CN104200217A - Hyperspectrum classification method based on composite kernel function - Google Patents
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Abstract
The invention provides a hyperspectrum classification method based on a composite kernel function. The hyperspectrum classification method comprises the steps of inputting a set of hyperspectrum images in N classes, taking a support vector machine as a base classifier, and meanwhile, randomly selecting S samples from every classes of the hyperspectrum images to form a training set and forming a test set with the left samples, determining the change range of each parameter, next, determining the optimal performance parameters, including a penalty factor and a kernel of the support vector machine by virtue of cross validation for K times, constructing a composite kernel function by use of a composite kernel construction policy and training the support vector machine, and circulating for N times by use of the parameters of a support vector machine decision function obtained in the training process to obtain decision function values of which the test set belongs to every classes and to form a matrix as shown in the specification, and then determining multiple classifier policies, namely finding the maximum values of every columns of the matrix as shown in the specification. The hyperspectrum classification method based on the composite kernel function has the characteristics of better description of distribution features of a data set, relatively high classification accuracy and the like. The time taken by parameter optimization of the hyperspectrum classification method is also relatively short in contrast with a traditional multi-kernel learning method.
Description
Technical field
What the present invention relates to is a kind of sorting technique of high spectrum image, particularly a kind of hyperspectral classification method based on new compound nucleus function (Hyperspectral Image Classification Based on A New Composite Kernel).
Background technology
In recent years, the development of satellite sensor had improved spatial resolution and spectral resolution, had simultaneously also shortened the access time, and then had created condition for the development of hyperspectral classification method.Neural network classifier, k nearest neighbor sorter, Bayes classifier, decision tree classifier and the sorter based on core etc. has been widely used in high spectrum field, and wherein the sorting technique based on kernel function is more and more paid close attention to.Support vector machine (Support Vector Machine, SVM) be the most typical sorting technique based on kernel function, in the time processing limited higher-dimension training sample, still can obtain good classification performance, make it in hyperspectral classification, occupy certain status.In view of the polyphyly of real data and the diversity of expression way, traditional monokaryon has been not enough to practical requirement.Nearly ten years, Multiple Kernel Learning (Multiple Kernel Learning, MKL) technology has obtained paying close attention to and development, mainly improves from four aspects: the 1) improvement of Multiple Kernel Learning strategy; As the simple Multiple Kernel Learning (Simple-MKL) that Rakotomamonjy etc. proposes, it uses gradient descent method to solve Multiple Kernel Learning problem.2) improvement of parameter optimization; The propositions such as Li are not used the parameter optimization mode of any protruding bound term.3) improvement of multiple kernel function combinations; As Xia etc. has utilized the combination of boosting.4) improvement of strategies; As the people such as Gu propose the representative Multiple Kernel Learning of hyperspectral classification.The most common Multiple Kernel Learning method is mixed nucleus function (Mixture Kernels, MKs), and by multiple kernel function linear weighted function summations, the validity of this kernel function has obtained checking and has been widely used in hyperspectral classification field.But it is in training process, and the time that parameter optimization consumes is huge also.
Summary of the invention
The object of the present invention is to provide a kind of better distribution characteristics of descriptor data set, and nicety of grading is relatively high, a kind of hyperspectral classification method based on compound nucleus function that the time that parameter optimization consumes is relatively short.
The object of the present invention is achieved like this:
Step 1: input one panel height spectrum picture, classification number is N;
Step 2: taking support vector machine as base sorter, from the each classification of described high spectrum image, choose randomly s sample composition training set simultaneously, residue sample composition test set, determine the variation range of each parameter, then the optimal performance parameter of determining support vector machine in conjunction with K cross validation, comprises penalty factor and nuclear parameter;
Step 3: utilize compound nucleus construction strategy, structure compound nucleus function, trains support vector machine;
Step 4: utilize the parameter of the support vector machine decision function that training process obtains, circulation N time, and then obtain the decision function value that test set belongs to every classification, composition matrix
wherein n
testrepresent the number of test sample book;
Step 5: determine multi-categorizer strategy, find matrix
the maximal value of every row, the prediction label of the corresponding each test sample book of its row sequence number,
i=1 ..., n
test.
Feature of the present invention is:
1, in parameter setting up procedure, the selection of base sorter can be used other sorters based on core to replace support vector machine.
