CN105160351A - Semi-monitoring high-spectral classification method based on anchor point sparse graph - Google Patents

Abstract

The invention discloses a semi-monitoring high-spectral classification method based on an anchor point sparse graph, and mainly solves the problems that the computational complexity is high and the storage amount is large during composition in the prior art. The method comprises the steps that 1) a training data set and a mark sample set are obtained from a high-spectral data set; 2) anchor points are selected randomly; 3) a sparse spatial-spectral relation matrix of sample points and the anchor points is established; 4) a Laplacian matrix of the graph is calculated; 5) labels of the anchor points are calculated; and 6) the types of unmarked sample points are obtained according to the obtained labels of the anchor points as well as the sparse spatial-spectral relation matrix. In the composition process, a small amount of anchor points are selected, the sparse spatial-spectral relation matrix is established according to spatial-spectral relation of the sample and anchor points, the complexity in composition of greatly is reduced, and the computation time is shortened. The method can be used for classified identification of high-spectral data.

Description

Based on the semi-supervised hyperspectral classification method of anchor point sparse graph

Technical field

The invention belongs to technical field of image processing, further relate to a kind of sorting technique, can be used for the classification of high spectrum image.

Background technology

In recent years, high-spectrum remote-sensing has become the cutting edge technology in remote sensing direction.Contain abundant space, spectrum and radiation information in high spectrum image, these information characteristics have made it all have huge application prospect in a lot of fields, such as geologic prospecting, precision agriculture, ocean detection, military surveillance etc.

High spectrum resolution remote sensing technique except can obtain determine material or ground properties spectral information except, the spatial relation between atural object can also be disclosed, namely achieve " collection of illustrative plates unification ".This makes high-spectrum remote-sensing can realize the relation obtaining spectral characteristic of ground and retain itself and surrounding atural object simultaneously.In addition, compared with common remote sensing, high-spectrum remote-sensing has the spectral coverage that number is more, wave band is narrower, therefore, it is possible to disclose those material properties that only just can show in narrow range, forms more complete spectroscopic data.These features of high spectrum image and its abundant empty spectrum information comprised, make it have unique advantage at terrain classification with in identifying, can significantly improve the degree of accuracy of Classification and Identification.

High-spectral data terrain classification is a primary study direction in high-spectral data research always.So-called high-spectral data terrain classification, just refer to the information that a kind of basis is collected, provide the data processing technique needing to carry out the affiliated kind of the ground object target of classifying, by giving the mark of a generic for the pixel in each high spectrum image, thus obtain the signature of all pixels.Carry out the space distribution situation that the signature after Classification and Identification can reflect all kinds of atural object, be conducive to comprehensively and be clearly familiar with the region studied, making high spectrum image have using value.

But while the spectral resolution of high-spectrum remote sensing data improves, its data dimension and data volume also significantly increase thereupon, calculating pressure when processing data is obviously increased, this is that the practical application of hyperspectral classification and identification brings difficulty.Many traditional multispectral data sorting algorithms are no longer applicable for high-spectral data, need the feature according to high-spectral data, the sorting algorithm being applicable to high-spectral data propose to reduce operand, improving nicety of grading.Current existing Hyperspectral data classification algorithm, according to whether there being marker samples to participate in training classifier, can by three classes below sorting technique:

(1) unsupervised segmentation algorithm

Unsupervised segmentation method refers to when the mark of all samples is all unknown, and whether only classify to sample according to similar between spectral characteristic in high-spectral data, this sorting technique belongs to a kind of partitioning scheme in fact, such as K mean cluster, ISODATA.Unsupervised segmentation algorithm is also referred to as cluster.The advantage of these class methods does not need marker samples, can use manpower and material resources sparingly.But owing to not having prior imformation, the classification accuracy rate of unsupervised segmentation method is not high, and can not obtain the specific category belonging to atural object.In addition, the computation process of unsupervised segmentation method is more consuming time.

