CN107491734A - Semi-supervised Classification of Polarimetric SAR Image method based on multi-core integration Yu space W ishart LapSVM - Google Patents

Semi-supervised Classification of Polarimetric SAR Image method based on multi-core integration Yu space W ishart LapSVM Download PDF

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CN107491734A
CN107491734A CN201710589220.6A CN201710589220A CN107491734A CN 107491734 A CN107491734 A CN 107491734A CN 201710589220 A CN201710589220 A CN 201710589220A CN 107491734 A CN107491734 A CN 107491734A
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spatial
sar image
wishart
pixel
lapsvm
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CN107491734B (en
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王敏
王勇
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SUZHOU WENJIE SENSING TECHNOLOGY Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V20/00—Scenes; Scene-specific elements
    • G06V20/10—Terrestrial scenes
    • G06V20/13—Satellite images
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/241—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2411—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on the proximity to a decision surface, e.g. support vector machines
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/241—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2415—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on parametric or probabilistic models, e.g. based on likelihood ratio or false acceptance rate versus a false rejection rate

Abstract

The present invention discloses a kind of semi-supervised Classification of Polarimetric SAR Image method based on multi-core integration Yu space W ishart LapSVM, mainly solves the problems, such as in existing sorting technique that nicety of grading caused by because the marker samples of polarimetric synthetic aperture radar full polarimetric SAR are less is low.Implementation step is：Polarization correlation matrix T is obtained, extracts its polarization characteristic vector and does normalized, establishes training sample set, constructs the steps such as Spatial Wishart manifold regular terms, calculates classification accuracy and output polarization SAR image classification results.The present invention had both solved the problems, such as that the unsupervised Classification of Polarimetric SAR Image accuracy rate of tradition was not high, it also avoid supervised classification method need a large amount of label datas and caused by handmarking it is difficult and the drawbacks of cost is high, joint using having label data and largely obtaining more preferable classifying quality without the cheap data of label on a small quantity, available for the target classification of Polarimetric SAR Image, detection and identification.

Description

Semi-supervised Polarimetric SAR Image based on multi-core integration Yu space W ishart LapSVM Sorting technique
Technical field
The invention belongs to technical field of image processing, is related to Classification of Polarimetric SAR Image method, available for Polarimetric SAR Image Terrain classification, in the technical field such as target identification.
Background technology
Polarization SAR (Polarimetric SAR) is the synthetic aperture radar that Polarimetry can be carried out to target, is led to The phase information for measuring and recording different polarized state combination echoes is crossed to target progress Polarimetry imaging.Polarization SAR Packet can carry out more fully expressing and describing to target, improve the knowledge to atural object containing more rich target scattering information Other ability, meanwhile, it has the advantages that round-the-clock, round-the-clock, high resolution, in object detection and recognition, classification and parameter Inverting etc. has very prominent advantage, therefore is widely used in the various fields such as military, agricultural, navigation.Polarization at present SAR imaging techniques have been developed rapidly, but corresponding Polarimetric SAR Image treatment technology can not also meet existing requirement.Therefore, Can be to the image processing techniques of the comprehensive deciphering of Polarimetric SAR Image progress there is an urgent need to develop.
Whether according to needing to have used label data in learning process, existing Classification of Polarimetric SAR Image method can divide For supervised classification and unsupervised segmentation.Supervised learning is to obtain an optimal models, then profit by the training of a large amount of marker samples The prediction to data untagged is realized with the optimal models, the polarization association side being distributed based on multiple Wishart proposed such as Lee et al. Sorting technique of the neutral net based on backpropagation that poor matrix supervised classification method, Heermann et al. are proposed etc..Without prison Educational inspector practise be by mining data inside structure and build-in attribute so as to complete to classify or cluster, its learning process need not be marked Data are signed, the polarization decomposed based on Freeman proposed such as Cloude et al. H/ α unsupervised segmentation methods, Lee et al. proposed SAR image unsupervised segmentation algorithms etc..