2, the determining of optimal performance parameter in parameter setting up procedure, is the mode that adopts grid search and K cross validation to combine.
3, in training process, the structure of compound nucleus function obtains by Nonlinear Mapping repeatedly, is calculated as follows:
K
1(x,z)＝φ
1(x)·φ
1(z)
K
2(x,z)＝φ
2[φ
1(x)]·φ
2[φ
1(z)]
...
K
M(x,z)＝φ
M[φ
M-1(x)]·φ
M[φ
M-1(z)]
Wherein K
m(x, z) represents the kernel function of sample x and z, φ
mrepresent Nonlinear Mapping function the M time.φ
mcan be Gaussian mapping, polynomial expression mapping or other Nonlinear Mapping, and in the time of M=2, the classification performance based on this compound Kernel function classifier can reach convergence state.
4,, in the time of M=2, the parameter optimization time of compound nucleus function will be much smaller than the parameter optimization time of traditional mixed nucleus function.
Based on These characteristics, a kind of hyperspectral classification method based on new compound nucleus function that the present invention proposes has the better distribution characteristics of descriptor data set, and relatively high of nicety of grading.Meanwhile, the time that its parameter optimization consumes is also relatively short with respect to traditional Multiple Kernel Learning method.
Brief description of the drawings
Fig. 1 is the hyperspectral classification method flow diagram based on a kind of compound nucleus function of the present invention.
Fig. 2 a-Fig. 2 b is high spectrum image Indian Pines, wherein: Fig. 2 a is that gray-scale map, Fig. 2 b are reference features classification.
Fig. 3 a-Fig. 3 b is bimonthly thread form simulated data sets classification boundaries vision figure, wherein: Fig. 3 a is that gaussian kernel function Gauss classification boundaries vision figure, Fig. 3 b are continuous Gaussian mapping compound nucleus function G (G) classification boundaries vision figure.Figure hollow core symbology test sample book, filled symbols represents training sample.
Fig. 4 is for high-spectral data collection Indian Pines different IPs function category performance comparison sheet 1.In form, Linear represents single linear kernel function, Polynomial represents single polynomial kernel function, Gauss represents single gaussian kernel function, MKs represents mixed nucleus function, G (G) represents continuous Gaussian mapping compound nucleus function, G (P) representative polynomial-Gaussian mapping compound nucleus function, P (G) represents Gauss-polynomial expression mapping compound nucleus function, P (P) represents continuous polynomial expression mapping compound nucleus function.
Fig. 5 is that different IPs function parameter is optimized time contrast table 2.
Fig. 6 is the different training sample number table 3 that affects on different IPs function category performance.
Embodiment
For example the present invention is described in more detail below in conjunction with accompanying drawing.
The present invention is a kind of hyperspectral classification method based on new compound nucleus function, comprises input process, parameter setting, training process, assorting process and output procedure five steps.Input process inputs a panel height spectrum picture; Parameter setting is the process of initialization and parameter optimization; Training process is taking support vector machine as base sorter, the process of training base sorter model; Assorting process is the model parameter of utilizing said process to obtain, thereby provides the decision function value process that test set belongs to every classification; Output procedure is to determine multi-categorizer strategy, and provides the process of test sample book prediction label.Provide detailed process below:
Concrete analysis step is as follows:
Step S1: input process.Input a panel height spectrum picture, N represents classification number.
Step S2: parameter setting.From image, in each classification, choose randomly s sample composition training set, residue sample composition test set.Determine the variation range of each parameter, then determine the optimal performance parameter of support vector machine in conjunction with K cross validation.This step is further comprising the steps:
Step S2.1: sample set determine; From N classification of high spectrum image, every class is chosen s sample composition randomly label training sample set D={ (x
1, y
1) ..., (x
n, y
n), wherein x
irepresent i spectral signature that has exemplar, y
irepresent sample x
ilabel, n=16s represents training sample number.Residue sample composition test set
n
testrepresent test sample book number.
