CN103593676A - High-spectral remote-sensing image classification method based on semi-supervision sparse discriminant embedding - Google Patents

Abstract

The invention provides a high-spectral remote-sensing image classification method based on semi-supervision sparse discriminant embedding. The method simplifies the dimension of high-spectral remote-sensing images in a semi-supervision sparse discriminant embedding algorithm, and combines advantages of neighborhood manifold structure and sparsity, wherein the sparse reconstruction relations among samples are reserved, the natural discrimination capability with sparse expression requires no manual selection of neighborhood property values, so that the difficulty in neighborhood parameter selection is reduced to certain extent; and a few of marked training samples and partial unmarked training samples are used to discover intrinsic attributes and low-dimension manifold structure contained in high-dimension data, so that the precision of natural object classification in the high-spectral remote-sensing images can be improved. At the same time, the method of the invention discriminately treat marked data and unmarked data, and the capability of gathering data points of the same natural-object classification is enhanced to the largest degree, thereby further improving the precision of natural object classification in the high-spectral remote-sensing images.

Description

The Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating

Technical field

The present invention relates to hyperspectral data processing method and applied technical field, be specifically related to a kind of Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating.

Background technology

High spectrum resolution remote sensing technique is fast-developing since the eighties in 20th century, its photologging the continuous spectrum of ground object target, the information comprising is abundanter, possessed identify a greater variety of ground object targets and more high precision carry out the ability of target classification.But because high-spectral data forms high-dimensional feature space by a large amount of wave bands, the complexity of most of algorithms is exponential relationship with dimension and increases, it is processed and needs larger calculated amount, and between its wave band, there is high correlation and redundancy, exist dimension very high simultaneously, during classification easily because Hughes phenomenon cannot obtain the problems such as desired result.Scientist finds by research: high-spectral data can be described as be in the stream shape (Manifold) on low-dimensional embedded space, that is: the point of higher dimensional space is observation space Zhang Chengyi stream shape under the acting in conjunction of minority independent variable, if can effectively find the primary variables that it is inherent, just can understand better essential attribute and the feature of high dimensional data.It is the effective way overcoming the above problems that dimension approximately subtracts, and can reduce the dimension of data, obtains the significant low-dimensional of high dimensional data and represents, to understand its inherent structure and subsequent treatment.

Up to now, in the research field of processing at high dimensional data, Chinese scholars has proposed a series of classic algorithm, wherein applying dimension-reduction algorithm more widely mainly comprises: principal component analysis (PCA) (Principal Component Analysis, PCA) and the sub-space learning method such as linear discriminant analysis (Linear Discriminant Analysis, LDA).And PCA and LDA based on hypothesis be that the embedding subspace of high-dimensional data space is linear, be hidden in more difficult being found of inherent attribute in high dimensional data, therefore cannot disclose the low dimensional manifold structure of high-spectral data.Locality preserving projections (Local Preserving Projrction, LPP) and neighborhood keep to embed algorithm (Neighborhood Preserving Embedding, NPE) etc. partial approach is by the local neighbor structure of neighbour figure retain sample, the non-linearity manifold that has kept to a certain extent raw data, but these two kinds of algorithms depend on artificial predefined neighbour figure, the performance obtaining often needs more training sample, exist and as neighbour's parameter, select the problems such as difficulty (as neighbour counts k, the wide σ of core), noise-sensitive, classifying quality is restricted.

Sparse maintenance projection (Sparsity Preserving Projections, SPP) be propose recently a kind of based on rarefaction representation theory without supervision dimension-reduction algorithm.This algorithm is different from the figure building mode (as K-neighbour) of classic method, and it utilizes the sparse Remodeling between sample to build figure, is sparse composition algorithm of overall importance, and is summed up as L1 Norm minimum problem.SPP algorithm not only utilizes the natural discriminating power of rarefaction representation, and without selecting artificially neighbour's parameter value, has alleviated to a certain extent the difficulty that neighbour's parameter is selected.In classification hyperspectral imagery, that often faces is a large amount of Unlabeled datas and relatively less has a flag data.Although SPP algorithm, without training sample is carried out to mark, does not effectively utilize the authentication information providing in marker samples.Therefore, how from flag data and Unlabeled data, to extract useful knowledge and improve learning performance, improve nicety of grading, particularly important in classification hyperspectral imagery field.

Summary of the invention

For prior art above shortcomings, the object of the present invention is to provide a kind of Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, it embeds algorithm by semi-supervised sparse discriminating, and that target in hyperspectral remotely sensed image is carried out to dimension is brief, utilize and have on a small quantity mark training sample and part Using Non-labeled Training Sample to find to contain inherent attribute and the low dimensional manifold structure at high dimensional data, to improve the nicety of grading to atural object classification in target in hyperspectral remotely sensed image.

To achieve these goals, the present invention has adopted following technological means:

The Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, comprises the steps:

1) read in target in hyperspectral remotely sensed image data;

2) each data point in target in hyperspectral remotely sensed image is generated to a spectroscopic data vector according to its spectral band, thereby by the spectroscopic data vector of each data point, formed the spectroscopic data matrix of view picture target in hyperspectral remotely sensed image;

3) from target in hyperspectral remotely sensed image selected part data point as sample number strong point, spectroscopic data vector by each sample number strong point forms sample data matrix, and according to the spectroscopic data vector at priori selected part sample number strong point from sample data matrix, carry out the mark of known atural object classification, generate corresponding sample class label;

4) each the spectroscopic data vector in sample data matrix is carried out to rarefaction representation, try to achieve the optimum sparse coefficient vector of each spectroscopic data vector, thereby obtain the sparse coefficient matrix that sample data matrix is corresponding;

5) by sample data matrix acceptance of the bid, be marked with the spectroscopic data vector at the sample number strong point of vectorial class label, build for measuring the neighbour figure of similarity between sample data matrix spectroscopic data vector;

6) according to neighbour, scheme to calculate neighbour's weight matrix that sample data matrix is corresponding;

7), according to objective optimization function, utilize sparse coefficient matrix that sample data matrix is corresponding and neighbour's weight matrix to calculate the projection matrix of target in hyperspectral remotely sensed image;

8) by projection matrix, target in hyperspectral remotely sensed image is projected to low-dimensional embedded space, obtain the embedding eigenmatrix of target in hyperspectral remotely sensed image;

9) using and embed eigenmatrix as the Classification and Identification feature of atural object classification in target in hyperspectral remotely sensed image, utilize K-nearest neighbour classification algorithm target in hyperspectral remotely sensed image to be carried out to the classification of atural object classification, draw the classification results of atural object classification.

In the above-mentioned Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, as further improvement project, described step 2) be specially:

Spectral reflection characteristic according to different spectral bands to atural object, is converted to by target in hyperspectral remotely sensed image the spectroscopic data matrix X that the capable B of Q is listed as _q={ x ₁, x ₂..., x _q..., x _q} ^t, wherein, Q represents data point bulk and the Q=M * N of target in hyperspectral remotely sensed image, B represents the spectral band number of target in hyperspectral remotely sensed image; Spectroscopic data matrix X _qin each line display target in hyperspectral remotely sensed image in the spectroscopic data value of a data point on each spectral band, each list shows in target in hyperspectral remotely sensed image that each data point is in the spectroscopic data value of a spectral band; x _qrepresent in target in hyperspectral remotely sensed image the spectroscopic data vector that the spectroscopic data value of a data point on each spectral band forms, q ∈ 1,2 ..., Q}; T is matrix transpose symbol.