Semi-supervised learning is a kind of supervised learning and the unsupervised learning method being combined, by using a small amount of mark sample Sheet, and a large amount of cheap unmarked samples of joint simultaneously, make full use of inherent structure and information that unmarked sample is contained Classifying quality is lifted, the handmarking both avoided caused by a large amount of flag datas are used in supervised learning is difficult, cost height etc. Problem, also efficiently solve the drawbacks of unsupervised learning nicety of grading is low.
Because supervision existing at present and unsupervised Classification of Polarimetric SAR Image method have its certain limitation, because This, studies the task of top priority that a kind of effective semi-supervised Classification of Polarimetric SAR Image method is the art.
The content of the invention
It is an object of the invention to overcome the intrinsic disadvantage of supervision and unsupervised Classification of Polarimetric SAR Image method in current area End and deficiency, propose a kind of semi-supervised Classification of Polarimetric SAR Image method based on multi-core integration Yu space W ishart-LapSVM, By the way that on the basis of a small amount of marker samples, nicety of grading is lifted using a large amount of cheap unmarked samples.
The technical scheme is that the cluster based on polarization SAR data assumes with Space Consistency it is assumed that construction Spatial- Wishart manifold regular terms, and higher-dimension, which reflects, to be realized to polarization characteristic vector using multinuclear Weighted Fusion mode Penetrate, so as to realize the semi-supervised polarization SAR terrain classification based on LapSVM, make full use of a large amount of cheap unmarked sample liftings Classifying quality.Its specific embodiment is as follows：
(1) Polarimetric SAR Image to be sorted is inputted, obtains its coherence matrix T that polarizes；
(2) based on the polarization coherence matrix T in Polarimetric SAR Image, joint space information, construction polarization characteristic is vectorial, and Do feature normalization processing；
(3) 1% data are randomly selected per class from Polarimetric SAR Image to be sorted to be marked, while combines 30% Data untagged, collectively form training sample set；
(4) assumed based on Space Consistency and the polarization coherence matrix of polarization SAR data obeys multiple Wishart distributions, if The similarity measurement criterion between Polarimetric SAR Image pixel is counted, and according to cluster it is assumed that construction Spatial-Wishart streams Shape regular terms；
(5) one group of kernel function is selected, nuclear matrix is merged based on multinuclear Weighted Fusion policy calculation, polarization characteristic vector is entered Row High Dimensional Mapping；
(6) using training sample set training Spatial-Wishart LapSVM, and rapid Optimum is carried out based on PCG algorithms Solve；
(7) trained Spatial-Wishart LapSVM models are utilized, and are based on the more classification policys of one-vs-one Tag Estimation is carried out to Non-labeled Training Sample and test sample；
(8) classification accuracy and output polarization SAR image classification results are calculated；
The present invention has advantages below compared with prior art：
1st, the invention belongs to a kind of semi-supervised Classification of Polarimetric SAR Image algorithm, expensive there can be mark just with a small amount of Count evidence, while makes full use of a large amount of cheap unmarked samples to obtain the inside inherent structure and attribute of data set in itself, So as to lift nicety of grading, with the classifying quality of less mark cost acquisition advantageously；
2nd, cluster of the present invention based on polarimetric SAR image data is assumed with Space Consistency it is assumed that utilizing the relevant square of polarization Battle array obeys the characteristic of multiple Wishart distributions, and combines space neighborhood information, constructs the similarity measurements between polarization SAR pixel Criterion is measured, so as to construct Spatial-Wishart manifold regular terms, a large amount of unmarked sample lifting niceties of grading is make use of, changes Kind classifying quality；
3rd, the present invention carries out the high dimensional feature mapping of polarization characteristic vector by multi-core integration mode, so as to efficiently solve The isomery characteristic of polarization characteristic, avoid the deficiency of single kernel function.
4th, the present invention is solved by the lower rapid Optimum that LapSVM models are carried out using PCG algorithms in original form, significantly Improve solving speed.
