CN104778482A - Hyperspectral image classifying method based on tensor semi-supervised scale cutting dimension reduction - Google Patents

Abstract

The invention discloses a hyperspectral image classifying method based on tensor semi-supervised scale cutting dimension reduction. The problems that as the dimensions of hyperspectral images are excessive, the calculation amount is large, and space information is lost in an existing method are mainly solved. The hyperspectral image classifying method includes the steps of expressing a hyperspectral data set as a sub-data cube set with the full-wave band; selecting a marked training set, a testing set and a total training set from the sub-data cube set; creating an inter-class dissimilarity matrix and an in-class dissimilarity matrix of the marked training set and a sample similarity matrix of the total training set; creating a tensor semi-supervised scale cutting objective function through the three matrixes; solving the objective function to obtain a projection matrix; projecting the marked training set and the testing set into low-dimensional space to obtain a new marked training set and a new testing set; inputting the new marked training set and the new testing set into a supporting vector machine for classifying, and obtaining class information of the testing set. By means of the hyperspectral image classifying method, the high classifying accuracy can be obtained, and the hyperspectral image classifying method can be used for map making and vegetation investigation.

Description

The hyperspectral image classification method that dimension about subtracts is cut based on the semi-supervised scale of tensor

Technical field

The invention belongs to technical field of image processing, relate to the dimensionality reduction of high dimensional data, for the classification to high-spectrum remote sensing.

Background technology

High-spectrum remote sensing process emerging is in recent years the cutting edge technology of remote sensing.High-spectrum remote sensing treatment technology utilizes imaging spectrometer with nano level spectral resolution, with tens or a hundreds of wave band simultaneously to earth's surface thing imaging, thus obtain the continuous spectrum information of atural object, make synchronously to obtain the spatial information of atural object, radiation information, spectral information become possibility, its the most significant characteristic is exactly " collection of illustrative plates unification ", and the development of these technology makes the mankind achieve qualitative leap in earth observation and information obtaining ability.

The Indian Pines data set that hyperspectral image data conventional in research has the unloaded visible ray/Infrared Imaging Spectrometer AVIRIS of NASA NASA jet propulsion laboratory to obtain and the University of Pavia data set that ROSIS spectrometer obtains.

Classification hyperspectral imagery is exactly that each pixel in high spectrum image is assigned to the process of going in corresponding classification by the feature combining high spectrum image.Although the spectrum information enriched that the image that high spectrum resolution remote sensing technique obtains comprises, spatial information, radiation information make classification become easier thing, but the classification of high spectrum image is still facing to huge difficulty and challenge: (1) data volume is large, storage, display etc. are faced with difficulty, wave band number is higher, and calculated amount is large; (2) dimension disaster, the redundant information that too high dimension brings can make nicety of grading reduce; (3) wave band number is many, and correlativity is high, thus increases the demand of number of training, because do not have enough samples, can reduce the reliability of disaggregated model parameter to a certain extent.Therefore, higher nicety of grading be expected, about will subtract the dimension of EO-1 hyperion, reduce data volume.

There is a lot of Dimensionality Reduction methods at present, supervision dimension is had about to subtract method, without supervision Dimensionality Reduction method and semi-supervised Dimensionality Reduction method according to there being the utilization power of marker samples to be divided into, such as principal component analysis (PCA) PCA and local linearly embedding LLE method belong to unsupervised approaches, linear discriminant analysis LDA belongs to measure of supervision, and semi-supervised discriminant analysis method SDA belongs to semi-supervised method.Having supervision dimension about to subtract method has utilized flag data to train exactly, tries to achieve lower dimensional space according to classification information.Supervise contrary with having, about subtract method there is no class mark information without supervision dimension, but by finding the immanent structure feature of data, select the low dimensional feature vector best embodying data structure.Semi-supervised methods combining has supervision and the feature without these two kinds of methods of supervision, and while considering classification information, the structural information of mining data itself, maximizes the utilization of resource, thus obtain better lower dimensional space.

And these methods based on vector need image vector, therefore, they have only relied on spectral property and have ignored space distribution.In order to solve these shortcomings, academia introduces a kind of high spectrum image based on tensor and represents, structure between space and spectrum is analyzed simultaneously, obtains good result.