In the above-mentioned Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, as further improvement project, the sample data matrix that described step 3) obtains is specially:

X={(x ₁,l ₁),(x ₂,l ₂),…,(x _i,l _i),…,(x _C,l _C),x _C+1,x _C+2,…,x _n} ^T；

Wherein, X represents sample data matrix, x _ithe spectroscopic data vector at the sample number strong point that expression is chosen from target in hyperspectral remotely sensed image, l _iexpression is to spectroscopic data vector x _ithe sample class label of mark, i ∈ { 1,2,, n}, n represents to choose the quantity as sample number strong point from target in hyperspectral remotely sensed image, before in sample data matrix X, C spectroscopic data vector has sample class label, remaining n-C spectroscopic data vector no specimen class label.

In the above-mentioned Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, as further improvement project, described step 4) is specially:

41) to any the spectroscopic data vector x in sample data matrix X _i, i ∈ 1,2 ..., n}, n represents from target in hyperspectral remotely sensed image, to choose the quantity as sample number strong point, utilizes other each spectroscopic data vector in sample data matrix X to set up x _isparse linear equation:

X _js _i=s _i,1x ₁+s _i,2x ₂+…+s _i,jx _j+…+s _i,i-1x _i-1+s _i,i+1x _i+1+…+s _i,nx _n；

Wherein, X _js _irepresent spectroscopic data vector x _irarefaction representation vector, X _jrepresent in sample data matrix X except x _ispectroscopic data vector set in addition, s _irepresent spectroscopic data vector x _isparse coefficient vector, that is:

s _i={s _i,1,s _i,2,…,s _i,j,…,s _i,i-1,s _i,i+1,…,s _i,n}；

S _i,jrepresent x _isparse linear equation in corresponding to spectroscopic data vector x _jsparse coefficient, j ∈ 1,2 ..., n} and j ≠ i;

42) according to rarefaction representation constraint condition

with loose constraint condition || x _i-X _js _i||≤ε is to x _isparse linear equation solve, obtain x _itime meet the optimum sparse coefficient vector of rarefaction representation constraint condition and loose constraint condition

for L1 norm operational symbol; || || be Euclidean distance operational symbol; ε is slack variable value, and 0< ε <10;

43) repeating step 41)～42), each the spectroscopic data vector x in sample data matrix X tried to achieve _ioptimum sparse coefficient vector

form sparse coefficient matrix corresponding to sample data matrix

$\tilde{S}=\{{\tilde{S}}_1,{\tilde{S}}_2,...,{\tilde{S}}_i,...,{\tilde{S}}_n\}.$

In the above-mentioned Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, as further improvement project, in described step 5), neighbour figure construction method is specially:

51) in sample data matrix X, any marks the spectroscopic data vector x of directed quantity class label _icorresponding data point, utilizes neighbour's data set of k neighbour's data point structure of this data point

represent spectroscopic data vector x _ithe spectroscopic data of any neighbour's data point vector among k neighbour's data point of institute's corresponding data point, d ∈ 1,2 ..., k};

52) by neighbour's data set knn (x _i) be two parts:

if |

and x _imark has different sample class labels };

knn _S(x _i)=knn(x _i)-knn _D(x _i)；

Wherein, knn _d(x _i) expression spectroscopic data vector x _ik neighbour's data point in come from different neighbour's data subset that the data point of different atural object classifications forms, knn _s(x _i) be neighbour's data set knn (x _i) in except different neighbour's data subset knn _d(x _i) similar neighbour's data subset of forming of part in addition;

53) repeating step 51)～52), the spectroscopic data vector of each mark directed quantity class label in sample data matrix X is built to corresponding similar neighbour's data subset;

53) build neighbour and scheme G _w: for the spectroscopic data vector x of each mark directed quantity class label in sample data matrix X _i, consider in sample data matrix X each other spectroscopic data vector x _j∈ X, j ≠ i, if meet x _j∈ knn _s(x _i), neighbour, scheme G _slimit of middle use connects x _iand x _jcorresponding two data points, have traveled through thus neighbour and have schemed G _sstructure.

In the above-mentioned Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, as further improvement project, the neighbour's weight matrix W in described step 6) _wbe calculated as follows:

Wherein, ω _{w, ij}represent two different spectroscopic data vector x in sample data matrix X _iand x _jbetween weight factor, thereby in sample data matrix X, the weight factor of every two different spectroscopic data vectors forms neighbour's weight matrix W _w; knn _s(x _i) and knn _s(x _j) represent respectively spectroscopic data vector x _iand x _jneighbour, scheme G _sin similar neighbour's data subset; α is similar weight parameter, and α >1.

In the above-mentioned Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, as further improvement project, described step 7) is specially:

Objective function J (V) is:

$J\left(V\right)=\underset{V}{\min }\left[\frac{\mathrm{tr}\left[V^{T}X(D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T)X^{T}V\right]}{\mathrm{tr}\left(V^{T}X{X}^{T}V\right)}\right];$

Wherein,

represent sparse coefficient matrix corresponding to sample data matrix X, W _wrepresent neighbour's weight matrix corresponding to sample data matrix X, V represents projection matrix; D _wfor diagonal matrix, and its diagonal entry

ω _{w, ij}represent two different spectroscopic data vector x in sample data matrix X _iand x _jbetween weight factor, i ∈ 1,2 ..., n}, j ∈ 1,2 ..., n}, n represents to choose the quantity as sample number strong point from target in hyperspectral remotely sensed image; Tr () represent to matrix ask mark operational symbol, T is matrix transpose symbol;

At V ^txX ^tunder the constraint condition of V=E, according to objective function J (V), obtain projection properties equation:

XS _γx ^tv=λ XX ^tv, wherein $S_{\mathrm{\&gamma;}}=D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T;$

Projection properties equation is carried out to generalized eigenvalue to be solved and obtains projection matrix V={v ₁, v ₂..., v _d; Wherein, v ₁, v ₂..., v _dfront d the eigenvalue of maximum λ that expression obtains projection properties equation solution ₁> λ ₂> ... > λ _dd corresponding proper vector, d<B; Wherein, B represents the spectral band number of target in hyperspectral remotely sensed image, E representation unit matrix.

In the above-mentioned Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, as further improvement project, in described step 8), the embedding eigenmatrix of target in hyperspectral remotely sensed image carries out projection by following formula and obtains:

Y=V ^TX _Q，

Wherein, Y represents the spectroscopic data matrix X of target in hyperspectral remotely sensed image _qby projection matrix V, project to the embedding eigenmatrix of low-dimensional embedded space, T is matrix transpose symbol.

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

1, the present invention is based on the Hyperspectral Remote Sensing Imagery Classification method that semi-supervised sparse discriminating embeds, adopting semi-supervised sparse discriminating to embed algorithm, that target in hyperspectral remotely sensed image is carried out to dimension is brief, combine the advantage of neighbour's manifold structure and sparse property, the sparse Remodeling between retain sample not only, and utilize the natural discriminating power of rarefaction representation, without selecting artificially neighbour's parameter value, alleviated to a certain extent the difficulty that neighbour's parameter is selected, utilize and have on a small quantity mark training sample and part Using Non-labeled Training Sample to find to contain inherent attribute and the low dimensional manifold structure at high dimensional data simultaneously, can improve the nicety of grading to atural object classification in target in hyperspectral remotely sensed image.