Brief description of the drawings
Fig. 1 is the FB(flow block) that the present invention realizes step；
Fig. 2 is the PauliRGB composite diagrams for the polarization SAR data that present invention emulation uses；
Fig. 3 is the truly substance markers figure of Polarimetric SAR Image used in the present invention；
Fig. 4 is the Classification of Polarimetric SAR Image experimental result picture of (Spatial-Wishart LapSVM) of the invention；
Fig. 5 is the Classification of Polarimetric SAR Image experimental result picture for supervising Wishart；
Fig. 6 is KNN Classification of Polarimetric SAR Image experimental result picture；
Fig. 7 is the distance between spatial neighborhood point schematic diagram.
Embodiment
The present invention is a kind of semi-supervised Classification of Polarimetric SAR Image side based on multi-core integration Yu space W ishart LapSVM Method, referring to Fig. 1, specific implementation step of the invention is as follows：
Step 1, input Polarimetric SAR Image to be sorted, obtain its coherence matrix T that polarizes.
Referring to Fig. 2, the Polarimetric SAR Image is a width Holland farmland figure, and its atural object classification to be sorted includes bare area, Ma Ling Potato, beet, barley, pea and wheat, different colours represent different atural object classifications in figure, and truly thing category label figure is shown in for it Fig. 3.
The present invention realizes the semi-supervised terrain classification to Polarimetric SAR Image, is tested with the classification experiments of 6 class atural objects in the figure Demonstrate,prove the actual classification effect of the present invention.
Step 2, based on the polarization coherence matrix T in Polarimetric SAR Image, obtain polarization characteristic vector, and do feature normalizing Change is handled.
The polarization coherence matrix of each pixel of (2a) Polarimetric SAR Image represents by 3 × 3 matrixes of dimension：
Wherein, Tij=Tji *,i≠j。
(2b) polarization coherence matrix contains whole polarization informations of polarization SAR data, has expression polarization SAR data The ability of feature.Accordingly, the polarization vector form of single pixel point is expressed as the form that following dimension is 9 × 1 by us：
I=(| T11|2,|T22|2,|T33|2,|Re[T12]|2,|Re[T13]|2,|Re[T23]|2,|Im[T21]|2,|Im[T23] |2,|Im[T31]|2)
(2c) utilization space information, the characteristic vector of each pixel are expressed as multiple pixel point features of its surrounding neighbors Connection
Close, can be expressed as：
xi=[..., Ii-1,Ii,Ii+1,......]；
(2c) sampling feature vectors of view picture Polarimetric SAR Image to be sorted are normalized；
Step 3, randomly select training sample set.
(3a) to Polarimetric SAR Image to be sorted, the sample point that each classification randomly selects 1% is marked, as mark Remember sample set；
(3b) is to Polarimetric SAR Image to be sorted, the unmarked sample point of uniform selection 30%, as unmarked sample Collection；
(3c) combined mark sample set and unmarked sample collection, collectively form training sample set；
Step 4, the cluster based on polarization SAR data assume with Space Consistency it is assumed that construction Spatial-Wishart streams Shape regular terms.
The polarization coherence matrix of (4a) based on polarization SAR is obeyed multiple Wishart and is distributed, between any two pixel of design Multiple Wishart distances：
Regard number and obey multiple Wishart distributions as the polarization coherence matrix T of n sample, its probability density function is：
Wherein, k (n, q)=πq(q-1)/2Γ(n)…Γ(n-q+1)
∑ in formula represents T mathematic expectaion, and n is to regard number, and k is normalization coefficient, and Γ is Gamma functions, and Tr is matrix Mark.Given wherein pixel j, pixel i polarization coherence matrix TiThe probability of generation is
Above formula is taken the logarithm likelihood, can obtain the similarity between pixel i and pixel j：
Lij(Ti|Tj)=qnln (n)+(n-q) ln | Ti|-nTr(Tj -1Ti)-nln(Tj)-ln(k(n,q))
Similarly, the similarity between pixel j and pixel i can be obtained：
Lji(Tj|Ti)=qnln (n)+(n-q) ln | Tj|-nTr(Ti -1Tj)-nln(Ti)-ln(k(n,q))
Thus, the similarity that we are defined between any two pixel in Polarimetric SAR Image is：
Wherein, C is a constant.