The people such as Dacheng Tao propose the method for tensor LDA for Gait Recognition in paper " General Tensor Discriminant Analysis and Gabor Featuresfor Gait Recognition " (PAMI 2007), and the method for LDA is mainly generalized in the calculating of tensor by the method.Although the method make use of the information of label, it can not process Singular variance and Multi-state data.

Summary of the invention

The object of the invention is to propose a kind of newly cut based on the semi-supervised scale of tensor the hyperspectral image classification method that dimension about subtracts, a small amount of marker samples and a large amount of data untaggeds is had to utilize, the immanent structure of mining data better, solve prior art to need image vector, spatial information lose and the problem of Singular variance and Multi-state data can not be processed, improve nicety of grading.

Technical thought of the present invention is: by learning the feature in image, appropriate symbolize general character between different pieces of information and the opposite sex, utilize the dimensionality reduction of tensor Related Computational Methods realization to high spectrum image, overcome " dimension disaster ", by finding the valuable intrinsic low dimensional structures information be embedded in high dimensional data, seek the essential laws of things, by mapping projections to a low dimensional feature space, obtain the expression that raw data is more simplified.Implementation step comprises as follows:

(1) high-spectral data collection A ∈ R is inputted ^{m × n × D}, this data set comprises c class atural object, and wherein m × n represents the number of image space size and pixel, and D represents total wave band number of data set;

(2) centered by each pixel of A, get the neighborhood block of 5*5, obtain Q and have full wave subdata cube, each subdata cube represents as a sample three rank tensors, obtains sample set wherein c _arepresent a sample, Q represents the total number of sample, Q=m × n;

(3) from sample set middle Stochastic choice is N number of has marker samples to be configured with mark training sample set corresponding class mark vector is designated as: all the other Q-N unmarked composition of sample test sample book collection , y _u∈ R ^{5 × 5 × D}, wherein, χ _tindicate t sample of mark training set, l _trepresent that t has the category label of mark belonging to training sample, y _urepresent u sample of test set;

(4) from Q-N unmarked sample, select h unmarked sample, with N number of have together with marker samples form total training set wherein, s _krepresent a kth training sample of total training set, N+ η is the number of samples of total training set, 1≤η≤Q-N;

(5) dissimilarity matrix B between the class marking training set X is configured with:

$B=\underset{p=1}{\overset{c}{\mathrm{\Σ}}}\underset{i\∈V_p}{\mathrm{\Σ}}\underset{j\∈V_P^{\′}}{\mathrm{\Σ}}\frac{1}{n_p{n}_{c\left(j\right)}}{\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_j){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_j){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)$

Wherein, V _prepresent that p class has the set of mark training sample, V _p' represent the set be made up of all samples in the set of mark training sample except p class sample, n _prepresent that p class has the number of samples in mark training set, n _{c (j)}represent that jth has the number of samples of class belonging to mark training sample, χ _irepresent that i-th of p class has mark training sample, χ _jrepresent V _p' in jth have mark training sample, U ₁represent the projection matrix of all band subdata cube horizontal direction, U ₁=1 _{5 × 5}, U ₂represent the projection matrix of all band subdata cube vertical direction, U ₂=1 _{5 × 5}, U ₁and U ₂the value of each element be 1, represent tensor and matrix carry out mould 1, mould 2 amasss, T represents transposition, () ∈ R ^{5 × 5 × D}represent a tensor, expression is contractd to the first long-pending rank of two tensors and second-order, and obtaining a size after contracing is the matrix of D × D, () ∈ R ^{5 × 5 × D}represent three rank tensors, () ₍₃₎∈ R ^{d × (5 × 5)}represent that tensor () is launched into a matrix by mode 3;

(6) dissimilarity matrix W in the class marking training set X is configured with:

$W=\underset{p=1}{\overset{c}{\mathrm{\Σ}}}\underset{i\∈V_p}{\mathrm{\Σ}}\underset{h\∈V_p}{\mathrm{\Σ}}\frac{1}{n_p{n}_p}{\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)$

Wherein, χ _hrepresent V _ph in training set has mark training sample;

