CN106951921B - SAR target identification method based on Bayes's Multiple Kernel Learning support vector machines - Google Patents
SAR target identification method based on Bayes's Multiple Kernel Learning support vector machines Download PDFInfo
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Abstract
The invention discloses a kind of SAR target identification methods based on Bayes's Multiple Kernel Learning support vector machines, mainly solve the problems, such as existing target identification method to SAR image target identification inaccuracy.Implementation step are as follows: 1) input original SAR image and pre-process, calculate the nuclear matrix of different characteristic；2) nuclear matrix is combined according to Multiple Kernel Learning method；3) Bayes's Multiple Kernel Learning supporting vector machine model is established to support vector machines according to combined nuclear matrix；4) Bayes's Multiple Kernel Learning supporting vector machine model is solved using expectation-maximization algorithm, obtains optimal solution；5) target identification is carried out to SAR image test data using optimal solution.The present invention has been effectively combined the deduction ability of bayes method and the separating capacity of Multiple Kernel Learning method, improves recognition performance, can be used for the classification to SAR image.
Description
Technical field
The invention belongs to Technology of Radar Target Identification field, in particular to a kind of SAR target identification method can be used for SAR
The classification of image.
Background technique
Synthetic aperture radar SAR is a kind of active sensor perceived using microwave, is imaged not by objective factor
Such as illumination, the influence of weather, can with round-the-clock, it is round-the-clock target is monitored, no matter in civil field or in military affairs
Field all has very high utility value.It include also a large amount of clutter, in addition in SAR image in SAR image in addition to comprising target
It include also a large amount of coherent spot, this makes detection, identification and identification to SAR image become very difficult；In addition, due to SAR
The different complexity with local environment of the configuration of target, it is impossible to obtain the training sample under all situations.Therefore, how to improve
The recognition performance of SAR target is an important research direction in radar target recognition.
Mainly divide in SAR target identification method following several:
First is that the method based on template matching；
Second is that the method based on model；
Third is that the classification method based on rarefaction representation；
Fourth is that the method based on classifier design, such as k nearest neighbor classifier, neural network classifier, support vector machines etc..
The support vector machines, it is a kind of sorting algorithm based on Statistical Learning Theory, by introducing kernel function, ingeniously
Solves the problems, such as the inner product operation in higher dimensional space wonderfully, so that kernel support vectors machine is in small sample, non-linear and high-dimensional mould
Peculiar advantage is shown in formula identification problem.
It is this that classifier made of single data characteristics combination supporting vector machine is known as monokaryon Learning support vector machine, by
It is different with the ability of distinction in the similitude of different data characteristics characterization data, choose different data characteristicses, monokaryon
It practises supporting vector chance and shows entirely different classification performance, therefore, monokaryon Learning support vector machine is only capable of showing a certain
The characteristic of data characteristics cannot embody the relevance between each data characteristics, so that the classification performance of classifier is influenced, so that
Object recognition rate decline.
Summary of the invention
It is an object of the invention to problems in view of the above shortcomings of the prior art, propose a kind of based on Bayes's Multiple Kernel Learning
The SAR target identification method of support vector machines, to improve target identification performance.