(2) supervised classification algorithm

First Supervised classification algorithm trains according to marker samples, and study obtains a sorter, then classifies to unlabelled sample with this sorter.Support vector machine (SVM) is method more common at present, and the method belongs to a kind of sorting technique of structure based risk minimization.In supervised classification algorithm, marker samples determines the levels of precision of classification, but in high-spectral data, carry out mark to sample needs to spend a large amount of manpower and materials, and obtains a large amount of unmarked sample ratios and be easier to.When marker samples number is less, the classifying quality of supervised classification algorithm is unsatisfactory, and this problem can the popularization of supervision sorting algorithm in Hyperspectral data classification field.

(3) semisupervised classification algorithm

Semisupervised classification algorithm utilizes marker samples and unmarked sample to carry out training classifier simultaneously, and this kind of algorithm can make full use of information in unmarked sample to improve nicety of grading, and improves the Generalization Capability of sorter.Wherein based on the semisupervised classification algorithm of figure, due to can clear and definite description and solve flow pattern hypothesis and to receive publicity gradually in recent years and developing, as LapSVM.But, a lot of for the classification samples quantity of high-spectral data, cause the calculated amount needed for composition and memory space too large, the learning method based on figure is met difficulty in utilization.

Summary of the invention

The object of the invention is to for based on the deficiency in the semisupervised classification algorithm of figure, a kind of semi-supervised hyperspectral classification method based on anchor point sparse graph is proposed, by building the relational matrix of sample and a small amount of anchor point, and utilizing a small amount of marker samples, realizing the classification to high-spectrum remote sensing data.

The technical scheme realizing the object of the invention is: by choosing a small amount of anchor point, the sparse empty genealogical relationship matrix of structure sample point and anchor point, figure Laplacian Matrix is obtained according to this relational matrix, thus calculate the label of anchor point, again according to the relation of sample point label and anchor point label, realize the classification to data.Concrete steps comprise as follows:

(1) training dataset X and marker samples collection Y is obtained from high-spectral data is concentrated.

(2) from training dataset middle random selecting m point, as anchor point, is expressed as label f (the v of sample _k) can be obtained by following formula:

$f\left(x_i\right)=\underset{k=1}{\overset{m}{\Σ}}{Z}_{ik}f\left(v_k\right)$

Wherein, f (v _k) represent the label of anchor point, Z _ikrepresent anchor point label f (v _k) to sample label f (x _i) contribution proportion weights.

(3) the sparse empty genealogical relationship matrix of sample point and anchor point is constructed

3a) for each sample point x _i, according to the space Euclidean distance d (x of this sample point and all anchor points _i, v _k), select on space length with x _is nearest anchor point;

3b) according to the empty genealogical relationship matrix of following formula compute sparse:

$Z_{ik}=\frac{K(x_i,v_k)}{\underset{k^{\&prime;}\&Element;<i>}{\&Sigma;}K(x_i,v_{k^{\&prime;}})},\&ForAll;k\&Element;<i>$

Wherein, kernel function selects gaussian kernel $K(x_i,v_k)=\exp (-||x_i-v_k|{|}_2^2/2{\mathrm{\&sigma;}}^2),<i>\&Subset;\&lsqb;1:m\&rsqb;$ Represent distance sample x _ithe location index of s nearest anchor point.

(4) according to following formula calculating chart Laplacian Matrix:

$\tilde{L}=Z^{T}Z-\left(Z^{T}Z\right){\mathrm{\&Lambda;}}^{-1}\left(Z^{T}Z\right)$

Wherein, represent a diagonal matrix and

(5) label of anchor point is calculated according to following formula:

$U^{*}={({Z_l}^T{Z}_l+\mathrm{\&gamma;}\tilde{L})}^{-1}{Z_l}^{T}Y$

Wherein, represent the submatrix corresponding to l marker samples in Z, γ > 0 represents regular parameter.

(6) according to solving the anchor point label U obtained ^*and sparse empty genealogical relationship matrix Z, the classification of unmarked sample point is calculated by following formula

${\hat{y}}_i=\arg \underset{j\&Element;\{1,...,c\}}{max}{Z}_i{u}_j(i=l+1,...,n)$

Wherein, Z _irepresent i-th row of Z, represent x _iwith the relation weight vector of m anchor point.