Step S2.2: parameter area determine; Adopting polynomial kernel function and gaussian kernel function is that basic kernel function is carried out the synthetic of compound nucleus function.Polynomial kernel is K
p(x, z)=φ
p(x) φ
p(z)=[(xz)+1]
d, its parameter is d, φ
p(x) the polynomial expression mapping function of expression sample x.Gaussian kernel is K
g(x, z)=φ
g(x) φ
g(z)=exp (|| x-z||
2/ σ
2), its Gauss's radius is σ, φ
g(x) the Gaussian mapping kernel function of expression sample x.The penalty factor of support vector machine, the variation range of Gauss's radius sigma and d is respectively: { 2
0, 2
1..., 2
8, { 2
-5, 2
-4..., 2
1and { 2
-2, 2
-1.., 2
4.
S2.3:K cross validation of step; In each parameter combinations situation, training sample set D is divided into K subset, retain successively a subset for test, remaining K-1 subset is used for training svm classifier device model.Cross validation repeats K time, and each subset is verified once, and the mean value of calculating K subseries precision.In the time that mean accuracy reaches maximal value, illustrate that this parameter combinations is optimum.
Step S3: training process.Utilize compound nucleus construction strategy, structure compound nucleus function, trains support vector machine.This step is further comprising the steps:
Step S3.1: the structure of compound nucleus function; Obtain compound nucleus function by Nonlinear Mapping repeatedly, be calculated as follows:
K
1(x,z)＝φ
1(x)·φ
1(z)
K
2(x,z)＝φ
2[φ
1(x)]·φ
2[φ
1(z)]
...
K
M(x,z)＝φ
M[φ
M-1(x)]·φ
M[φ
M-1(z)]
Wherein K
m(x, z) represents the kernel function of sample x and z, φ
mrepresent Nonlinear Mapping function the M time.φ
mcan be Gaussian mapping, polynomial expression mapping or other Nonlinear Mapping, and in the time of M=2, the classification performance based on this compound Kernel function classifier can reach convergence state.In the time of M=2, K
g (G), K
g (P), K
p (G)and K
p (P)be respectively continuous Gaussian mapping compound nucleus function, polynomial expression-Gaussian mapping compound nucleus function, Gauss-polynomial expression mapping compound nucleus function and continuously polynomial expression mapping compound nucleus function.Expression formula is as follows:
K
G(G)(x,z)＝φ
G[φ
G(x)]·φ
G[φ
G(z)]
＝exp[-||φ
G(x)-φ
G(z)||
2/σ
2 2]
(1)
＝exp[-[φ
G(x)·φ
G(x)+φ
G(z)·φ
G(z)-2φ
G(x)·φ
G(z)]/σ
2 2]
＝exp[-[K
G(x,x)+K
G(z,z)-2K
G(x,z)]/σ
2 2]
K
G(P)(x,z)＝φ
G[φ
P(x)]·φ
G[φ
P(z)]
＝exp[-||φ
P(x)-φ
P(z)||
2/σ
2 2]
(2)
＝exp[-[φ
P(x)·φ
P(x)+φ
P(z)·φ
P(z)-2φ
P(x)·φ
P(z)]/σ
2 2]
＝exp[-[K
P(x,x)+K
P(z,z)-2K
P(x,z)]/σ
2 2]
Wherein x and z represent two pixels, σ
2represent Gauss's radius of Gaussian mapping for the second time, d
2represent the polynomial parameters of polynomial expression mapping for the second time.In attention formula (1) (3), Gauss's radius of Gaussian mapping is σ for the first time
1, similarly, in formula (2) (4), the polynomial parameters of polynomial expression mapping is for the first time d
1.
Step S3.2: the training of support vector machine; Support vector machine is trained to the weight vectors of supported vector machine decision function and threshold alpha
*and b
*.
Step S4: assorting process.Utilize the parameter of the support vector machine decision function that training process obtains, circulation N time, and then obtain the decision function value that test set belongs to every classification, composition matrix
wherein n
testrepresent the number of test sample book.
Step S5: output procedure.Determine multi-categorizer strategy, find matrix
the maximal value of every row, the prediction label of the corresponding each test sample book of its row sequence number,
i=1 ..., n
test.
Step S5.1: multi-categorizer strategy determine; Adopt " a pair of remaining " multi-categorizer strategy that many classification problems are changed into multiple two classification problems.
Step S5.2: the calculating of nicety of grading; Calculate respectively overall nicety of grading (the Overall Accuracy that adopts support vector machine in different composite kernel function situation, OA), Kappa coefficient (Kappa Statistic, Kappa), the nicety of grading of average nicety of grading (Average Accuracy, AA) and each classification.