Assuming that the prior probability p (T of all pixels pointi) equal, if
Then the similitude between pixel i and j is more than the similitude between pixel k and j.
Further log-likelihood function is simplified, constant term in formula and outlier are removed, and takes opposite number, can be with Obtain the multiple Wishart distances between pixel：
(4b) is based on multiple Wishart distance metrics criterion and space between the polarization SAR pixel defined in (4a) Uniformity constructs the Spatial-Wishart similarities between polarization SAR pixel it is assumed that joint space neighborhood information.
The distance between the practically thing distance away from central pixel point, spatial neighborhood point r determines in simulation spatial neighbors window Justice is as shown in Fig. 7：
Wherein, width is neighbour's window width, r1=1,r3=2,It is respectively：
With the 1- Neighbor Points (such as a points) of 1 unit of central pixel point space length；
With central pixel point space lengthIndividual unit- Neighbor Points (such as b points)；
With the 2- Neighbor Points (such as c points) of 2 units of central pixel point space length；
With central pixel point space lengthIndividual unit- Neighbor Points (such as d points)；
With central pixel point space lengthIndividual unitNeighbor Points (such as e points)；
K neighbours number and spatial neighborhood window width width are set, its final Spatial-Wishart similarities definition It is as follows：
Wherein, r is space length between pixel in spatial neighborhood window, and σ is the parameter of Gaussian function, Nk(Ti) it is Ti K- neighbours, Ns(Ti) it is TiSpatial neighbors.
Thus the defined Spatial-Wishat similarities based on spatial neighbors constraint can make full use of its space Neighborhood information, noise jamming is eliminated, improve classification accuracy.
(4c) by build neighbour's figure represent in data manifold structure, figure interior joint represent mark and unmarked sample This, they pass through side right value WijConnection.By combining using mark and unmarked sample, based on cluster hypothesis and Space Consistency It is assumed that the LapSVM constructed Spatial-Wishart manifold regular terms is defined as follows：
Wherein, L is figure Laplce matrix L=D-W；D is diagonal matrix, and its diagonal entry is the degree on each summit, I.e.W is side right matrix, and its element is calculated as shown in (4b).
Step 5, based on multinuclear Weighted Fusion policy calculation merge nuclear matrix, to polarization characteristic vector carry out High Dimensional Mapping.
(5a) selectes one group of kernel function, chooses Gaussian kernel, linear kernel and polynomial kernel herein, is designated as k respectivelyr,kl,kp；
(5b) does the High Dimensional Mapping of multinuclear Weighted Fusion to polarization SAR characteristic vector, i.e., based on set kernel function group It is as follows to calculate its Gram matrix：
K=(kij)=((1- μ1-μ2)•kr(xi,xj)+μ1•kl(xi,xj)+μ2•kp(xi,xj))
=(1- μ1-μ2)Kr+μ1Kl+μ2KpI, j=1, l+u
Wherein K is Gram matrixes, μ1,μ2∈ [0,1] is the regulatory factor of each kernel function proportion；
Step 6, Spatial-Wishart LapSVM are trained using training sample set, and carried out quickly based on PCG algorithms Optimization Solution；
(6a) is assumed with Space Consistency it is assumed that structure as described in step (4) by the cluster combined to polarization SAR data Make Spatial-Wishart manifold regular terms：
(6b) is by comprising the Spatial-Wishart manifold regular terms, constructing Spatial-Wishart LapSVM moulds Type：
(6c) representation theorem points out that the semi-supervised frameworks of LapSVM are in HKSolution in space can be expressed as：
Therefore, the problem optimizes solution and can be expressed as in original form：
Referring to S.Melacci, M.Belkin.Laplacian Support Vector Machines Trained in the Primal.Journal of Machine Learning Research,2011,12(3):1149-1184, above formula problem Preconditioned conjugate gradient can be based on and decline the progress rapid Optimum solution of (PCG) algorithm.
Step 7, trained LapSVM models are utilized, and based on the more classification policys of one-vs-one to unmarked training sample This and test sample carry out Tag Estimation.