The technical scheme of the present invention is realized as follows:
One, technical thought
The present invention combines Bayesian inference with Multiple Kernel Learning method, for the On The Choice of different data feature, draws
Enter Multiple Kernel Learning method, it has good generalization ability and stronger learning ability；Meanwhile branch is inferred with Bayesian inference
Hold the solution of vector machine primal problem.Its implementation is: firstly, pre-processing to original SAR image, obtaining image area, frequency
The three kinds of data characteristicses in domain and sparse coefficient and the nuclear matrix for calculating separately corresponding radial kernel function RBF；Again, using Multiple Kernel Learning
Three kinds of nuclear matrix are combined by algorithm；Finally, with the combination nuclear matrix reasoning Bayesian model of training data and obtaining optimal
Solution, and classify to the combination nuclear matrix of test data, implementation step includes the following:
(A) SAR image pre-treatment step:
A1 an original SAR image: I={ i) is inputtedmn| 1≤m≤M, 1≤n≤N }, wherein imnIndicate original SAR figure
The magnitude pixel value of picture, M indicate the line number of SAR image, and N indicates the columns of SAR image；
A2 binary segmentation) is carried out to original SAR image I, and calculates the mass center for obtaining SAR image
A3 original SAR image I) is subjected to circular shifting, makes mass centerIt is moved to the center of image, is matched
Quasi- image I1；
A4) to registration image I1Logarithmic transformation, median filtering and image interception are successively carried out, the image of SAR image is obtained
Characteristic of field I2, and by image characteristic of field I2Column vector；
A5) to registration image I1Image interception and two-dimension fourier transform are done, and zero-frequency is moved into picture centre, obtains frequency
Characteristic of field I3, and by frequency domain character I3Column vector；
A6) respectively to SAR image training set and test set repetitive process A1)~A4) obtain the training number of image characteristic of field
According to collection TtrWith test data set Tte；
A7) respectively to SAR image training set and test set repetitive process A1)~A5) obtain the training data of frequency domain character
Collect PtrWith test data set Pte；
A8) using KSVD algorithm to image characteristic of field training set TtrStudy, obtains dictionary D and and TtrCorresponding sparse system
Number feature training dataset Str, in conjunction with dictionary D and image area characteristic test data set Tte, it is calculated using OMP algorithm sparse
Coefficient characteristics test data set Ste；
(B) Multiple Kernel Learning step:
B1) using radial kernel function RBF, in conjunction with image characteristic of field training dataset TtrWith test data set Tte, calculate
To the nuclear matrix K of image characteristic of field training datasetttr(Ttr,Ttr) and image area characteristic test data set nuclear matrix Ktte(Ttr,
Tte)；
B2) using radial kernel function RBF, in conjunction with frequency domain character training dataset PtrWith test data set Pte, it is calculated
The nuclear matrix K of frequency domain character training datasetptr(Ptr,Ptr) and frequency domain character test data set nuclear matrix Kpte(Ptr,Pte)；
B3) using radial kernel function RBF, in conjunction with sparse coefficient feature training dataset StrWith test data set Ste, calculate
Obtain the nuclear matrix K of sparse coefficient feature training datasetstr(Str,Str) and sparse coefficient characteristic test data set nuclear matrix
Kste(Str,Ste)；
B4) combine step B1)~B3) in the training set nuclear matrix and test set nuclear matrix of the three kinds of features that are calculated,
The combination nuclear matrix K for obtaining SAR image training set is calculated using core combined methodtr(V',Vtr) and test set combination nuclear matrix
Kte(V',Vte), wherein V' indicates basal orientation quantity set, VtrIndicate SAR image training dataset, VteIndicate SAR image test data
Collection；
(C) Bayesian inference step:
C1 the combination nuclear matrix K of SAR image training set) is usedtr(V',Vtr) establish Bayes's Multiple Kernel Learning supporting vector
Machine model；
C2 Bayes's Multiple Kernel Learning supporting vector machine model) is solved using expectation-maximization algorithm EM, it is more to obtain Bayes
The optimal solution β ' of core Learning support vector machine model；
C3) using the optimal solution β ' of Bayes's Multiple Kernel Learning supporting vector machine model obtained in step C2), in conjunction with SAR
The combination nuclear matrix K of image measurement collectionte(V',Vte), SAR image target category label y is calculatedte。
Compared with the prior art, the invention has the following advantages:
The present invention combines Bayes's supporting vector machine model with Multiple Kernel Learning method, proposes based on Bayes's multicore
The SAR target identification method of Learning support vector machine, so that Multiple Kernel Learning method is better than monokaryon in terms of choosing data characteristics
Learning method better reflects the relevance between different data feature, improves target identification performance significantly.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is in the present invention to SAR image preprocessing process schematic diagram.
Specific embodiment
Implementation steps and effect of the invention are described further with reference to the accompanying drawing:
Steps are as follows for realization of the invention referring to Fig.1.
Step 1, pretreatment is carried out to SAR image and nuclear matrix calculates.