For validity of the present invention is described, spy carries out following experimental demonstration.Experimental data is from bimonthly thread form (Two Moons) simulated data sets and true high-spectral data collection (Indian Pines).
1) Two Moons: this simulated data sets comprises two classifications, contains respectively 96 and 104 pixels, and each pixel is by two character representations.
2) Indian Pines: this high-spectrum remote sensing is from the Indian agricultural in the Indiana, USA northwestward of obtaining for 1992, and it comprises 144 × 144 pixels, 16 classifications, 220 wave bands, because the factors such as noise are removed 20 wave bands wherein.Image is removed the monitoring data that has that comprises 16 class vegetation beyond background.
First parameters more of the present invention are set: first from every class, choose randomly s sample composition D={ (x
1, y
1) ..., (x
n, y
n), residue sample composition test set
the method of selecting ten cross validations (K=10) and grid search to combine is estimated optimum parameter, the penalty factor of support vector machine, and the variation range of Gauss's radius sigma and d is respectively: { 2
0, 2
1..., 2
8, { 2
-5, 2
-4..., 2
1and { 2
-2, 2
-1.., 2
4.For the compound nucleus function proposing, make Nonlinear Mapping number of times M=2, now classification performance convergence.
In first group of experiment, primary study use SVM is base sorter, adopt respectively gaussian kernel (Gauss Kernel) and compound nucleus function (continuous Gaussian Nonlinear Mapping G (G) Composite Kernel), the distribution situation of classification boundaries.As shown in Figure 2, a) b) compound nucleus function G (G) classification boundaries of gaussian kernel function Gauss classification boundaries.During by the more known employing compound nucleus of this group function, the classification boundaries of SVM is the distribution situation of descriptor data set better, and nicety of grading is also relatively high.
The impact of primary study different IPs function on classification performance in second group of experiment.The parameter of this group experiment is set to s=10.Experimental result is as shown in table 1, can be summarized as: 1, for single kernel function, the nicety of grading that the nicety of grading that gaussian kernel function obtains obtains compared with linear kernel (Linear Kernel) and polynomial kernel (Polynomial Kernel) is high; 2, when adopting mixed nucleus function (Mixture Kernels, MKs), i.e. linear weighted function summation mixed nucleus, can effectively improve the nicety of grading of single kernel function; 3,, compared with other kernel form, while adopting compound nucleus function, the nicety of grading of SVM is higher, and G (G) compound nucleus best performance.
The impact of primary study different IPs function on the parameter optimization time in the 3rd group of experiment.This group experiment all adopts cross validation, i.e. K=10 ten times.Experimental result is as table 2, known in the time of Nonlinear Mapping number of times M=2, more single core, and the time that compound nucleus function parameter is optimized is longer, meanwhile, the time that its optimization time will consume much smaller than mixed nucleus function.
The impact of the different training sample numbers of primary study on different IPs function performance in the 4th group of experiment.This group experiment makes s, and in set, { in 5,10,50,100}, change, experimental result is as shown in table 3, is summarized as: 1,, along with s increases, the classification capacity of different IPs function has obviously improved, but the difference between different IPs function diminishes; 2,, under Small Sample Size, more can embody the advantage of kernel function; 3, each kernel function, it is not constant effective, its validity is relevant with the actual distribution situation of data set.If the performance that kernel function can obtain under certain conditions, just illustrate that so this kernel function is effective.Based on this, the compound nucleus function in the present invention is effective kernel function.