2, the present invention is based in the Hyperspectral Remote Sensing Imagery Classification method of semi-supervised sparse discriminating embedding, utilized a kind of sparse discriminating incorporation model based on semi-supervised, only by the low volume data point in data sample, mark, and bound fraction unlabeled data point is learnt, can realize the atural object category classification to view picture target in hyperspectral remotely sensed image, be suitable for large, the indistinct degree of data volume target in hyperspectral remotely sensed image data high, that ground known sample data are few to carry out the classification of atural object classification.

3, the present invention is based in the Hyperspectral Remote Sensing Imagery Classification method of semi-supervised sparse discriminating embedding, by distinguishing treat labeled data with without labeled data, difference by weight parameter arrange outstanding labeled data with without labeled data in the difference that obtains low-dimensional diagnostic characteristics significance level, realization still keeps its neighbor relationships between identical atural object categorical data point in low-dimensional embedded space, gathering property between the data point of the identical atural object classification of maximum increase, thereby help on the other hand to improve the nicety of grading to atural object classification in target in hyperspectral remotely sensed image.

Accompanying drawing explanation

Fig. 1 is the process flow diagram that the present invention is based on the Hyperspectral Remote Sensing Imagery Classification method of semi-supervised sparse discriminating embedding;

Fig. 2 is Indian Pine data centralization " Hay_windrowed " in the embodiment of the present invention two, " Soybeans_min ", " Woods ", " Corn_notill ", " Grass_pasture ", the distribution on ground situation map of " Grass_trees " six kinds of true atural object classifications;

Fig. 3 is the classifying quality figure that adopts PCA+1NN classification to obtain to Indian Pine data set in the embodiment of the present invention two;

Fig. 4 is the classifying quality figure that adopts LDA+1NN classification to obtain to Indian Pine data set in the embodiment of the present invention two;

Fig. 5 is the classifying quality figure that adopts NPE+1NN classification to obtain to Indian Pine data set in the embodiment of the present invention two;

Fig. 6 is the classifying quality figure that adopts SPP+1NN classification to obtain to Indian Pine data set in the embodiment of the present invention two;

Fig. 7 is the classifying quality figure that adopts SSDE+1NN method (being the inventive method) classification to obtain to Indian Pine data set in the embodiment of the present invention two;

Embodiment

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

In order to solve supervise algorithm, need to there is in a large number flag data and without supervise algorithm, there is no effectively to utilize the deficiency that has the authentication information that flag data provides, the present invention proposes a kind of based on semi-supervised sparse discriminating embedding (Semi-supervised Sparsity Discriminant Embedding, can be abbreviated as SSDE) Hyperspectral Remote Sensing Imagery Classification method, the method combines the advantage of neighbour's manifold structure and sparse property, the sparse Remodeling between retain sample not only, and utilize the natural discriminating power of rarefaction representation, without selecting artificially neighbour's parameter value, alleviated to a certain extent the difficulty that neighbour's parameter is selected, utilize simultaneously and have on a small quantity mark training sample and a large amount of Using Non-labeled Training Sample to find to contain inherent attribute and the low dimensional manifold structure at high dimensional data, thereby improve the nicety of grading to atural object classification in target in hyperspectral remotely sensed image.

With reference to Fig. 1, the present invention is based on the Hyperspectral Remote Sensing Imagery Classification method that semi-supervised sparse discriminating embeds, comprise the steps:

1) read in target in hyperspectral remotely sensed image data;

2) each data point in target in hyperspectral remotely sensed image is generated to a spectroscopic data vector according to its spectral band, thereby by the spectroscopic data vector of each data point, formed the spectroscopic data matrix of view picture target in hyperspectral remotely sensed image;

3) from target in hyperspectral remotely sensed image selected part data point as sample number strong point, spectroscopic data vector by each sample number strong point forms sample data matrix, and according to the spectroscopic data vector at priori selected part sample number strong point from sample data matrix, carry out the mark of known atural object classification, generate corresponding sample class label;

4) each the spectroscopic data vector in sample data matrix is carried out to rarefaction representation, try to achieve the optimum sparse coefficient vector of each spectroscopic data vector, thereby obtain the sparse coefficient matrix that sample data matrix is corresponding;

5) by sample data matrix acceptance of the bid, be marked with the spectroscopic data vector at the sample number strong point of vectorial class label, build for measuring the neighbour figure of similarity between sample data matrix spectroscopic data vector;

6) according to neighbour, scheme to calculate neighbour's weight matrix that sample data matrix is corresponding;

7), according to objective optimization function, utilize sparse coefficient matrix that sample data matrix is corresponding and neighbour's weight matrix to calculate the projection matrix of target in hyperspectral remotely sensed image;

8) by projection matrix V, target in hyperspectral remotely sensed image is projected to low-dimensional embedded space, obtain the embedding eigenmatrix Y of target in hyperspectral remotely sensed image;

9) using and embed eigenmatrix Y as the Classification and Identification feature of atural object classification in target in hyperspectral remotely sensed image, utilize K-nearest neighbour classification algorithm target in hyperspectral remotely sensed image to be carried out to the classification of atural object classification, draw the classification results of atural object classification.

As the Hyperspectral Remote Sensing Imagery Classification further improvements in methods scheme that the present invention is based on semi-supervised sparse discriminating embedding, target in hyperspectral remotely sensed image data have reflected the spectral reflection characteristic of atural object to different-waveband, according to the capable N of the data point bulk M * N(M of a target in hyperspectral remotely sensed image row data point) and spectral band count B, if make Q=M * N, each data point in target in hyperspectral remotely sensed image can be generated to a spectroscopic data vector according to its spectral band, thereby target in hyperspectral remotely sensed image is converted to the spectroscopic data matrix of the capable B row of Q.Thus, described step 2) be specially:

Spectral reflection characteristic according to different spectral bands to atural object, is converted to by target in hyperspectral remotely sensed image the spectroscopic data matrix X that the capable B of Q is listed as _q={ x ₁, x ₂..., x _q..., x _q} ^t, wherein, Q represents data point bulk and the Q=M * N of target in hyperspectral remotely sensed image, B represents the spectral band number of target in hyperspectral remotely sensed image; Spectroscopic data matrix X _qin each line display target in hyperspectral remotely sensed image in the spectroscopic data value of a data point on each spectral band, each list shows in target in hyperspectral remotely sensed image that each data point is in the spectroscopic data value of a spectral band; x _qrepresent in target in hyperspectral remotely sensed image the spectroscopic data vector that the spectroscopic data value of a data point on each spectral band forms, q ∈ 1,2 ..., Q}; T is matrix transpose symbol.

As the Hyperspectral Remote Sensing Imagery Classification further improvements in methods scheme that the present invention is based on semi-supervised sparse discriminating embedding, in the inventive method, that selected part data point forms sample data matrix as sample number strong point from target in hyperspectral remotely sensed image, and in these sample number strong points, can learn according to priori the atural object classification at part sample number strong point wherein, and be marked.Therefore the sample data matrix that, described step 3) obtains is specially:

X={(x ₁,l ₁),(x ₂,l ₂),…,(x _i,l _i),…,(x _C,l _C),x _C+1,x _C+2,…,x _n} ^T；

Wherein, X represents sample data matrix, x _ithe spectroscopic data vector at the sample number strong point that expression is chosen from target in hyperspectral remotely sensed image, l _iexpression is to spectroscopic data vector x _ithe sample class label of mark, i ∈ { 1,2,, n}, n represents to choose the quantity as sample number strong point from target in hyperspectral remotely sensed image, before in sample data matrix X, C spectroscopic data vector has sample class label, remaining n-C spectroscopic data vector no specimen class label.That is to say, the quantity of choosing the spectroscopic data vector that carries out known atural object classification mark according to priori from sample data matrix is designated as C.

