7b) is extractedThe power spectrum characteristic of each High Range Resolution in individual High Range Resolution, obtains power spectrum characteristic test Sample setAnd by test sample collectionCorresponding category label passes through category of test label set Represent：Wherein,The total number of test sample is represented,N-th of sample is represented,Represent n-th The category label of class sample

(8) discrimination of radar target is obtained：

(8a) is using cluster indicator variable h_nTo test sample collectionClustered, and cluster result is projected by c classes sample Matrix A_cIn the projection subspace for projecting to unlimited largest interval linear discriminant projection model, test feature sample set is obtainedIts In, test feature sample setIn include multiple subsets；

The c class classifier parameters ω that (8b) passes through preservation_cSampled result, to test feature sample setClassified, obtained Test sample collectionCategory label collection

(8c) is by category of test label setWith test sample collectionCategory label collectionIt is compared, obtains the knowledge of radar target Not other rate.

2. the radar target identification method according to claim 1 based on unlimited largest interval linear discriminant projection model, Characterized in that, the unlimited largest interval linear discriminant projection model of structure described in step (2), realizes that step is：

υ_c| α~Beta (1, α), θ_c|G₀~G₀, c=1,2 ..., ∞

h_n| π (υ)~Mult (π (υ)), x_n|h_n=c；θ_c~p (x | θ_c), n=1 ..., N

Wherein, υ_cTo cut rod scale parameter,Represent to cut rod length every time, α is υ_cPrior distribution Parameter alpha~Ga (e₀,f₀)；θ_cRepresent x_nDistributed constant, θ_cBe distributed as G₀, G₀Base distribution is represented, if base is distributed as Normal- Wishart is distributed, i.e. G₀~NW ({ μ_c,Σ_c}|μ₀,W₀,ν₀,β₀)；h_nIt is x_nIndicator, work as h_nX is represented during=c_nBelong to C classes, i.e. x_n~p (x | θ_c)；

(2b) represents the projection model in each cluster：

Projection model based on MMLDP models can be expressed as：z_n~N (A^Τx_n,I), Wherein, A represents global projection matrix A=[a₁,a₂,…,a_k], a_kRepresent A kth row, x_nRepresent n-th of sample, κ_kFor a_k's Prior distribution parameter, c₀And d₀For κ_kThe hyper parameter of parameter；

Then the projection model in each cluster can be expressed as：

z_n|h_n=c, A_c~N (A_c ^Τx_n,I_p),A_c=[a_c1,a_c2..., a_ck..., a_cK]

<mrow> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mi>k</mi> </mrow> </msub> <mo>~</mo> <mi>N</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&kappa;</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&kappa;</mi> <mi>k</mi> </msub> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>

Wherein, as cluster indicator variable h_nWhen equal to c, z_nIt is A just to obey average_c ^Τx_n, covariance matrix is I_pNormal state point Cloth, p represents unit matrix I dimension；

(2c) represents the model of hidden variable SVM classifier in each cluster：

Set c-th hidden variable SVM classifier parameter obey prior distribution asBy each hidden variable The prior distribution of SVM classifier is brought into each hidden variable SVM classifier respectively, obtains hidden variable grader in each cluster Model, can be expressed as：

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>~</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>|</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&beta;</mi> <mi>c</mi> </msub> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>,</mo> <mi>&lambda;</mi> <mo>,</mo> <msub> <mi>&beta;</mi> <mi>c</mi> </msub> <mo>|</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>&Proportional;</mo> <munderover> <mo>&Pi;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>&lambda;</mi> <mi>n</mi> </msub> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>|</mo> <msub> <mi>&beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>&beta;</mi> <mi>c</mi> </msub> <mo>|</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>

<mrow> <mo>&Proportional;</mo> <munderover> <mo>&Pi;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>&lambda;</mi> <mi>n</mi> <mrow> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mi>n</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>(</mo> <mrow> <msup> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mi>T</mi> </msup> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>+</mo> <mi>b</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msub> <mi>&lambda;</mi> <mi>n</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>|</mo> <mn>0</mn> <mo>,</mo> <msup> <msub> <mi>&beta;</mi> <mi>c</mi> </msub> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>I</mi> <mo>)</mo> </mrow> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>