1a) input a width original SAR image as shown in Fig. 2 (a): I={ imn| 1≤m≤M, 1≤n≤N }, wherein imn
Indicate the magnitude pixel value of original SAR image, M indicates the line number of SAR image, and N indicates the columns of SAR image；
1b) using the SAR figure for becoming power Ostu partitioning algorithm to original SAR image I progress binary segmentation, after being divided
As I'；
1c) by after segmentation SAR image I' and original SAR image I carry out dot product calculating, SAR image after obtained dot product
As shown in Fig. 2 (b), and calculate the mass center of SAR image after dot product
In formula, i'mnThe pixel value of SAR image after expression dot product；
Original SAR image I 1d) is subjected to circular shifting, so that mass centerImage center location is moved to, is registrated
SAR image I1, as shown in Fig. 2 (c)；
1e) to registration SAR image I1It carries out image interception and obtains interception SAR image I0, as shown in Fig. 2 (d)；
1f) to interception SAR image I0It does logarithmic transformation and obtains logarithm SAR image I " ', as shown in Fig. 2 (e)；
Median filter process 1g) is done to logarithm SAR image I " ', obtains image characteristic of field I2, as shown in Fig. 2 (f), will scheme
Image field feature I2Column vector；
1h) to registration SAR image I1Image interception and two-dimension fourier transform are done, and zero-frequency is moved into picture centre, is obtained
To frequency domain character I3, and by frequency domain character I3Column vector；
1i) training set to original SAR image and test set repeat 1a respectively)~1g), obtain the training of image characteristic of field
Data set TtrWith test data set Tte；
1j) training set to original SAR image and test set repeat 1a respectively)~1h), obtain the training number of frequency domain character
According to collection PtrWith test data set Pte；
1k) using KSVD algorithm to image characteristic of field training set TtrStudy, obtains dictionary D and and TtrCorresponding sparse system
Number feature training dataset Str, in conjunction with dictionary D and image area characteristic test data set Tte, it is calculated using OMP algorithm sparse
Coefficient characteristics test data set Ste。
Step 2, Multiple Kernel Learning calculating is carried out to three kinds of SAR image features obtained in step 1.
2a) using radial kernel function RBF, in conjunction with image characteristic of field training dataset TtrWith test data set Tte, calculate
To the nuclear matrix K of image characteristic of field training datasetttr(Ttr,Ttr) and image area characteristic test data set nuclear matrix Ktte(Ttr,
Tte), wherein radial direction kernel function RBF is expressed as follows:
In formula, two data points of q' and q expression the same space, K (q', q) indicate the radial kernel functional value being calculated,
σ indicates radial kernel functional parameter；
2b) using radial kernel function RBF, in conjunction with frequency domain character training dataset PtrWith test data set Pte, it is calculated
The nuclear matrix K of frequency domain character training datasetptr(Ptr,Ptr) and frequency domain character test data set nuclear matrix Kpte(Ptr,Pte)；
2c) using radial kernel function RBF, in conjunction with sparse coefficient feature training dataset StrWith test data set Ste, calculate
Obtain the nuclear matrix K of sparse coefficient feature training datasetstr(Str,Str) and sparse coefficient characteristic test data set nuclear matrix
Kste(Str,Ste)；
2d) combine step 2a)~2c) in the training set nuclear matrix of three kinds of features that is calculated, use core combined method
Calculate the combination nuclear matrix K for obtaining SAR image training settr(V',Vtr):
Ktr(V',Vtr)=ηtKttr(Ttr,Ttr)+ηpKptr(Ptr,Ptr)+ηsKstr(Str,Str)
In formula, ηtThe combination coefficient of expression image area characteristic data set nuclear matrix, value 0.5,
ηpThe combination coefficient of expression frequency domain character data set nuclear matrix, value 0.5,
ηsIndicate the combination coefficient of sparse coefficient feature nuclear matrix；Value is 0.5；
2e) combine step 2a)~2c) in the test set nuclear matrix of three kinds of features that is calculated, use core combined method
Calculate the combination nuclear matrix K for obtaining SAR image test sette(V',Vte):
Kte(V',Vte)=ηtKtte(Ttr,Tte)+ηpKpte(Ptr,Pte)+ηsKste(Str,Ste)。
Step 3, Bayes's Multiple Kernel Learning supporting vector machine model is constructed.