As the Hyperspectral Remote Sensing Imagery Classification further improvements in methods scheme that the present invention is based on semi-supervised sparse discriminating embedding, the present invention has adopted the method for rarefaction representation from sample data matrix, to extract the inherent popular structure feature of the data point of different atural object classifications in whole target in hyperspectral remotely sensed image.Rarefaction representation (Sparsity Representation, SR; Can referring to prior art document " FKInaba; EOTSalles.Face Recognition Based on Sparse Representation and Joint Sparsity Model with Matrix Completion[J] .IEEE Latin America Transactions; 2012.Vol.10 (1): 1344-1351. ") at first for compression and the expression of signal, for incomplete and strongly disturbing data, there is good robustness, be now successfully applied to the fields such as signal processing, statistics and pattern-recognition.Its core concept is by signal x ∈ R ^mbe decomposed into a series of base signals

linear combination

and wish s as much as possible _icoefficient is that 0(is vectorial S=[s ₁, s ₂..., s _n] ^tsparse as far as possible), the signal with nonzero coefficient has disclosed principal character and the immanent structure of original signal.Its mathematical model is as follows:

$\underset{s_i}{\min }\left|\right|s_i|{|}_0;s.t.x_i=X_j{s}_i;$

In formula, X=[x ₁, x ₂..., x _n] ∈ R ^{m * n}for base signal matrix, s _i∈ R ⁿwith removing signal x in base signal matrix X _iremaining sample of signal set X _jcarry out the sparse coefficient vector of rarefaction representation reconstruction, || s _i|| ₀represent s _il0 norm, for weighing s _isparse property.Wherein the L0 norm of vector represents the number of nonzero element in vector.Therefore but owing to minimizing L0 norm problem, be a NP-hard problem, solve difficulty, at coefficient enough under sparse condition, L0 Norm minimum problem can be converted into L1 Norm minimum problem:

$\underset{s_i}{\min }{\left|\right|s}_i{\left|\right|}_1;s.t.x_i=X_j{s}_i,1={\left\{1\right\}}^T{s}_i;$

In formula, || s _i|| ₁represent sparse coefficient vector s _il1 norm, { 1} ∈ R ⁿrepresent complete 1 vector.Vector s _il1 norm can be expressed as: ${\mathrm{\&Sigma;}}_{i=1}^n\left|s_i\right|,$ ? $s_i=[s_{i1},...,s_{\mathrm{ij}},...,s_{\mathrm{ii}-1},0,s_{\mathrm{ii}+1},...,s_{\mathrm{in}}{]}^T\&Element;R^n;$ S _ijexpression is to sample x _ithe sparse coefficient being reconstructed, that is:

x _i=s _i,1x ₁+s _i,2x ₂+…+s _i,jx _j+…+s _i,i-1x _i-1+s _i,i+1x _i+1+…+s _i,nx _n；

For each x _i∈ X, calculates corresponding sparse coefficient vector s _i, just can obtain the sparse coefficient matrix S=[s of training sample ₁, s ₂..., s _n].

Yet, owing to may having noise in high-spectrum remote sensing data, therefore may cause x _irarefaction representation there is error.For this reason, the present invention is based in the Hyperspectral Remote Sensing Imagery Classification method of semi-supervised sparse discriminating embedding, considered may have noise error problem in high-spectrum remote sensing, spectroscopic data vector has been carried out to rarefaction representation solution procedure and introduced the loose constraint condition that slack variable ε builds.Based on this, described step 4) is specially:

41) to any the spectroscopic data vector x in sample data matrix X _i, i ∈ 1,2 ..., n}, n represents from target in hyperspectral remotely sensed image, to choose the quantity as sample number strong point, utilizes other each spectroscopic data vector in sample data matrix X to set up x _isparse linear equation:

X _js _i=s _i,1x ₁+s _i,2x ₂+…+s _i,jx _j+…+s _i,i-1x _i-1+s _i,i+1x _i+1+…+s _i,nx _n；

Wherein, X _js _irepresent spectroscopic data vector x _irarefaction representation vector, X _jrepresent in sample data matrix X except x _ispectroscopic data vector set in addition, s _irepresent spectroscopic data vector x _isparse coefficient vector, that is:

s _i={s _i,1,s _i,2,…,s _i,j,…,s _i,i-1,s _i,i+1,…,s _i,n}；

S _i,jrepresent x _isparse linear equation in corresponding to spectroscopic data vector x _jsparse coefficient, j ∈ 1,2 ..., n} and j ≠ i;

42) according to rarefaction representation constraint condition

with loose constraint condition || x _i-X _js _i||≤ε is to x _isparse linear equation solve, obtain x _itime meet the optimum sparse coefficient vector of rarefaction representation constraint condition and loose constraint condition

for L1 norm operational symbol, || s _i|| ₁represent sparse coefficient vector s _il1 norm; || || be Euclidean distance operational symbol, || x _i-X _js _i|| represent to ask spectroscopic data vector x _iwith its rarefaction representation vector X _js _ieuclidean distance value; ε is slack variable value, and 0< ε <10;

43) repeating step 41)～42), each the spectroscopic data vector x in sample data matrix X tried to achieve _ioptimum sparse coefficient vector

form sparse coefficient matrix corresponding to sample data matrix

$\tilde{S}=\{{\tilde{S}}_1,{\tilde{S}}_2,...,{\tilde{S}}_i,...,{\tilde{S}}_n\}.$

As the Hyperspectral Remote Sensing Imagery Classification further improvements in methods scheme that the present invention is based on semi-supervised sparse discriminating embedding, in described step 5), neighbour figure construction method is specially:

51) in sample data matrix X, any marks the spectroscopic data vector x of directed quantity class label _icorresponding data point, utilizes neighbour's data set of k neighbour's data point structure of this data point

represent spectroscopic data vector x _ithe spectroscopic data of any neighbour's data point vector among k neighbour's data point of institute's corresponding data point, d ∈ 1,2 ..., k};

52) by neighbour's data set knn (x _i) be two parts:

if

and x _imark has different sample class labels };

knn _S(x _i)=knn(x _i)-knn _D(x _i)；

Wherein, knn _d(x _i) expression spectroscopic data vector x _ik neighbour's data point in come from different neighbour's data subset that the data point of different atural object classifications forms, knn _s(x _i) be neighbour's data set knn (x _i) in except different neighbour's data subset knn _d(x _i) similar neighbour's data subset of forming of part in addition;

53) repeating step 51)～52), the spectroscopic data vector of each mark directed quantity class label in sample data matrix X is built to corresponding similar neighbour's data subset;

53) build neighbour and scheme G _w: for the spectroscopic data vector x of each mark directed quantity class label in sample data matrix X _i, consider in sample data matrix X each other spectroscopic data vector x _j∈ X, j ≠ i, if meet x _j∈ knn _s(x _i), neighbour, scheme G _slimit of middle use connects x _iand x _jcorresponding two data points, have traveled through thus neighbour and have schemed G _sstructure.

Neighbour, scheme G _sin, a spectroscopic data vector x _isimilar neighbour's data subset knn _s(x _i) in may to have part spectroscopic data vector to state be not mark class label, but data point corresponding to these spectroscopic datas vectors all with spectroscopic data vector x _icorresponding data point is enough near, very possible and spectroscopic data vector x _ibelong to identical atural object classification, embodied thus the similarity between spectroscopic data vector in sample data matrix.