Wherein, λ=[λ₁,λ₂,…,λ_c..., λ_C] represent hidden variable SVM classifier in hidden variable, λ_cRepresent c-th of hidden variable Hidden variable in SVM classifier；

Di Li Cray process DP mixed models, projection model and hidden variable SVM classifier are unified in Bayesian models by (2d) Under framework, unlimited largest interval linear discriminant projection model is obtained, its hierarchical structure formula is：

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&upsi;</mi> <mi>c</mi> </msub> <mo>|</mo> <mi>&alpha;</mi> <mo>~</mo> <mi>B</mi> <mi>e</mi> <mi>t</mi> <mi>a</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mo>;</mo> <mi>&alpha;</mi> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>e</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&pi;</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>&upsi;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&upsi;</mi> <mi>c</mi> </msub> <munderover> <mo>&Pi;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>c</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&upsi;</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>

h_n| π (υ)~Disc (π (υ))

x_n|h_n=c, { μ_c,Σ_c}~p (x_n|{μ_c,Σ_c), n=1 ..., N.

y_n,{λ_n}_c|{z_n,h_n=c }, ω_c~φ (y_n,λ_n|ω_c,z_n), c=1 ..., ∞

<mrow> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>~</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>|</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>&beta;</mi> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mi>m</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>~</mo> <mi>N</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&kappa;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&kappa;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mi>m</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>

{μ_c,Σ_c}~NW (μ₀,W₀,ν₀,β₀)

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>|</mo> <mo>{</mo> <msub> <mi>&mu;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <mi>c</mi> </msub> <mo>}</mo> <mo>,</mo> <mi>&pi;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>c</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <msub> <mi>&pi;</mi> <mi>c</mi> </msub> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>;</mo> <msub> <mi>&mu;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

3. the radar target identification method according to claim 1 based on unlimited largest interval linear discriminant projection model, Characterized in that, the unlimited pseudo- Posterior distrbutionp of largest interval linear discriminant projection model joint of definition described in step (3), it has The body form of expression is：

<mrow> <mtable> <mtr> <mtd> <mrow> <mo>&Proportional;</mo> <munderover> <mi>&Pi;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>&lsqb;</mo> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>|</mo> <mrow> <mo>{</mo> <mrow> <msub> <mi>&mu;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <mi>c</mi> </msub> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <msub> <mi>h</mi> <mi>n</mi> </msub> <mo>=</mo> <mi>c</mi> </mrow> <mo>)</mo> </mrow> <mi>&phi;</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>&lambda;</mi> <mi>n</mi> </msub> <mo>|</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> </mrow> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>|</mo> <msubsup> <mi>A</mi> <mi>c</mi> <mi>T</mi> </msubsup> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>,</mo> <mi>I</mi> </mrow> <mo>)</mo> </mrow> <mi>p</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>h</mi> <mi>n</mi> </msub> <mo>=</mo> <mi>c</mi> <mo>|</mo> <mi>&upsi;</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&times;</mo> <munderover> <mi>&Pi;</mi> <mrow> <mi>c</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <mi>N</mi> <mi>W</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>{</mo> <mrow> <msub> <mi>&mu;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <mi>c</mi> </msub> </mrow> <mo>}</mo> </mrow> <mo>|</mo> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&nu;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&beta;</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> <munderover> <mi>&Pi;</mi> <mrow> <mi>c</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <mrow> <mo>&lsqb;</mo> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>|</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> </mrow> <mo>)</mo> </mrow> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&beta;</mi> <mi>c</mi> </msub> <mo>|</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&times;</mo> <munderover> <mi>&Pi;</mi> <mrow> <mi>c</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <munderover> <mi>&Pi;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <mrow> <mo>&lsqb;</mo> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>|</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&kappa;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> </mrow> <mo>)</mo> </mrow> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&kappa;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&rsqb;</mo> </mrow> <munderover> <mi>&Pi;</mi> <mrow> <mi>c</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <mi>b</mi> <mi>e</mi> <mi>t</mi> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>&upsi;</mi> <mi>c</mi> </msub> <mo>|</mo> <mn>1</mn> <mo>,</mo> <mi>&alpha;</mi> </mrow> <mo>)</mo> </mrow> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <mrow> <mi>&alpha;</mi> <mo>|</mo> <msub> <mi>e</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>.</mo> </mrow> 3