3a) give sample setWherein, xlIndicate training sample,
ylIndicate that training label, q indicate sample dimension, L indicates sample size, T representing matrix transposition symbol；Support vector machines maximum side
The unconfined condition expression formula of edge classifier are as follows:
In formula, first item is regular terms, and Section 2 is penalty term；Indicate augmentation vector,It indicates
Augmentation weight, γ indicate reconciliation parameter；
The augmentation weight solution of support vector machines maximal margin classifier 3b) is obtained according to Lagrange duality In formula, αjIndicate Lagrange coefficient；
It willIt is updated in penalty term, obtains:Mapping function φ is introduced in penalty term
() obtains introducing the penalty term expression formula after mapping function:
Enable β in formulaj=αjyj,Obtain final penalty term expression formula:
In formula,β=(β1,…,βj,…,βL),Indicate augmentation vectorWith augmentation vectorKernel function value, Δ indicate training sample matrix；
3c) construction regular terms isThe regular terms is added with final penalty term, obtains final objective function d
(β) are as follows:
In formula, κ indicates reconciliation parameter；
3d) in calculating target function regular terms negative index, and be defined as pseudo- prior density function:
3e) the index of the final penalty term negative in calculating target function, is defined as pseudo- likelihood distribution function:
In formula, y=(y1,…,yl,…,yL), Δ ' indicate training sample matrix；
3f) according to step 3d) and step 3e) in calculated result, obtain pseudo- Posterior distrbutionp function:
P (β | y, K (Δ, Δ ')) ∝ p (β) p (y | β, K (Δ, Δ ')),
3h) use the combination nuclear matrix K of SAR image training datasettr(V',Vtr) replacement step 3f) and in K (Δ, Δ '),
Establish Bayes's Multiple Kernel Learning supporting vector machine model:
p(β|y,Ktr(V',Vtr))∝p(β)p(y|β,Ktr(V',Vtr))
In formula, Ktr(V',Vtr)=(Ktr(V',v1),…,Ktr(V',vl),…,Ktr(V',vL)), Ktr(V',vl) indicate
Basal orientation collection and training sample do the vector constituted after inner product calculating, and p (y | β, Ktr(V',Vtr)) it is after introducing combination nuclear matrix
Pseudo- likelihood distribution function, in which:
Step 4, Bayes's Multiple Kernel Learning supporting vector machine model is solved.
4a) with containing λlIntegral expression characterize step 3h) in introduce combination nuclear matrix after pseudo- likelihood distribution function:
Wherein, pseudo- likelihood distribution function has lower relational expression:
p(yl|β,Ktr(V',vl))=∫ p (yl,λl|β,Ktr(V',vl))dλl
Wherein, vlIndicate training sample, λlIndicate hidden variable, p (yl,λl|β,Ktr(V',vl)) it is after hidden variable is added
Pseudo- likelihood distribution function；
4b) according to the pseudo- likelihood distribution function after addition hidden variable in step 4a), in Bayes's Multiple Kernel Learning supporting vector
New variables λ is introduced in machine model, obtains new relational expression:
p(β,λ|y,Ktr(V',Vtr))∝p(β)p(y,λ|β,Ktr(V',Vtr))
Wherein,
In formula, λ indicates hidden variable vector, λ=(λ1,…,λl,…,λL)；
The Posterior distrbutionp function of λ 4c) is obtained according to the new relational expression in step 4b):
In formula,
4d) according to 4c) obtained in λ Posterior distrbutionp function, obtain λlCondition Posterior Distribution:
In formula,Indicate broad sense dead wind area, according toWithBetween conversion close
System, obtainsCondition Posterior Distribution:
In formula,Indicate dead wind area, the obedience symbol in~expression distribution function；
4e) according to 4d) inCondition Posterior Distribution and the property of dead wind area obtainDesired value:
4f) relational expression and 4e new according to obtained in step 4b)) obtained inDesired value, use expectation
It maximizes algorithm EM and solves Bayes's Multiple Kernel Learning supporting vector machine model, obtain Bayes's Multiple Kernel Learning supporting vector machine model
Iterative solution β(m+1)Expression formula:
In formula, m indicates the m times the number of iterations, and I indicates unit matrix,It indicatesThe m times expectation iteration
Value；
Maximum number of iterations 4g) is set as M', repeats step 4f), the iteration stopping when the number of iterations reaches M', final
To the optimal solution β ' of Bayes's Multiple Kernel Learning supporting vector machine model:
Step 5, SAR image target identification category label is calculated.
5a) using the optimal solution β ' of Bayes's Multiple Kernel Learning supporting vector machine model obtained in step 4g), in conjunction with SAR
Image measurement data set Kte(V',Vte), SAR image target identification label y is obtained using following formulate:
yte=sgn (β 'TKte(V',Vte))
In formula, sgn () indicates sign function.