Compared with prior art, the present invention has following advantage:

The present invention is by choosing a small amount of anchor point, the sparse empty genealogical relationship matrix of structure sample point and anchor point, overcome existing based on calculated amount and memory space excessive shortcoming during composition in the semi supervise algorithm of figure, figure Laplacian Matrix is obtained according to sparse empty genealogical relationship matrix computations, thus calculate the label of anchor point, again according to the relation of sample point label and anchor point label, obtain the label of sample point, realize the classification to data.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is experiment high-spectral data IndianPines and the authentic signature figure thereof that the present invention emulates use;

Fig. 3 is the classification results comparison diagram of every class when marking 10 samples.

Embodiment

With reference to Fig. 1, the present invention is described in further detail.

Step 1: concentrate from high-spectral data and obtain training dataset X and marker samples collection Y.

1a) concentrate at high-spectral data, the data composing training sample data collection X ∈ R of Stochastic choice 40% ^{d × n}, remaining 60% data are as test sample book data set T ∈ R ^{d × t}, wherein, d represents the dimension of training set sample and test set sample, R ⁿrepresent that N ties up real number space, n represents the sum of training set sample, and t represents the sum of test set sample; In embodiment IndianPines data centralization of the present invention, sample dimension d is 200, and the total n of training set sample is 4146;

1b) in training dataset X, every class random selecting k composition of sample marker samples collection Y ∈ R ^{l × c}, its c is classification number, and l=k × c is marker samples sum, as sample x _ilabel y _iduring=j, Y _ij=1; In embodiment IndianPines data centralization of the present invention, c is that 16, k gets { 3,5,8,10}.

Step 2: from training dataset middle random selecting m point, as anchor point, is expressed as label f (the v of sample _k) can be obtained by following formula:

$f\left(x_i\right)=\underset{k=1}{\overset{m}{\&Sigma;}}{Z}_{ik}f\left(v_k\right)$

Wherein, f (v _k) represent the label of anchor point, Z _ikrepresent anchor point label f (v _k) to sample label f (x _i) contribution proportion weights.In embodiment IndianPines data centralization of the present invention, anchor point number m=1000.

Step 3: the sparse empty genealogical relationship matrix of structure sample point and anchor point

3a) for each sample point x _i, according to the space Euclidean distance d (x of this sample point and all anchor points _i, v _k), select on space length with x _is nearest anchor point.In embodiment IndianPines data centralization of the present invention, make s=3.

3b) according to the empty genealogical relationship matrix of following formula compute sparse:

$Z_{ik}=\frac{K(x_i,v_k)}{\underset{k^{\&prime;}\&Element;<i>}{\&Sigma;}K(x_i,v_{k^{\&prime;}})},\&ForAll;k\&Element;<i>$

Wherein, kernel function selects gaussian kernel $K(x_i,v_k)=\exp (-||x_i-v_k|{|}_2^2/2{\mathrm{\&sigma;}}^2),<i>\&Subset;\&lsqb;1:m\&rsqb;$ Represent distance sample x _ithe location index of s nearest anchor point.

Step 4: according to following formula calculating chart Laplacian Matrix:

$\tilde{L}=Z^{T}Z-\left(Z^{T}Z\right){\mathrm{\&Lambda;}}^{-1}\left(Z^{T}Z\right)$

Wherein, represent a diagonal matrix and

Step 5: the label calculating anchor point according to following formula:

$U^{*}={({Z_l}^T{Z}_l+\mathrm{\&gamma;}\tilde{L})}^{-1}{Z_l}^{T}Y$

Wherein, represent the submatrix corresponding to l marker samples in Z, γ > 0 represents regular parameter.In embodiment IndianPines data centralization of the present invention, make γ=0.01.