(7) the similarity matrix M of all samples in total training set S is constructed:

$M=\frac{1}{2}\underset{i^{\′},j^{\′}}{\overset{N+\mathrm{\η}}{\mathrm{\Σ}}}{m}_{i^{\′}{j}^{\′}}\left({\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_{i^{\′}}-{\mathrm{\χ}}_{j^{\′}}){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_{i^{\′}}-{\mathrm{\χ}}_{j^{\′}}){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)\right)$

Wherein, m _i'j'represent sample c _i'and c _j'between similarity, χ _i'represent the individual training sample of i-th in S ', χ _j'jth in expression S ' individual training sample;

(8) by having dissimilarity matrix B between the class of mark training set, having dissimilarity matrix W and the semi-supervised scale of similarity matrix M structure tensor in the class of mark training set to cut objective function:

$U_3^{*}=\underset{U_3}{\arg \max }\frac{\mathrm{tr}\left(U_3^T{\mathrm{BU}}_3\right)}{\mathrm{tr}\left(U_3^T(W+\mathrm{\βM})U_3\right)}$

Wherein, parameter beta be one fine setting parameter, its value by people for being appointed as 0.001, U ₃for the projection matrix on required feature dimensions direction, the mark of tr representing matrix;

(9) cut objective function to the semi-supervised scale of tensor to solve, obtain the projection matrix in feature dimensions direction

(10) mark training set will be had respectively and test set project to by the lower dimensional space opened, obtain newly after projecting having mark training set with new test set wherein be t the new feature tensor having mark training sample, be the new feature tensor of u test sample book, represent tensor and matrix carry out mould 3 to amass;

(11) new there is mark training set category label collection with new test set be input in supporting vector machine SVM and classify, obtain the classification results of test set wherein, l _u' represent category label belonging to u test sample book.The present invention compared with prior art, has the following advantages:

The first, the present invention carries out dimensionality reduction owing to adopting dimension reduction algorithm to hyperspectral image data, then classifies, and greatly reduces calculated amount, improves the speed of classification.

Second, the present invention is based at an area of space among a small circle, the atural object classification that high spectrum image is corresponding is single, the feature of very large similarity is had between pixel, each schedule of samples is shown as one and there is full wave subdata cube, utilize tensor computation, avoid and image is carried out vectorization process, regional space correlativity and light Spectral correlation can be maximally utilised;

3rd, the present invention, compared with existing tensor LDA method, does not need each class data to meet the variance distributions such as Gauss, but constructs dissimilarity matrix by the dissimilarity calculated between sample and sample, eliminates the impact at class center.

4th, this invention takes full advantage of the information that marker samples provides, and finds the projector space that can keep the separability of class better, simultaneously owing to make use of the geometry information of unmarked sample mining data, therefore can reflect the geometric properties of data essence;

Contrast experiment shows, the present invention effectively reduces the complexity of calculating, improves the classification accuracy of high-spectrum remote sensing.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is the Indian Pines image that the present invention emulates employing;

Fig. 3 is that the present invention and existing method are to the classification results figure of Indian Pines image.

Concrete implementing measure

Below in conjunction with accompanying drawing, the technical scheme of invention and effect are described further.

With reference to Fig. 1, as follows to performing step of the present invention:

Step 1, input high-spectral data collection A ∈ R ^{m × n × D}, this data set comprises c=16 class atural object, and wherein m × n represents the number of image space size and pixel, and D represents total wave band number of data set, and R represents real number field;

Step 2, has chosen mark training set X, test set Y and total training set S.

Centered by each pixel of A, 2a) get the neighborhood block of 5*5, obtain Q and have full wave subdata cube, each subdata cube represents as a sample three rank tensors, obtains sample set wherein c _arepresent a sample, Q represents the total number of sample, Q=m × n;

2b) from sample set middle Stochastic choice is N number of has marker samples to be configured with mark training sample set corresponding class mark vector is designated as: all the other Q-N unmarked composition of sample test sample book collection , y _u∈ R ^{5 × 5 × D}, wherein, χ _tindicate t sample of mark training set, l _trepresent that t has the category label of mark belonging to training sample, y _urepresent u sample of test set;

2c) from Q-N unmarked sample, select h unmarked sample, with N number of have together with marker samples form total training set wherein, s _krepresent a kth training sample of total training set, N+ η is the number of samples of total training set, 1≤η≤Q-N.