So far, the classification to SAR target is completed.
Effect of the invention is by below further illustrating the experiment of measured data:
1. experiment scene and parameter:
Data used in experiment are that disclosed dynamic obtains with static object and identifies MSTAR data set.In the data
It concentrates, chooses under 17 ° of pitch angles BMP2SN9563, BTR70C71, T72SN132 model image data as training data, 15 °
For the lower 7 kinds of model image datas of pitch angle as test data, BMP2SN9566, BMP2SNC21 are referred to as the variant of BMP2SN9563,
T72SNS7, T72SN812 are the variant of T72SN132, and original image size is 128 × 128.
This experiment data type used and sample number are as shown in table 1:
1 MSTAR experimental data of table
Experiment parameter setting is as follows:
SAR image picture size size after pretreatment is 63 × 63；The corresponding radial nuclear parameter σ of image characteristic of fieldt
=1, the corresponding radial nuclear parameter σ of frequency domain characterp=0.1, the corresponding radial nuclear parameter σ of sparse coefficient features=1, Bayes is more
New reconciliation parameter κ=0.01 in core Learning support vector machine model；
2. experiment content and result:
Classified with the method for the present invention and other existing 5 kinds of methods to MSTAR three classes data set, wherein the 1st kind is
Linear SVM, the 2nd kind is monokaryon Learning support vector machine, and the 3rd kind is Multiple Kernel Learning support vector machines, and the 4th kind is shellfish
This support vector machines of leaf, the 5th kind is Bayes's monokaryon Learning support vector machine；
The experimental procedure for carrying out target identification with the method for the present invention is as follows:
Firstly, pre-processing to the MSTAR three classes data in experiment, and three kinds of spies are calculated using radial kernel function
Levy nuclear matrix, i.e. image characteristic of field nuclear matrix, frequency domain character nuclear matrix and sparse coefficient feature nuclear matrix；
Then, these three feature kernel matrixes are combined using combination kernel method, obtain MSTAR three classes data
Training dataset and test data set；
Then, the training dataset of MSTAR three classes data is updated to Bayes's Multiple Kernel Learning support vector machines respectively
In the expression formula of optimal solution's expression and hidden variable desired value, maximum number of iterations is set, Bayes's multicore is finally obtained
Practise the optimal solution of support vector machines；
Finally, target knowledge is calculated according to the test data set of optimal solution combination MSTAR three classes data obtained above
Other label.
The recognition result of MSTAR three classes data and the recognition result of other 5 kinds of methods will be compared with the method for the present invention, such as
Table 2.
The Comparative result table of 2 the method for the present invention of table and other methods to MSTAR three classes data
As can be seen from Table 2: Bayes's Multiple Kernel Learning supporting vector machine model proposed by the present invention is to three classification of SAR image
Target discrimination is 99.12%, is significantly increased compared to the result with other methods, illustrates that this method knows SAR image target
Other performance is obviously improved.
Claims (4)
1. a kind of SAR target identification method based on Bayes's Multiple Kernel Learning support vector machines, comprising:
(A) SAR image pretreatment and nuclear matrix calculate step:
A1 an original SAR image: I={ i) is inputtedmn| 1≤m≤M, 1≤n≤N }, wherein imnIndicate the amplitude picture of SAR image
Element value, M indicate the line number of original SAR image, and N indicates the columns of original SAR image；
A2 binary segmentation) is carried out to original SAR image I, and calculates the mass center for obtaining SAR image
A3 original SAR image I) is subjected to circular shifting, makes mass centerIt is moved to the center of image, obtains registration figure
As I1；
A4) to registration SAR image I1Logarithmic transformation, median filtering and image interception are successively carried out, the image area of SAR image is obtained
Feature I2, and by image characteristic of field I2Column vector；