As the Hyperspectral Remote Sensing Imagery Classification further improvements in methods scheme that the present invention is based on semi-supervised sparse discriminating embedding, the neighbour's weight matrix W in described step 6) _wbe calculated as follows:

Wherein, ω _{w, ij}represent two different spectroscopic data vector x in sample data matrix X _iand x _jbetween weight factor, thereby in sample data matrix X, the weight factor of every two different spectroscopic data vectors forms neighbour's weight matrix W _w; knn _s(x _i) and knn _s(x _j) represent respectively spectroscopic data vector x _iand x _jneighbour, scheme G _sin similar neighbour's data subset; α is similar weight parameter, and α >1.

If two data points have identical class label, show that two data points belong to identical atural object classification, in order to embody labeled data point (data point with sample class label) by weight factor, in the otherness that obtains low-dimensional diagnostic characteristics significance level, neighbour is schemed to G with unlabeled data point (data point of no specimen class label) _sthe value that weight factor is given on the limit of middle connection unlabeled data point is 1, and neighbour is schemed to G _shigher similar weight parameter α is given on limit between the data point of the identical atural object classification of middle connection, with similar weight parameter α, give prominence to the effect of the data point of the identical atural object classification marking, the data point that makes Dimensionality Reduction process identical atural object classification in the low-dimensional embedded space obtaining is assembled more; Therefore the value of α is greater than 1, between data point with realization identical atural object classification in low-dimensional embedded space, still keep its neighbor relationships, distance between the data point of different atural object classifications maximizes as far as possible, gathering property between the data point of the identical atural object classification of maximum increase, thus help on the other hand to improve the nicety of grading to atural object classification in target in hyperspectral remotely sensed image.The value of similar weight parameter α is also unsuitable excessive, and generally, the span of similar weight parameter α is that 1< α <100 is comparatively suitable.

As the Hyperspectral Remote Sensing Imagery Classification further improvements in methods scheme that the present invention is based on semi-supervised sparse discriminating embedding, described step 7) is specially:

Objective function J (V) is:

$J\left(V\right)=\underset{V}{\min }\left[\frac{\mathrm{tr}\left[V^{T}X(D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T)X^{T}V\right]}{\mathrm{tr}\left(V^{T}X{X}^{T}V\right)}\right];$

Wherein,

represent sparse coefficient matrix corresponding to sample data matrix X, W _wrepresent neighbour's weight matrix corresponding to sample data matrix X, V represents projection matrix; D _wfor diagonal matrix, and its diagonal entry

ω _{w, ij}represent two different spectroscopic data vector x in sample data matrix X _iand x _jbetween weight factor, i ∈ 1,2 ..., n}, j ∈ 1,2 ..., n}, n represents to choose the quantity as sample number strong point from target in hyperspectral remotely sensed image; Tr () represent to matrix ask mark operational symbol,

expression is asked for mark, tr (V ^txX ^tv) represent to ask for V ^txX ^tthe mark of V; T is matrix transpose symbol.

Above-mentioned objective function J (V) has used for reference sparse maintenance projection (SparsityPreservingProjections, SPP).SPP is by sparse reconstruction processing, also retain sample overall situation Near-neighbor Structure in the time of the sparse reconfiguration information of retain sample, can from original sample, extract and possess certain distinctive internal characteristics like this, and do not need to select artificially neighbour's parameter value (can referring to prior art document " Y Fu; S C Yan; T S Huang.Classification and feature extraction by simplexization[J] .IEEE Trans.on Information Forensics and Security; 2008, Vol.3 (1): 91-100. ").Objective function can be defined as thus:

$J\left(v\right)=\underset{V}{\min }{\left|\right|V^T{x}_i-X{\tilde{s}}_i\left|\right|}^2{\mathrm{\&omega;}}_{w,\mathrm{ij}};$

The simple algebraic operation of process:

$\begin{array}{c}\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}{\left|\right|V^T{x}_i-V^{T}X{\tilde{s}}_j\left|\right|}^2{\mathrm{\&omega;}}_{w,\mathrm{ij}}\\ =\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}(V^T{x}_i-V^{T}X{\tilde{s}}_j){(V^T{x}_i-V^{T}X{\tilde{s}}_j)}^T{\mathrm{\&omega;}}_{w,\mathrm{ij}}\\ =V^T\left(\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}(x_i-X{\tilde{s}}_j){\mathrm{\&omega;}}_{w,\mathrm{ij}}{(x_i-X{\tilde{s}}_j)}^T\right)V\\ =V^T\left(\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}({\mathrm{Xe}}_i-X{\tilde{s}}_j){\mathrm{\&omega;}}_{w,\mathrm{ij}}{(X{e}_i-X{\tilde{s}}_j)}^T\right)V\\ =V^{T}X(\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}(e_i{\mathrm{\&omega;}}_{w,\mathrm{ij}}{e}_i^T-e_i{\mathrm{\&omega;}}_{w,\mathrm{ij}}{\tilde{s}}_j^T-{\tilde{s}}_j{\mathrm{\&omega;}}_{w,\mathrm{ij}}{e}_i^T+{\tilde{s}}_j{\mathrm{\&omega;}}_{w,\mathrm{ij}}{\tilde{s}}_j^T)X^{T}V\\ =V^{T}X(\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}{e}_i{\mathrm{\&omega;}}_{w,\mathrm{ij}}{e}_i^T-\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}{e}_{\mathrm{ij}}{\mathrm{\&omega;}}_{w,\mathrm{ij}}{\tilde{s}}_j^T-\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}{\tilde{s}}_j{\mathrm{\&omega;}}_{w,\mathrm{ij}}{e}_i^T+\underset{\mathrm{ij}}{\mathrm{\&Sigma;}}{s}_j{\mathrm{\&omega;}}_{w,\mathrm{ij}}{s}_j^T)X^{T}V\\ =V^{T}X(D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T)X^{T}V\\ =V^{T}X{S}_{\mathrm{\&gamma;}}{X}^{T}V\end{array}$

Wherein, e _ifor n-dimensional vector (wherein i element is 1, and all the other are 0); Just obtained thus objective function J (V):

$J\left(V\right)=\underset{V}{\min }\left[\frac{\mathrm{tr}\left[V^{T}X(D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T)X^{T}V\right]}{\mathrm{tr}\left(V^{T}X{X}^{T}V\right)}\right];$

For fear of degenerate solution, increase constraint condition tr (V ^txX ^tv)=1, i.e. V ^txX ^tv=E, simultaneously easy in order to explain, order $S_{\mathrm{\&gamma;}}=D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T;$ Objective function can be expressed as:

J(V)=argminV ^TXS _γX ^TV，s.t.V ^TXX ^TV=E；

It is carried out to lagrange's method of multipliers and solve, another J (V) is zero to the partial derivative of V, can obtain:

$\frac{\&PartialD;}{\&PartialD;V}(V^{T}X{S}_{\mathrm{\&gamma;}}{X}^{T}V-\mathrm{\&lambda;}(V^{T}X{X}^{T}V-E))=0;$

Above formula can be expressed as following generalized eigenvalue Solve problems:

XS _γX ^TV=λXX ^TV。

Therefore, at V ^txX ^tunder the constraint condition of V=E, according to objective function J (V), obtain projection properties equation:

XS _γx ^tv=λ XX ^tv, wherein $S_{\mathrm{\&gamma;}}=D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T;$

Projection properties equation is carried out to generalized eigenvalue to be solved and obtains projection matrix V={v ₁, v ₂..., v _d; Wherein, v ₁, v ₂..., v _dfront d the eigenvalue of maximum λ that expression obtains projection properties equation solution ₁> λ ₂> ... > λ _dd corresponding proper vector, d<B; Wherein, B represents the spectral band number of target in hyperspectral remotely sensed image, E representation unit matrix.