Step 6: according to solving the anchor point label U obtained ^*and sparse empty genealogical relationship matrix Z, the classification of unmarked sample point is calculated by following formula

${\hat{y}}_i=\arg \underset{j\&Element;\{1,...,c\}}{max}{Z}_i{u}_j(i=l+1,...,n)$

Wherein, Z _irepresent i-th row of Z, represent x _iwith the relation weight vector of m anchor point.

Effect of the present invention can be further illustrated by following emulation experiment.

1. emulation experiment condition.

This experiment adopts IndianPines data set as experimental data, and adopt software MATLABR2008a as emulation tool, allocation of computer is IntelCorei5/2.4G/4G.

IndianPines high-spectral data 92AV3C: the IndianPines test ground of this scene northwestward, the state of Indiana that to be AVIRIS sensor obtain in June, 1992, this size of data is 145 × 145, each pixel has 220 wave bands, remove containing noisy 20 wave bands, only retain 200 remaining wave bands, these data comprise 16 class atural objects altogether, Fig. 2 (a) gives IndianPines high-spectral data, and Fig. 2 (b) gives the authentic signature figure of IndianPines high-spectral data.

2. emulation experiment content.

Emulation 1, the IndianPines high-spectral data that Fig. 2 (a) gives carries out the emulation experiment under different marker samples number, and contrasts with following three kinds of sorting techniques under the authentic signature that the inventive method is given at Fig. 2 (b): 1) support vector machine (SVM); 2) Laplacian support vector machine (LapSVM); 3) empty spectrum is in conjunction with Laplacian support vector machine (SS-LapSVM).

In experiment, figure regular parameter γ=0.01 of the present invention, anchor point number is m=1000, chooses nearest anchor point number s=3.In table 1, OA represents overall accuracy, and AA represents mean accuracy, and Kappa represents Kappa coefficient.

Table 1 gives marker samples number and gets that { during 3,5,8,10}, the mean value of 20 simulation results is got in experiment respectively.

Table 1: the present invention and the comparing result of other method under different marker samples number

As seen from Table 1, the present invention is { during 3,5,8,10}, be the highest in four kinds of methods that nicety of grading is listed in table in every class marker samples number.And have compared with measure of supervision SVM, the classifying quality of other three kinds of methods will be got well, and illustrates that the use of unmarked sample can improve the precision of classification.Spatial information is very large on the impact of hyperspectral classification, so add the present invention of spatial information and SS-LapSVM method all has greatly improved in nicety of grading.The more important thing is in patterning process, LapSVM and SS-LapSVM needs the figure building n × n scale, and in the present invention, only need build the figure of n × m, the anchor point number m chosen is less than n, and only choose the individual nearest anchor point of s by space length, make figure more sparse, thus reduce required calculated amount greatly, shorten computing time.

Emulation 2, when being 10 to every class marker samples number, uses four kinds of methods in emulation 1 to classify to high-spectral data.The label result of classification as shown in Figure 3.Fig. 3 (a) ~ (d) is respectively the result queue figure of SVM, LapSVM, SS-LapSVM and the inventive method.

As can be seen from Figure 3, the present invention is compared with other method, and the space structure consistance of classification is better, and nicety of grading is high, demonstrates validity of the present invention.

Claims (2)

1., based on a semi-supervised hyperspectral classification method for anchor point sparse graph, comprise the following steps:

(1) training sample data collection X and marker samples classification matrix Y is obtained from high-spectral data is concentrated;

(2) from training sample data collection a middle random selecting m sample, as anchor point, is expressed as anchor point collection wherein, x _ifor i-th training sample in training sample data collection X, n is the number of training sample, v _kfor a kth anchor point in anchor point collection V, m is the number of anchor point;

For the arbitrary sample x in training sample data collection X _i, sample x _ilabel f (x _i) obtained by following formula:

$f\left(x_i\right)=\underset{k=1}{\overset{m}{\&Sigma;}}{Z}_{ik}f\left(v_k\right)$

Wherein, f (x _i) ∈ R ^{1 × c}with f (v _k) ∈ R ^{1 × c}represent sample x respectively _ilabel and anchor point v _klabel, c represents classification number, Z _ikrepresent anchor point label f (v _k) to sample label f (x _i) contribution proportion weights;