A5) to registration SAR image I1Image interception and two-dimension fourier transform are done, and zero-frequency is moved into picture centre, obtains frequency domain
Feature I3, and by frequency domain character I3Column vector；
A6) respectively to original SAR image training set and test set repetitive process A1)~A4) obtain the training number of image characteristic of field
According to collection TtrWith test data set Tte；
A7) respectively to original SAR image training set and test set repetitive process A1)~A5) obtain the training data of frequency domain character
Collect PtrWith test data set Pte；
A8) using KSVD algorithm to image characteristic of field training set TtrStudy, obtains dictionary D and and TtrCorresponding sparse coefficient feature
Training dataset Str, in conjunction with dictionary D and image area characteristic test data set Tte, sparse coefficient spy is calculated using OMP algorithm
Levy test data set Ste；
(B) Multiple Kernel Learning step:
B1) using radial kernel function RBF, in conjunction with image characteristic of field training dataset TtrWith test data set Tte, figure is calculated
The nuclear matrix K of image field feature training datasetttr(Ttr,Ttr) and image area characteristic test data set nuclear matrix Ktte(Ttr,Tte)；
B2) using radial kernel function RBF, in conjunction with frequency domain character training dataset PtrWith test data set Pte, frequency domain is calculated
The nuclear matrix K of feature training datasetptr(Ptr,Ptr) and frequency domain character test data set nuclear matrix Kpte(Ptr,Pte)；
B3) using radial kernel function RBF, in conjunction with sparse coefficient feature training dataset StrWith test data set Ste, it is calculated
The nuclear matrix K of sparse coefficient feature training datasetstr(Str,Str) and sparse coefficient characteristic test data set nuclear matrix Kste
(Str,Ste)；
B4) combine step B1)~B3) in the training set nuclear matrix and test set nuclear matrix of the three kinds of features that are calculated, use
Core combined method calculates the combination nuclear matrix K for obtaining SAR image training settr(V',Vtr) and test set combination nuclear matrix Kte
(V',Vte), wherein V' indicates basal orientation quantity set, VtrIndicate SAR image training dataset, VteIndicate SAR image test data set；
(C) Bayesian inference step:
C1 the combination nuclear matrix K of SAR image training set) is usedtr(V',Vtr) establish Bayes's Multiple Kernel Learning support vector machines mould
Type；
C2 Bayes's Multiple Kernel Learning supporting vector machine model) is solved using expectation-maximization algorithm EM, obtains Bayes's multicore
Practise the optimal solution β ' of support vector machines；
C3) using the optimal solution β ' of Bayes's Multiple Kernel Learning supporting vector machine model obtained in step C2), in conjunction with SAR image
The combination nuclear matrix K of test sette(V',Vte), SAR image target identification category label y is calculatedte。
2. according to the method described in claim 1, wherein step B4) in calculated using core combined method and obtain SAR image training
The combination nuclear matrix K of collectiontr(V',Vtr) and test set combination nuclear matrix Kte(V',Vte), it is to be incited somebody to action using combination nuclear matrix function
B1)~B3) the obtained training set nuclear matrix of three kinds of features is added with test set nuclear matrix, obtain SAR image training number
According to the combination nuclear matrix K of collectiontr(V',Vtr) and SAR image test data set combination nuclear matrix Kte(V',Vte):
Ktr(V',Vtr)=ηtKttr(Ttr,Ttr)+ηpKptr(Ptr,Ptr)+ηsKstr(Str,Str)
Kte(V',Vte)=ηtKtte(Ttr,Tte)+ηpKpte(Ptr,Pte)+ηsKste(Str,Ste)
In formula, ηtThe combination coefficient of expression image area characteristic data set nuclear matrix, value 0.5,
ηpThe combination coefficient of expression frequency domain character data set nuclear matrix, value 0.5,
ηsIndicate the combination coefficient of sparse coefficient feature nuclear matrix；Value is 0.5；
The combination nuclear matrix function representation is as follows:
In formula, K'(N, Nv) indicate combination nuclear matrix, ηuIndicate combination coefficient, N and NvIndicate two groups of data points of the same space, Ku
(N,Nv) indicate to need combined nuclear matrix, U indicates the number of nuclear matrix, R+Indicate positive real number collection.