The selection of proper vector number d can be calculated by following formula:

$\frac{{\mathrm{\&lambda;}}_1+{\mathrm{\&lambda;}}_1+...+{\mathrm{\&lambda;}}_d}{{\mathrm{\&lambda;}}_1+{\mathrm{\&lambda;}}_1+...+{\mathrm{\&lambda;}}_B}\&GreaterEqual;\mathrm{\&eta;};$

Wherein, η is energy reserving coefficient, from eigenwert, selects to keep d the eigenwert of energy η, gets 0< η≤1, and then selects d eigenvalue of maximum characteristic of correspondence vector v ₁, v ₂..., v _d, form projection matrix V={v ₁, v ₂..., v _d.

As the Hyperspectral Remote Sensing Imagery Classification further improvements in methods scheme that the present invention is based on semi-supervised sparse discriminating embedding, in described step 8), the embedding eigenmatrix of target in hyperspectral remotely sensed image carries out projection by following formula and obtains:

Y=V ^TX _Q，

Wherein, Y represents the spectroscopic data matrix X of target in hyperspectral remotely sensed image _qby projection matrix V, project to the embedding eigenmatrix of low-dimensional embedded space, T is matrix transpose symbol.Thus, utilize the spectroscopic data matrix X of projection matrix V to target in hyperspectral remotely sensed image _qthe logical brief embedding eigenmatrix Y obtaining of dimension that carries out, can find better the inherent manifold structure of data, Extraction and discrimination feature, therefore obtain better projecting direction, more be conducive to classification, even if therefore utilize simple classification processing scheme, using and embed eigenmatrix Y as the Classification and Identification feature of atural object classification in target in hyperspectral remotely sensed image, can obtain better nicety of grading.In the inventive method, adopted K-nearest neighbour classification algorithm target in hyperspectral remotely sensed image to be carried out to the classification of atural object classification.

The present invention is based on the Hyperspectral Remote Sensing Imagery Classification method that semi-supervised sparse discriminating embeds, adopt semi-supervised sparse discriminating to embed algorithm (Semi-supervised Sparsity Discriminant Embedding, referred to as SSDE) that target in hyperspectral remotely sensed image is carried out to dimension is brief, in conjunction with K-nearest neighbour classification algorithm, realizes the classification to atural object classification in target in hyperspectral remotely sensed image.In order to verify the validity of the inventive method, below by two embodiment, on Indian Pine and Washington DC Mall target in hyperspectral remotely sensed image data set, test, and under identical sample condition, by the present invention is based on Hyperspectral Remote Sensing Imagery Classification method that semi-supervised sparse discriminating embeds with based on PCA(Principal Component Analysis, principal component analysis (PCA)), LDA(Linear Discriminant Analysis, linear discriminant analysis), NPE(Neighborhood Preserving Embedding, neighborhood keeps embedding) and SPP(Sparsity Preserving Projections, sparse maintenance projection) the constructed Hyperspectral Remote Sensing Imagery Classification method of algorithm compares.In experiment, by adjusting its parameter, make each algorithm reach optimum efficiency, be specifically set to: PCA drops to 50 dimensions, LDA dimension drops to classification number-1 dimension, NPE neighbour k=5; Sorting technique of the present invention and all adopt arest neighbors sorting algorithm to classify based on PCA, LDA, NPE, the constructed sorting technique of SPP algorithm, Baseline represents raw data directly to use arest neighbors sorting algorithm (being the K-nearest neighbour classification algorithm of K=1) to classify.

Embodiment mono-:

The Washington DC Mall target in hyperspectral remotely sensed image data set adopting in this experiment is the regional area on Washington D.C. country square.This data set has 191 wave bands, and wave band is spaced apart 10nm, and spatial resolution is 3m.Wherein known atural object classification comprises " building ", " woods ", " (cobbled path) path ", " road ", " ”,“ lake, lawn " and " shade " 7 classes.In experiment, for the every kind of sorting technique that participates in contrast, carry out four kinds of classification experiments respectively, four kinds of classification experiments choose at random 2 respectively from every class atural object, 4, 6, 8 data points are as there being classification point, from residue training sample, choose at random 60 data without class label as unmarked sample, form training sample set, remaining total data point is as test sample book, four kinds of classification experiments are remembered respectively and are 2-lab, 4-lab, 6-lab, 8-lab, the every kind of sorting technique that participates in contrast gets for the final nicety of grading of each classification experiments the mean value that repeats to test ten gained niceties of grading.At Washington DC Mall data set, test, use respectively PCA, LDA, NPE, SPP and SSDE algorithm (in basic invention sorting technique, the semi-supervised sparse discriminating that adopts embeds algorithm) to carry out dimensionality reduction to it, then utilize arest neighbors sorting algorithm (being the K-nearest neighbour classification algorithm of K=1) to classify.Table 1 listed various different sorting techniques in this experiment the final nicety of grading to Washington DC Mall data set.

Table 1

In table 1, Baseline represents raw data directly by arest neighbors sorting algorithm, to classify, PCA+1NN, LDA+1NN, NPE+1NN, SPP+1NN represent respectively based on PCA, LDA, NPE, SPP in conjunction with the constructed Hyperspectral Remote Sensing Imagery Classification method of arest neighbors sorting algorithm, and SSDE+1NN represents the present invention is based on the Hyperspectral Remote Sensing Imagery Classification method that semi-supervised sparse discriminating embeds.As can be seen from Table 1, training sample is more, and the prior imformation obtaining from sample is just more comprehensive, just can more effectively reflect the low dimensional manifold structure of data, and the overall classification accuracy of various sorting techniques also increases.LDA+1NN is supervise algorithm, utilize the classification information Extraction and discrimination feature that has marker samples, so nicety of grading is higher than PCA+1NN.Although NPE+1NN and SPP+1NN are the local neighbor structures of having utilized training data, but SPP+1NN extracts and possesses certain distinctive low dimensional feature by the sparse reconfiguration information of retain sample time from training sample, so classifying quality is better than NPE+1NN.SSDE+1NN sorting technique of the present invention is when the sparse Remodeling that utilizes training sample is built figure, can make full use of and have on a small quantity classification mark and a large amount of unmarked training sample, discovery is hidden in the inherent geometry in high-spectral data, more be conducive to dimensionality reduction, the additive method nicety of grading of comparing has raising in various degree, can obtain optimal classification precision at lower dimension.

Embodiment bis-:

The Indian Pine target in hyperspectral remotely sensed image data set adopting in experiment is a farming region that has covered northwest, American I ndiana state.The data point space size of this data set is 145 * 145, has the known atural object classification of 220 wave bands and 17 classes.Consider the impact of noise, this experiment is therefrom chosen 200 wave bands and is selected 6 classes to test from the more atural object classification of data point, this 6 class the 5th classification is respectively " Hay_windrowed ", " Soybeans_min ", " Woods ", " Corn_notill ", " Grass_pasture ", " Grass_trees ".In experiment, for the every kind of sorting technique that participates in contrast, carry out four kinds of classification experiments respectively, four kinds of classification experiments choose at random 2 respectively from every class atural object, 4, 6, 8 data points that have class label, from residue training sample, choose at random 60 data without class label as unmarked sample, form training sample set, remaining total data point is as test sample book collection, four kinds of classification experiments are remembered respectively and are 2-lab, 4-lab, 6-lab, 8-lab, the every kind of sorting technique that participates in contrast gets for the final nicety of grading of each classification experiments the mean value that repeats to test ten gained niceties of grading.Table 2 listed various different sorting techniques in this experiment the final nicety of grading to Indian Pine data set.