(7a) needs to train according to the more classification policys of classification number m and one-vs-one of sample to be sortedIt is individual The disaggregated models of Spatial-Wishart LapSVM bis-；
(7b) to unmarked sample collection and test sample collection, with what is trainedIndividual Spatial-Wishart The disaggregated models of LapSVM bis- are predicted respectively, are voted, classification of the classification most using number of votes obtained as the pixel.
Step 8, calculate classification accuracy and output polarization SAR image classification results.
The effect of the present invention can be further illustrated by following emulation：
1. simulated conditions and emulation content：
This example is under the systems of Intel (R) Core (TM) i3CPU 2.53GHz Windows 7, Matlab R2013a fortune On row platform, the present invention and KNN and supervision Wishart Classification of Polarimetric SAR Image emulation experiments are completed.
2. emulation experiment content
A. the emulation of Classification of Polarimetric SAR Image algorithm of the present invention
The present invention is applied on the Polarimetric SAR Image in as shown in Figure 2 300 × 270 Dutch farmland, the polarization SAR figure The atural object classification to be sorted of picture includes bare area, potato, beet, barley, six big region of pea and wheat.Fig. 4 is with the present invention Method Fig. 2 is classified obtained by the simulation experiment result figure, its all kinds of classification results mark is as shown in FIG..
B. the emulation of Wishart and KNN Classification of Polarimetric SAR Image algorithms is supervised
Existing supervision Wishart Classification of Polarimetric SAR Image algorithms are applied to the Dutch agriculture as shown in Figure 2 300 × 270 On the Polarimetric SAR Image in field, the simulation experiment result is as shown in figure 5, its all kinds of classification results marks as shown in FIG..
KNN polarization SAR sorting algorithms are applied on the Polarimetric SAR Image in as shown in Figure 2 300 × 270 Dutch farmland, The simulation experiment result is as shown in fig. 6, its all kinds of classification results marks as shown in FIG..
3. the simulation experiment result
From fig. 4, it can be seen that the present invention has preferable subjectivity to regard the simulation experiment result obtained by Classification of Polarimetric SAR Image Feel effect, higher classification accuracy, region consistency is high, for the classification results distinction of 6 class atural objects to be sorted in Fig. 2 Preferably.
From Fig. 5,6 as can be seen that the obtained the simulation experiment result subjective vision effects of existing supervision Wishart are general, mistake Misclassification is serious, and edge blurry, region consistency is low, for 6 class atural objects to be sorted in Fig. 2 classification results distinction compared with Difference.
Emulation experiment more than can illustrate, for the classification of Polarimetric SAR Image, the present invention has certain advantage, Overcome original technology and apply the deficiency on Polarimetric SAR Image, classification accuracy can be obtained merely with a small amount of marker samples Higher effect, obtaining Accurate classification simultaneously, greatly reducing its sample labeling cost.
In summary, the present invention is substantially better than existing KNN and supervision for the classifying quality of Polarimetric SAR Image Classifying quality of the Wishart sorting techniques to Polarimetric SAR Image.So the present invention effectively overcome it is of the prior art a variety of Shortcoming and have high industrial utilization.
The above-described embodiments merely illustrate the principles and effects of the present invention, not for the limitation present invention.It is any ripe Know the personage of this technology all can carry out modifications and changes under the spirit and scope without prejudice to the present invention to above-described embodiment.Cause This, those of ordinary skill in the art is complete without departing from disclosed spirit and institute under technological thought such as Into all equivalent modifications or change, should by the present invention claim be covered.