3. according to the method described in claim 1, wherein step C1) in using SAR image training set combination nuclear matrix Ktr
(V',Vtr) Bayes's Multiple Kernel Learning supporting vector machine model is established, it carries out as follows:
C11 sample set) is givenWherein, xlIndicate training sample, ylTable
Indicating number, q indicate sample dimension, and L indicates sample size, T representing matrix transposition；Support vector machines maximal margin classifier
Unconfined condition expression formula are as follows:
In formula, first item is regular terms, and Section 2 is penalty term；Indicate augmentation vector,Indicate augmentation
Weight, γ indicate reconciliation parameter；
C12 the augmentation weight solution of support vector machines maximal margin classifier) is obtained according to Lagrange duality In formula, αjIndicate Lagrange coefficient, yjIndicate j-th of sample corresponding label；
It willIt is updated in penalty term, obtains:Mapping function φ is introduced in penalty term
() obtains introducing the penalty term expression formula after mapping function:
Enable β in formulaj=αjyj,Obtain final penalty term:
In formula,β=(β1,…,βj,…,βL), L is indicated
Sample size,Indicate augmentation vectorWith augmentation vectorKernel function value, Δ indicate training sample matrix；
C13) construction regular terms isThe regular terms is added with final penalty term, obtains final objective function d (β)
Are as follows:
In formula, κ indicates reconciliation parameter；
C14) in calculating target function regular terms negative index, and be defined as pseudo- prior density function:
C15) the index of the final penalty term negative in calculating target function, is defined as pseudo- likelihood distribution function:
In formula, y=(y1,…,yl,…,yL), Δ ' indicate training sample matrix；
C16) according to step C14) and step C15) in calculated result, obtain pseudo- Posterior distrbutionp function:
P (β | y, K (Δ, Δ ')) ∝ p (β) p (y | β, K (Δ, Δ ')),
C17 the combination nuclear matrix K of SAR image training dataset) is usedtr(V',Vtr) replacement step C16) and in K (Δ, Δ '), build
Vertical Bayes's Multiple Kernel Learning supporting vector machine model are as follows:
p(β|y,Ktr(V',Vtr))∝p(β)p(y|β,Ktr(V',Vtr))
In formula, Ktr(V',Vtr)=(Ktr(V',v1),…,Ktr(V',vl),…,Ktr(V',vL)),p(y|β,Ktr(V',Vtr)) be
Pseudo- likelihood distribution function after introducing combination nuclear matrix, in which:
4. method according to claim 1 or 3, wherein step C2) in using expectation-maximization algorithm EM solve Bayes
Multiple Kernel Learning supporting vector machine model obtains the optimal solution β ' of Bayes's Multiple Kernel Learning support vector machines, carries out as follows:
C21) with containing λlIntegral expression characterization introduce combination nuclear matrix after pseudo- likelihood distribution function:
Wherein, ylIndicate specimen number, vlIndicate training sample, Ktr(V',vl) indicate that basal orientation quantity set and training sample make inner product meter
The vector constituted after calculation, λlIndicate hidden variable；
C22) according to above-mentioned new pseudo- likelihood distribution function, new variables is introduced in Bayes's Multiple Kernel Learning supporting vector machine model
λ obtains new relational expression:
p(β,λ|y,Ktr(V',Vtr))∝p(β)p(y,λ|β,Ktr(V',Vtr))
Wherein,
In formula, y indicates label set, y=(y1,…,yl,…,yL), λ indicates hidden variable vector, λ=(λ1,…,λl,…,λL),
L indicates sample size；
C23 the Posterior distrbutionp function of λ) is obtained according to new relational expression:
In formula,
C24) according to C23) obtained in λ Posterior distrbutionp function, obtain λlCondition Posterior Distribution:
In formula,Indicate broad sense dead wind area, according toWithBetween transformational relation, obtain
It arrivesCondition Posterior Distribution:
In formula,Indicate dead wind area: indicate the obedience symbol in probability distribution；
C25) according to C24) inCondition Posterior Distribution and the property of dead wind area obtainDesired value:
E(λl -1)=| 1-y βTKtr(V',vl)|-1,
C26) according to C23) obtained in λ Posterior distrbutionp function and C22) obtained in new relational expression, use expectation
It maximizes algorithm EM and solves Bayes's Multiple Kernel Learning supporting vector machine model, obtain Bayes's Multiple Kernel Learning supporting vector machine model
Iterative solution β(m′+1)Expression formula:
In formula, the secondary the number of iterations of m ' expression m ', I indicates unit matrix,It indicatesThe secondary expectation iteration of m '
Value；
C27 maximum number of iterations) is set as M', repeats step C26), the iteration stopping when the number of iterations reaches M' finally obtains
The optimal solution β ' of Bayes's Multiple Kernel Learning supporting vector machine model:
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