(3) the sparse empty genealogical relationship matrix of sample point and anchor point is constructed

3a) for each training sample x _i, calculate the space Euclidean distance of all anchor points in this sample point and anchor point collection V wherein, x _ijrepresent sample x _ia jth feature, v _kjrepresent anchor point v _ka jth feature, d represents sample x _iwith anchor point v _kintrinsic dimensionality, according to result of calculation, select on space length with sample x _is nearest anchor point;

3b) according to the element in following formula compute sparse empty genealogical relationship matrix Ζ:

$Z_{ik}=\frac{K(x_i,v_k)}{\underset{k^{\&prime;}\&Element;<i>}{\&Sigma;}K(x_i,v_{k^{\&prime;}})},\&ForAll;k\&Element;<i>$

Wherein, gaussian kernel function is selected calculate sample x _iwith anchor point v _kspectrum distance from, σ is the parameter of gaussian kernel function, and <i> represents distance sample x _ithe location index set of s nearest anchor point, the span of <i> is [1:m], Ζ ∈ R ^{n × m}represent sparse empty genealogical relationship matrix, n and m represents the number of training sample and the number of anchor point respectively, Z _ikrepresent the element of sparse empty genealogical relationship matrix Ζ i-th row jth row;

(4) according to following formula calculating chart Laplacian Matrix:

$\tilde{L}=Z^{T}Z-\left(Z^{T}Z\right){\mathrm{\&Lambda;}}^{-1}\left(Z^{T}Z\right)$

Wherein, Ζ represents sparse empty genealogical relationship matrix, represent a diagonal matrix and represent figure Laplacian Matrix;

(5) label of anchor point is calculated according to following formula:

$U^{*}={({Z_l}^T{Z}_l+\mathrm{\&gamma;}\tilde{L})}^{-1}{Z_l}^{T}Y$

Wherein, U ^*represent the corresponding label of all anchor points, U ^*=[f (v ₁), f (v ₂) ..., f (v _m)] ^t∈ R ^{m × c}, row k represents the label of a kth anchor point, and c represents classification number, Y expressive notation sample class matrix, Y ∈ R ^{l × c}, the sum of l expressive notation sample, represent the submatrix that row corresponding with l marker samples in sparse empty genealogical relationship matrix Z is formed, γ > 0 represents regular parameter;

(6) according to the anchor point label U obtained ^*and sparse empty genealogical relationship matrix Z, the classification of unmarked sample is calculated by following formula:

${\hat{y}}_i=\arg \underset{j\&Element;\{1,...,c\}}{max}{Z}_i{u}_j,(i=l+1,...,n)$

Wherein, represent the category label of i-th unmarked sample, Z _irepresent i-th row of sparse empty genealogical relationship matrix Z, u _jrepresent anchor point label U ^*jth row.

2. the semi-supervised hyperspectral classification method based on anchor point sparse graph according to claim 1, concentrates from high-spectral data in step (1) and obtains training sample data collection X and marker samples classification matrix Y, comprise the steps:

1a) concentrate at high-spectral data, the data composing training sample data collection X of Stochastic choice 40%, X ∈ R ^{d × n}, remaining 60% data are as test sample book data set T, T ∈ R ^{d × t}, wherein, d represents the intrinsic dimensionality of sample in training sample data collection X and test sample book data set T, R ⁿrepresent that N ties up real number space, n represents the sum of sample in training sample data collection X, and t represents the sum of sample in test sample book data set T;

1b) in training sample data collection X, choose l training sample and obtain marker samples data set wherein, x _ifor marker samples data set X _lin i-th marker samples, the number of l expressive notation sample, to marker samples data set X _lin sample mark, obtain the classification of each marker samples, structure classes mark matrix Y ∈ R ^{l × c}, wherein c represents classification number, and the sum of l expressive notation sample, as marker samples x _ibelong to jth class, i.e. marker samples x _ilabel y _iduring=j, the element of the i-th row jth row in marker samples classification matrix Y is Y _ij=1, other element of this row is zero.