Claims (6)

1. a kind of semi-supervised Classification of Polarimetric SAR Image method based on multi-core integration Yu space W ishart LapSVM, including such as Lower step：
(1) Polarimetric SAR Image to be sorted is inputted, obtains its coherence matrix T that polarizes；
(2) based on the polarization coherence matrix T in Polarimetric SAR Image, polarization characteristic vector is obtained, and do feature normalization processing；
(3) 1% data are randomly selected per class from Polarimetric SAR Image to be sorted to be marked, while combines 30% nothing Flag data, collectively form training sample set；
(4) assumed based on Space Consistency and the polarization coherence matrix of polarization SAR data obeys multiple Wishart distributions, design pole Change the similarity measurement criterion between SAR image pixel, and according to cluster it is assumed that constructing Spatial-Wishart manifolds just Then item；
(5) one group of kernel function is selected, nuclear matrix is merged based on multinuclear Weighted Fusion policy calculation, polarization characteristic vector is carried out high Dimension mapping；
(6) using training sample set training Spatial-Wishart LapSVM, and rapid Optimum is carried out based on PCG algorithms and asked Solution；
(7) trained Spatial-Wishart LapSVM models are utilized, and based on the more classification policys of one-vs-one to nothing Training sample and test sample is marked to carry out Tag Estimation；
(8) classification accuracy and output polarization SAR image classification results are calculated.
2. the semi-supervised Polarimetric SAR Image according to claim 1 based on multi-core integration Yu space W ishart LapSVM Sorting technique, it is characterised in that the polarization correlation matrix based on Polarimetric SAR Image wherein described in step (2) obtains each picture The characteristic vector of vegetarian refreshments, it is to carry out in accordance with the following steps：
(2a) is based on the polarization correlation matrix T that each pixel dimension of Polarimetric SAR Image is 3 × 3, can express characteristic vector It is 9 × 1 vector forms for following dimension：
I=(| T11|2,|T22|2,|T33|2,|Re[T12]|2,|Re[T13]|2,|Re[T23]|2,|Im[T21]|2,|Im[T23]|2,| Im[T31]|2) (2b)
Utilization space information, the characteristic vector of each pixel are expressed as the joint of multiple pixel point features of its surrounding neighbors, X can be expressed asi=[..., Ii-1,Ii,Ii+1,......]；
(2c) sampling feature vectors of view picture Polarimetric SAR Image to be sorted are normalized.
3. the semi-supervised Polarimetric SAR Image according to claim 1 based on multi-core integration Yu space W ishart LapSVM Sorting technique, it is characterised in that the construction Spatial-Wishart manifolds regular terms wherein described in step (4) is as follows Carry out：
The polarization coherence matrix of (4a) based on polarization SAR pixel is obeyed multiple Wishart and is distributed, between any two pixel of design Spatial-Wishart similarities：
Regard number and obey multiple Wishart distributions as the polarization coherence matrix T of n sample, its probability density function is：
Wherein, k (n, q)=πq(q-1)/2Γ(n)…Γ(n-q+1)
∑ in formula represents T mathematic expectaion, and n is to regard number, and k is normalization coefficient, and Γ is Gamma functions, and Tr is the mark of matrix. Given wherein pixel j, pixel i polarization coherence matrix TiThe probability of generation is
Above formula is taken the logarithm likelihood, the similarity between pixel i and pixel j can be obtained：
Lij(Ti|Tj)=qnln (n)+(n-q) ln | Ti|-nTr(Tj -1Ti)-nln(Tj)-ln(k(n,q))
Similarly, the similarity between pixel j and pixel i can be obtained：
Lji(Tj|Ti)=qnln (n)+(n-q) ln | Tj|-nTr(Ti -1Tj)-nln(Ti)-ln(k(n,q))
Thus, the similarity that we are defined between any two pixel in Polarimetric SAR Image is：
L(Ti,Tj)
=Lij(Ti,Tj)+Lji(Tj,Ti)
=qnln (n)+(n-q) ln | Ti|-nTr(Tj -1Ti)-nln(Tj)-ln(k(n,q)
+qnln(n)+(n-q)ln|Tj|-nTr(Ti -1Tj)-nln(Ti)-ln(k(n,q)
=-qln | Ti|-nTr(Tj -1Ti)-nTr(Ti -1Tj)-qln|Tj|+C
Wherein, C is a constant.
Assuming that the prior probability p (T of all pixels pointi) equal, if
Then the similitude between pixel i and j is more than the similitude between pixel k and j.