Table 2

In table 2, Baseline represents raw data directly by arest neighbors sorting algorithm, to classify, PCA+1NN, LDA+1NN, NPE+1NN, SPP+1NN represent respectively based on PCA, LDA, NPE, SPP in conjunction with the constructed Hyperspectral Remote Sensing Imagery Classification method of arest neighbors sorting algorithm, and SSDE+1NN represents the present invention is based on the Hyperspectral Remote Sensing Imagery Classification method that semi-supervised sparse discriminating embeds.By table 2, can be drawn, the nicety of grading of SSDE+1NN sorting technique of the present invention is still the highest, SSDE+1NN sorting technique of the present invention is in the situation that having marker samples fewer, not only can utilize the natural distinguishing ability of rarefaction representation, and can utilize a small amount of mark and a large amount of unmarked sample to find the manifold structure in data, to improve nicety of grading.The present invention is sorted in 2,4,6,8 situations that have a mark training sample, and its final nicety of grading has improved respectively 4.19%, 7.75%, 6.72 and 10.18% than SPP+1NN sorting technique, and can reach quickly higher classification rate.

What Fig. 2～Fig. 7 showed is Indian Pine data centralization " Hay_windrowed ", " Soybeans_min ", " Woods ", " Corn_notill ", " Grass_pasture ", the distribution on ground situation of " Grass_trees " six kinds of true atural object classifications, and the experiment classifying quality figure that with PCA, LDA, NPE, SPP and SSDE algorithm, it is carried out dimensionality reduction, then utilizes the conscientious classification of arest neighbors sorting algorithm to obtain respectively.Wherein, Fig. 2 is Indian Pine data centralization " Hay_windrowed ", " Soybeans_min ", " Woods ", " Corn_notill ", " Grass_pasture ", the distribution on ground situation map of " Grass_trees " six kinds of true atural object classifications; The classifying quality figure of Fig. 3 for adopting PCA+1NN classification to obtain to Indian Pine data set; The classifying quality figure of Fig. 4 for adopting LDA+1NN classification to obtain to Indian Pine data set; The classifying quality figure of Fig. 5 for adopting NPE+1NN classification to obtain to Indian Pine data set; The classifying quality figure of Fig. 6 for adopting SPP+1NN classification to obtain to Indian Pine data set; The classifying quality figure of Fig. 7 for adopting SSDE+1NN method (being sorting technique of the present invention) classification to obtain to Indian Pine data set.From Fig. 2～Fig. 7, can draw, SPP compare PCA, LDA, NPE scheduling algorithm, nicety of grading is improved to some extent, embody and utilize rarefaction representation to carry out the advantage of nature discriminating power, but because its essence remains without supervise algorithm, the authentication information that can not effectively utilize marker samples to provide, so classifying quality lifting is relatively limited.In the sparse Remodeling of the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating that the present invention proposes between retain sample, by utilizing, there are on a small quantity mark and a large amount of Using Non-labeled Training Sample Extraction and discrimination feature, comparing, to obtain classifying quality figure better for other algorithms, and nicety of grading also has obvious lifting.

In sum, by the above embodiments one and embodiment bis-, can see, in Hyperspectral Remote Sensing Imagery Classification, that often faces is a large amount of Unlabeled datas and relatively less has a flag data, and mark training sample cost is higher, therefore be sometimes unpractical, how introduce half prison and learn to promote nicety of grading and seem particularly important.The present invention proposes a kind of new Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, the method combines the advantage of neighbour's manifold structure and sparse property, the sparse Remodeling between retain sample not only, and utilize the natural discriminating power of rarefaction representation, without selecting artificially neighbour's parameter value, alleviated to a certain extent the difficulty that neighbour's parameter is selected, by introducing a small amount of markd training sample and a large amount of Using Non-labeled Training Sample, obtain the inherent manifold structure of data simultaneously, realizing diagnostic characteristics extracts, can improve the nicety of grading to atural object classification in target in hyperspectral remotely sensed image, more be conducive to classification.At above-described embodiment, the classification experiments result of Indian Pine and Washington DC Mall target in hyperspectral remotely sensed image data set is shown, the sorting technique that the present invention proposes can utilize rarer mark training sample find in target in hyperspectral remotely sensed image in pent up structure.In the situation that choose at random 2,4,6,8, there are classification mark and 60 data without classification mark as training sample, the final nicety of grading best result of sorting technique of the present invention has not reached 77.36% and 97.85%, and nicety of grading participates in the Hyperspectral Remote Sensing Imagery Classification method of contrast apparently higher than other.

It should be noted that, above embodiment is unrestricted the present invention with explanation technical solution of the present invention only.Although the present invention is had been described in detail with reference to preferred embodiment, those of ordinary skill in the art is to be understood that, can modify or be equal to replacement technical scheme of the present invention, and not departing from the spirit and scope of technical solution of the present invention, it all should be encompassed among claim scope of the present invention.

Claims (8)

1. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating, is characterized in that, comprises the steps:

1) read in target in hyperspectral remotely sensed image data;

2) each data point in target in hyperspectral remotely sensed image is generated to a spectroscopic data vector according to its spectral band, thereby by the spectroscopic data vector of each data point, formed the spectroscopic data matrix of view picture target in hyperspectral remotely sensed image;

3) from target in hyperspectral remotely sensed image selected part data point as sample number strong point, spectroscopic data vector by each sample number strong point forms sample data matrix, and according to the spectroscopic data vector at priori selected part sample number strong point from sample data matrix, carry out the mark of known atural object classification, generate corresponding sample class label;

4) each the spectroscopic data vector in sample data matrix is carried out to rarefaction representation, try to achieve the optimum sparse coefficient vector of each spectroscopic data vector, thereby obtain the sparse coefficient matrix that sample data matrix is corresponding;

5) by sample data matrix acceptance of the bid, be marked with the spectroscopic data vector at the sample number strong point of vectorial class label, build for measuring the neighbour figure of similarity between sample data matrix spectroscopic data vector;

6) according to neighbour, scheme to calculate neighbour's weight matrix that sample data matrix is corresponding;

7), according to objective optimization function, utilize sparse coefficient matrix that sample data matrix is corresponding and neighbour's weight matrix to calculate the projection matrix of target in hyperspectral remotely sensed image;

8) by projection matrix, target in hyperspectral remotely sensed image is projected to low-dimensional embedded space, obtain the embedding eigenmatrix of target in hyperspectral remotely sensed image;

9) using and embed eigenmatrix as the Classification and Identification feature of atural object classification in target in hyperspectral remotely sensed image, utilize K-nearest neighbour classification algorithm target in hyperspectral remotely sensed image to be carried out to the classification of atural object classification, draw the classification results of atural object classification.

2. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating according to claim 1, is characterized in that described step 2) be specially:

Spectral reflection characteristic according to different spectral bands to atural object, is converted to by target in hyperspectral remotely sensed image the spectroscopic data matrix X that the capable B of Q is listed as _q={ x ₁, x ₂..., x _q..., x _q} ^t, wherein, Q represents data point bulk and the Q=M * N of target in hyperspectral remotely sensed image, B represents the spectral band number of target in hyperspectral remotely sensed image; Spectroscopic data matrix X _qin each line display target in hyperspectral remotely sensed image in the spectroscopic data value of a data point on each spectral band, each list shows in target in hyperspectral remotely sensed image that each data point is in the spectroscopic data value of a spectral band; x _qrepresent in target in hyperspectral remotely sensed image the spectroscopic data vector that the spectroscopic data value of a data point on each spectral band forms, q ∈ 1,2 ..., Q}; T is matrix transpose symbol.

3. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating according to claim 1, is characterized in that, the sample data matrix that described step 3) obtains is specially:

X={(x ₁,l ₁),(x ₂,l ₂),…,(x _i,l _i),…,(x _C,l _C),x _C+1,x _C+2,…,x _n} ^T；

Wherein, X represents sample data matrix, x _ithe spectroscopic data vector at the sample number strong point that expression is chosen from target in hyperspectral remotely sensed image, l _iexpression is to spectroscopic data vector x _ithe sample class label of mark, i ∈ { 1,2,, n}, n represents to choose the quantity as sample number strong point from target in hyperspectral remotely sensed image, before in sample data matrix X, C spectroscopic data vector has sample class label, remaining n-C spectroscopic data vector no specimen class label.

4. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating according to claim 1, is characterized in that, described step 4) is specially:

41) to any the spectroscopic data vector x in sample data matrix X _i, i ∈ 1,2 ..., n}, n represents from target in hyperspectral remotely sensed image, to choose the quantity as sample number strong point, utilizes other each spectroscopic data vector in sample data matrix X to set up x _isparse linear equation:

X _js _i=s _i,1x ₁+s _i,2x ₂+…+s _i,jx _j+…+s _i,i-1x _i-1+s _i,i+1x _i+1+…+s _i,nx _n；

Wherein, X _js _irepresent spectroscopic data vector x _irarefaction representation vector, X _jrepresent in sample data matrix X except x _ispectroscopic data vector set in addition, s _irepresent spectroscopic data vector x _isparse coefficient vector, that is:

s _i={s _i,1,s _i,2,…,s _i,j,…,s _i,i-1,s _i,i+1,…,s _i,n}；

S _i,jrepresent x _isparse linear equation in corresponding to spectroscopic data vector x _jsparse coefficient, j ∈ 1,2 ..., n} and j ≠ i;

42) according to rarefaction representation constraint condition

with loose constraint condition || x _i-X _js _i||≤ε is to x _isparse linear equation solve, obtain x _itime meet the optimum sparse coefficient vector of rarefaction representation constraint condition and loose constraint condition

for L1 norm operational symbol; || || be Euclidean distance operational symbol; ε is slack variable value, and 0< ε <10;

43) repeating step 41)～42), each the spectroscopic data vector x in sample data matrix X tried to achieve _ioptimum sparse coefficient vector

form sparse coefficient matrix corresponding to sample data matrix

$\tilde{S}=\{{\tilde{S}}_1,{\tilde{S}}_2,...,{\tilde{S}}_i,...,{\tilde{S}}_n\}.$

5. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating according to claim 1, is characterized in that, in described step 5), neighbour figure construction method is specially:

51) in sample data matrix X, any marks the spectroscopic data vector x of directed quantity class label _icorresponding data point, utilizes neighbour's data set of k neighbour's data point structure of this data point

represent spectroscopic data vector x _ithe spectroscopic data of any neighbour's data point vector among k neighbour's data point of institute's corresponding data point, d ∈ 1,2 ..., k};

52) by neighbour's data set knn (x _i) be two parts:

if

and x _imark has different sample class labels };

knn _S(x _i)=knn(x _i)-knn _D(x _i)；

Wherein, knn _d(x _i) expression spectroscopic data vector x _ik neighbour's data point in come from different neighbour's data subset that the data point of different atural object classifications forms, knn _s(x _i) be neighbour's data set knn (x _i) in except different neighbour's data subset knn _d(x _i) similar neighbour's data subset of forming of part in addition;

53) repeating step 51)～52), the spectroscopic data vector of each mark directed quantity class label in sample data matrix X is built to corresponding similar neighbour's data subset;

53) build neighbour and scheme G _w: for the spectroscopic data vector x of each mark directed quantity class label in sample data matrix X _i, consider in sample data matrix X each other spectroscopic data vector x _j∈ X, j ≠ i, if meet x _j∈ knn _s(x _i), neighbour, scheme G _slimit of middle use connects x _iand x _jcorresponding two data points, have traveled through thus neighbour and have schemed G _sstructure.

6. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating according to claim 1, is characterized in that the neighbour's weight matrix W in described step 6) _wbe calculated as follows:

Wherein, ω _{w, ij}represent two different spectroscopic data vector x in sample data matrix X _iand x _jbetween weight factor, thereby in sample data matrix X, the weight factor of every two different spectroscopic data vectors forms neighbour's weight matrix W _w; knn _s(x _i) and knn _s(x _j) represent respectively spectroscopic data vector x _iand x _jneighbour, scheme G _sin similar neighbour's data subset; α is similar weight parameter, and α >1.

7. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating according to claim 1, is characterized in that, described step 7) is specially:

Objective function J (V) is:

$J\left(V\right)=\underset{V}{\min }\left[\frac{\mathrm{tr}\left[V^{T}X(D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T)X^{T}V\right]}{\mathrm{tr}\left(V^{T}X{X}^{T}V\right)}\right];$

Wherein,

represent sparse coefficient matrix corresponding to sample data matrix X, W _wrepresent neighbour's weight matrix corresponding to sample data matrix X, V represents projection matrix; D _wfor diagonal matrix, and its diagonal entry

ω _{w, ij}represent two different spectroscopic data vector x in sample data matrix X _iand x _jbetween weight factor, i ∈ 1,2 ..., n}, j ∈ 1,2 ..., n}, n represents to choose the quantity as sample number strong point from target in hyperspectral remotely sensed image; Tr () represent to matrix ask mark operational symbol, T is matrix transpose symbol;

At V ^txX ^tunder the constraint condition of V=E, according to objective function J (V), obtain projection properties equation:

XS _γx ^tv=λ XX ^tv, wherein $S_{\mathrm{\&gamma;}}=D_w-W_w{\tilde{S}}^T-\tilde{S}{W}_w+\tilde{S}{D}_w{\tilde{S}}^T;$

Projection properties equation is carried out to generalized eigenvalue to be solved and obtains projection matrix V={v ₁, v ₂..., v _d; Wherein, v ₁, v ₂..., v _dfront d the eigenvalue of maximum λ that expression obtains projection properties equation solution ₁> λ ₂> ... > λ _dd corresponding proper vector, d<B; Wherein, B represents the spectral band number of target in hyperspectral remotely sensed image, E representation unit matrix.

8. the Hyperspectral Remote Sensing Imagery Classification method embedding based on semi-supervised sparse discriminating according to claim 1, is characterized in that, in described step 8), the embedding eigenmatrix of target in hyperspectral remotely sensed image carries out projection by following formula and obtains:

Y=V ^TX _Q，

Wherein, Y represents the spectroscopic data matrix X of target in hyperspectral remotely sensed image _qby projection matrix V, project to the embedding eigenmatrix of low-dimensional embedded space, T is matrix transpose symbol.

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