4. the target identification method based on unlimited largest interval linear discriminant projection model according to claims 1, Characterized in that, the pseudo- Posterior distrbutionp expression of the unlimited largest interval linear discriminant projection model joint of expression described in step (5) FormulaThe Condition Posterior Distribution of parameters, realizes that step is：

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>;</mo> <msub> <mi>&mu;</mi> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> </msub> <mo>)</mo> </mrow> </mrow>

Wherein：

β_cFor the hyper parameter of c class graders；

(5b) represents c class sample projection matrixes A_cKth row a_c,kCondition Posterior Distribution, its form of expression is：

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>&mu;</mi> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </msub> <mo>)</mo> </mrow> </mrow>

Wherein：

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&mu;</mi> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </msub> <mo>=</mo> <msub> <mi>&Sigma;</mi> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </msub> <munder> <mo>&Sigma;</mo> <mrow> <msub> <mi>&tau;</mi> <mi>n</mi> </msub> <mo>=</mo> <mi>c</mi> </mrow> </munder> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msub> <mi>x</mi> <mi>n</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&Sigma;</mi> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <munder> <mi>&Sigma;</mi> <mrow> <msub> <mi>&tau;</mi> <mi>n</mi> </msub> <mo>=</mo> <mi>c</mi> </mrow> </munder> <msub> <mi>x</mi> <mi>n</mi> </msub> <msubsup> <mi>x</mi> <mi>n</mi> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>&kappa;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mi>I</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>

x_nRefer to c class samples, κ_c,kRepresent a_c,kParameter inside prior distribution, κ_ck~Ga (c₀,d₀)；

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>u</mi> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <msub> <mi>z</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </msub> <mo>)</mo> </mrow> </mrow>

Wherein：

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&Sigma;</mi> <msub> <mi>z</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msubsup> <mi>&omega;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> <mn>2</mn> </msubsup> <msub> <mi>&lambda;</mi> <mi>n</mi> </msub> </mfrac> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&mu;</mi> <msub> <mi>z</mi> <mrow> <mi>n</mi> <mi>k</mi> <mo>,</mo> </mrow> </msub> </msub> <mo>=</mo> <msub> <mi>&Sigma;</mi> <msub> <mi>z</mi> <mrow> <mi>n</mi> <mi>k</mi> <mo>,</mo> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>T</mi> </msubsup> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <msub> <mi>&omega;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <msubsup> <mi>&xi;</mi> <mi>n</mi> <mrow> <mo>-</mo> <mi>k</mi> </mrow> </msubsup> <msub> <mi>&lambda;</mi> <mi>n</mi> </msub> </mfrac> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>

Wherein WithThe average and covariance matrix of difference respective conditions Posterior distrbutionp；

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <mo>{</mo> <msub> <mi>&mu;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <mi>c</mi> </msub> <mo>}</mo> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>&Proportional;</mo> <munder> <mo>&Pi;</mo> <mrow> <msub> <mi>&tau;</mi> <mi>n</mi> </msub> <mo>=</mo> <mi>c</mi> </mrow> </munder> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>|</mo> <mo>{</mo> <msub> <mi>&mu;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <mi>c</mi> </msub> <mo>}</mo> <mo>)</mo> </mrow> <mi>N</mi> <mi>W</mi> <mrow> <mo>(</mo> <mo>{</mo> <msub> <mi>&mu;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>&Sigma;</mi> <mi>c</mi> </msub> <mo>}</mo> <mo>|</mo> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&nu;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&beta;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>~</mo> <mi>N</mi> <mi>W</mi> <mrow> <mo>(</mo> <msubsup> <mi>&mu;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>W</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>&upsi;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> </mrow>