Further log-likelihood function is simplified, constant term in formula and outlier are removed, and takes opposite number, can be obtained Multiple Wishart distances between pixel：
(4b) is based on the similarity measurement criterion between the polarization SAR pixel defined in (4a), while combines utilization space Neighborhood information constructs Spatial-Wishart similarities effectively to overcome noise jamming present in Polarimetric SAR Image；
K neighbours number and spatial neighborhood window width width are set, its final Spatial-Wishart similarity is defined as follows：
Wherein, r is space length between pixel in spatial neighborhood window, and σ is the parameter of Gaussian function, Nk(Ti) it is TiK- Neighbour, Ns(Ti) it is TiSpatial neighbors.
Thus the defined Spatial-Wishat similarities based on spatial neighbors constraint can make full use of its spatial neighborhood Information, noise jamming is eliminated, improve classification accuracy.
(4c) by build neighbour's figure represent in data manifold structure, figure interior joint represent mark and unmarked sample, They pass through side right value WijConnection.By combining using mark and unmarked sample, assumed based on cluster false with Space Consistency If the LapSVM constructed Spatial-Wishart manifold regular terms is defined as follows：
Wherein, L is figure Laplce matrix L=D-W；D is diagonal matrix, and its diagonal entry is the degree on each summit, i.e.,W is side right matrix, and its element is calculated as shown in (4b).
4. the semi-supervised Polarimetric SAR Image according to claim 1 based on multi-core integration Yu space W ishart LapSVM The High Dimensional Mapping based on the realization of multi-core integration weighted strategy to characteristic vector described in sorting technique, wherein step (5), by as follows Step is carried out：
(5a) selectes one group of kernel function, chooses Gaussian kernel, linear kernel and polynomial kernel herein, is designated as k respectivelyr,kl,kp；
(5b) does the High Dimensional Mapping of multinuclear Weighted Fusion to polarization SAR characteristic vector, i.e., based on set kernel function group：
K=(kij)=((1- μ1-μ2)·kr(xi,xj)+μ1·kl(xi,xj)+μ2·kp(xi,xj))
=(1- μ1-μ2)Kr+μ1Kl+μ2KpI, j=1 ... l+u
K is Gram matrixes, μ1,μ2∈ [0,1] is the regulatory factor of each kernel function proportion.
5. the semi-supervised Polarimetric SAR Image according to claim 1 based on multi-core integration Yu space W ishart LapSVM The training and solution based on Spatial-Wishart LapSVM described in sorting technique, wherein step (6), enters as follows OK：
(6a) is assumed with Space Consistency it is assumed that construction as described in step (4) by the cluster combined to polarization SAR data Spatial-Wishart manifold regular terms：
(6b) is by comprising the Spatial-Wishart manifold regular terms, constructing Spatial-Wishart LapSVM models：
(6c) representation theorem points out that the semi-supervised frameworks of LapSVM are in HKSolution in space can be expressed as：
Therefore, the problem optimizes solution and can be expressed as in original form：
Referring to S.Melacci, M.Belkin.Laplacian Support Vector Machines Trained in the Primal.Journal of Machine Learning Research,2011,12(3):1149-1184, above formula problem can be with (PCG) algorithm is declined based on preconditioned conjugate gradient and carries out rapid Optimum solution.
6. the semi-supervised Polarimetric SAR Image according to claim 1 based on multi-core integration Yu space W ishart LapSVM Described in sorting technique, wherein step (7) based on the Spatial-Wishart LapSVM models trained to unmarked sample Collection and test sample collection carry out Tag Estimation, carry out as follows：
(7a) needs to train according to the more classification policys of classification number m and one-vs-one of sample to be sortedIt is individual The disaggregated models of Spatial-Wishart LapSVM bis-；
(7b) to unmarked sample collection and test sample collection, with what is trainedIndividual Spatial-Wishart LapSVM Two disaggregated models are predicted respectively, are voted, classification of the classification most using number of votes obtained as the pixel.
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CN113409891A (en) * 2021-05-25 2021-09-17 电子科技大学长三角研究院(衢州) Method, device, equipment and storage medium for predicting DNA6mA modification class
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CN115223050B (en) * 2022-04-28 2023-08-18 湖北工程学院 Polarized satellite image analysis method

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