Claims (3)
1. a kind of hyperspectral classification method based on compound nucleus function, is characterized in that:
Step 1: input one panel height spectrum picture, classification number is N;
Step 2: taking support vector machine as base sorter, from the each classification of described high spectrum image, choose randomly s sample composition training set simultaneously, residue sample composition test set, determine the variation range of each parameter, then the optimal performance parameter of determining support vector machine in conjunction with K cross validation, comprises penalty factor and nuclear parameter;
Step 3: utilize compound nucleus construction strategy, structure compound nucleus function, trains support vector machine;
Step 4: utilize the parameter of the support vector machine decision function that training process obtains, circulation N time, and then obtain the decision function value that test set belongs to every classification, composition matrix
wherein n
testrepresent the number of test sample book;
Step 5: determine multi-categorizer strategy, find matrix
the maximal value of every row, the prediction label of the corresponding each test sample book of its row sequence number,
2. a kind of hyperspectral classification method based on compound nucleus function according to claim 1, is characterized in that: described step 2 specifically comprises:
Step 2.1: every class is chosen s sample composition randomly from N classification of high spectrum image label training sample set D={ (x
1, y
1) ..., (x
n, y
n), wherein x
irepresent i spectral signature that has exemplar, y
irepresent sample x
ilabel, n=16s represents training sample number, residue sample composition test set
n
testrepresent test sample book number;
Step 2.2: adopting polynomial kernel function and gaussian kernel function is that basic kernel function is carried out the synthetic of compound nucleus function, and polynomial kernel is K
p(x, z)=φ
p(x) φ
p(z)=[(xz)+1]
d, its parameter is d, φ
p(x) the polynomial expression mapping function of expression sample x; Gaussian kernel is K
g(x, z)=φ
g(x) φ
g(z)=exp (|| x-z||
2/ σ
2), its Gauss's radius is σ, φ
g(x) the Gaussian mapping kernel function of expression sample x; The penalty factor of support vector machine, the variation range of Gauss's radius sigma and d is respectively: { 2
0, 2
1..., 2
8, { 2
-5, 2
-4..., 2
1and { 2
-2, 2
-1.., 2
4;
Step 2.3: in each parameter combinations situation, training sample set D is divided into K subset, retain successively a subset for test, remaining K-1 subset is used for training svm classifier device model, cross validation repeats K time, and each subset is verified once, and the mean value of calculating K subseries precision, in the time that mean accuracy reaches maximal value, this parameter combinations is optimum.
3. a kind of hyperspectral classification method based on compound nucleus function according to claim 1 and 2, is characterized in that: described step 3 specifically comprises:
Step 3.1: obtain compound nucleus function by Nonlinear Mapping repeatedly, be calculated as follows:
K
1(x,z)＝φ
1(x)·φ
1(z)
K
2(x,z)＝φ
2[φ
1(x)]·φ
2[φ
1(z)]
...
K
M(x,z)＝φ
M[φ
M-1(x)]·φ
M[φ
M-1(z)]
Wherein K
m(x, z) represents the kernel function of sample x and z, φ
mrepresent Nonlinear Mapping function the M time; φ
mgaussian mapping, polynomial expression mapping or other Nonlinear Mapping, and in the time of M=2, the classification performance based on this compound Kernel function classifier reaches convergence state; In the time of M=2, K
g (G), K
g (P), K
p (G)and K
p (P)be respectively continuous Gaussian mapping compound nucleus function, polynomial expression-Gaussian mapping compound nucleus function, Gauss-polynomial expression mapping compound nucleus function and continuously polynomial expression mapping compound nucleus function; Expression formula is as follows:
K
G(G)(x,z)＝φ
G[φ
G(x)]·φ
G[φ
G(z)]＝exp[-||φ
G(x)-φ
G(z)||
2/σ
2 2] (1)＝exp[-[φ
G(x)·φ
G(x)+φ
G(z)·φ
G(z)-2φ
G(x)·φ
G(z)]/σ
2 2]＝exp[-[K
G(x,x)+K
G(z,z)-2K
G(x,z)]/σ
2 2]
K
G(P)(x,z)＝φ
G[φ
P(x)]·φ
G[φ
P(z)]＝exp[-||φ
P(x)-φ
P(z)||
2/σ
2 2] (2)＝exp[-[φ
P(x)·φ
P(x)+φ
P(z)·φ
P(z)-2φ
P(x)·φ
P(z)]/σ
2 2]＝exp[-[K
P(x,x)+K
P(z,z)-2K
P(x,z)]/σ
2 2]
Wherein x and z represent two pixels, σ
2represent Gauss's radius of Gaussian mapping for the second time, d
2represent the polynomial parameters of polynomial expression mapping for the second time; In formula (1) (3), Gauss's radius of Gaussian mapping is σ for the first time
1, in formula (2) (4), the polynomial parameters of polynomial expression mapping is for the first time d
1;
Step 3.2: support vector machine is trained to the weight vectors of supported vector machine decision function and threshold alpha
*and b
*.
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