Wherein：

<mrow> <msubsup> <mi>&mu;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>N</mi> <mi>c</mi> </msub> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&beta;</mi> <mn>0</mn> </msub> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> </mrow>

<mrow> <msubsup> <mi>W</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>W</mi> <mn>0</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>N</mi> <mi>c</mi> </msub> <msub> <mover> <mi>&Sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>N</mi> <mi>c</mi> </msub> <msub> <mi>&beta;</mi> <mn>0</mn> </msub> <mo>(</mo> <mrow> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>c</mi> </msub> </mrow> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>/</mo> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow>

<mrow> <msubsup> <mi>&upsi;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>&upsi;</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mi>c</mi> </msub> </mrow>

<mrow> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mo>&prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>&beta;</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mi>c</mi> </msub> </mrow>

N_cThe quantity of c class samples is represented,The average of c class samples is represented,Represent the covariance matrix of c class samples Average；

P (h | -)=Disc (h；π)

And π_cSubmit to restraint for

p(υ_c|-)∝p(h|υ)Beta(υ_c；1, α)~Beta (υ_c；ρ_a,ρ_b)

Wherein ρ_a=1+N_c,N_kRepresent the quantity of kth class sample；

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msubsup> <mi>&lambda;</mi> <mi>n</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>=</mo> <mi>I</mi> <mi>G</mi> <mrow> <mo>(</mo> <mo>|</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <msubsup> <mi>&omega;</mi> <mi>c</mi> <mi>T</mi> </msubsup> <msub> <mi>z</mi> <mi>n</mi> </msub> <msup> <mo>|</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

Wherein IG () represents dead wind area；

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>&beta;</mi> <mi>c</mi> </msub> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>&Proportional;</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>c</mi> </msub> <mo>|</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&beta;</mi> <mi>c</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> <mo>)</mo> </mrow> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mn>0</mn> <mo>&prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>b</mi> <mn>0</mn> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> </mrow>

Wherein

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>&kappa;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>&Proportional;</mo> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>|</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&kappa;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>I</mi> <mo>)</mo> </mrow> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <msubsup> <mi>c</mi> <mn>0</mn> <mo>&prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>d</mi> <mn>0</mn> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> </mrow>

Wherein

<mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>|</mo> <mo>-</mo> <mo>)</mo> </mrow> <mo>&Proportional;</mo> <munderover> <mo>&Pi;</mo> <mrow> <mi>c</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>D</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>B</mi> <mi>e</mi> <mi>t</mi> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>&upsi;</mi> <mi>c</mi> </msub> <mo>;</mo> <mn>1</mn> <mo>,</mo> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>;</mo> <msub> <mi>e</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>~</mo> <mi>G</mi> <mi>a</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>;</mo> <msubsup> <mi>e</mi> <mn>0</mn> <mo>&prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>f</mi> <mn>0</mn> <mo>&prime;</mo> </msubsup> <mo>)</mo> </mrow> </mrow>

Wherein

5. the target identification method based on unlimited largest interval linear discriminant projection model according to claims 1, Characterized in that, described in step (8b) to test feature sample setClassified, obtain test sample collectionCategory label CollectionRealize that step is：

<mrow> <msub> <mi>&rho;</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mn>0</mn> </msub> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>T</mi> <mn>0</mn> </msub> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&omega;</mi> <mi>c</mi> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msubsup> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>n</mi> <mi>t</mi> </msubsup> </mrow>

ρ=[ρ₁,ρ₂,...,ρ_c,...,ρ_D]

Wherein,Represent test samplePrediction category label,Represent hidden variable SVM in c-th of cluster of the t times sampling The weight coefficient of grader, m=1,2 ..., C, t=1,2 ..., T₀, ρ_cRepresent the average defeated of c-th hidden variable SVM classifier Go out,Represent to solve the corresponding m values of maximum.