Step 3, dissimilarity matrix W in dissimilarity matrix B and class between the class being configured with mark training set X.

P class in mark training set X 3a) will be had to have marker samples to form similar sample set p=1,2 ..., c, wherein χ _irepresent that i-th of p class has mark training sample, n _prepresent set V _pin have mark training sample number;

3b) all composition of sample inhomogeneity sample sets in the set of mark training sample except p class sample will be had wherein χ _jrepresent V _p' in jth have mark training sample, n _{c (j)}represent that jth has the number of samples of class belonging to mark training sample;

3c) calculate similar sample set V _pin have marker samples and inhomogeneity sample set V _p' in the class having the dissimilarity between marker samples to obtain each class between dissimilarity matrix B _p:

$B_p=\underset{i\∈V_p}{\mathrm{\Σ}}\underset{j\∈V_P^{\′}}{\mathrm{\Σ}}\frac{1}{n_p{n}_{c\left(j\right)}}{\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_j){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_j){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)$

U ₁represent the projection matrix of all band subdata cube horizontal direction, U ₁=1 _{5 × 5}, U ₂represent the projection matrix of all band subdata cube vertical direction, U ₂=1 _{5 × 5}, U ₁and U ₂the value of each element be 1, represent tensor and matrix carry out mould 1, mould 2 amasss, T represents transposition, expression is contractd to the first long-pending rank of two tensors and second-order, and obtaining a size after contracing is the matrix of D × D, () ∈ R ^{5 × 5 × D}represent three rank tensors, () ₍₃₎∈ R ^{d × (5 × 5)}represent that tensor () is launched into a matrix by mode 3 _,t represents transposition;

3d) calculate similar sample set V _pin the dissimilarity had between marker samples, dissimilarity matrix W in the class obtaining each class _p:

$W_p=\underset{i\∈V_p}{\mathrm{\Σ}}\underset{h\∈V_p}{\mathrm{\Σ}}\frac{1}{n_p{n}_p}{\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)$

χ _hrepresent V _ph in training set has mark training sample;

3e) to step 3c) each class have mark training sample class between dissimilarity matrix B _psue for peace, obtain mark training set class between dissimilarity matrix B:

$B=\underset{p=1}{\overset{c}{\mathrm{\Σ}}}{B}_P=\underset{p=1}{\overset{c}{\mathrm{\Σ}}}\underset{i\∈V_p}{\mathrm{\Σ}}\underset{j\∈V_P^{\′}}{\mathrm{\Σ}}\frac{1}{n_p{n}_{c\left(j\right)}}{\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)$

3f) to step 3d) each class have mark training sample class in dissimilarity matrix W _psue for peace, obtain mark training set class between dissimilarity matrix W:

$W=\underset{p=1}{\overset{c}{\mathrm{\Σ}}}{W}_P=\underset{p=1}{\overset{c}{\mathrm{\Σ}}}\underset{i\∈V_p}{\mathrm{\Σ}}\underset{h\∈V_p}{\mathrm{\Σ}}\frac{1}{n_p{n}_p}{\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_i-{\mathrm{\χ}}_h){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)$

Step 4, constructs without supervision sample similarity matrix M according to total training set S.

4a) calculate the similarity between any two samples in total training set S:

Wherein, m _i'j'represent sample c _i'and c _j'between similarity, χ _i'represent the individual training sample of i-th in S ', χ _j'jth in expression S ' individual training sample, δ is nuclear parameter;

4b) calculate without supervision sample similarity matrix M according to total training set S:

$M=\frac{1}{2}\underset{i^{\′},j^{\′}}{\overset{N+\mathrm{\η}}{\mathrm{\Σ}}}{m}_{i^{\′}{j}^{\′}}\left({\mathrm{mat}}_3\left(\left(({\mathrm{\χ}}_{i^{\′}}-{\mathrm{\χ}}_{j^{\′}}){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\χ}}_{i^{\′}}-{\mathrm{\χ}}_{j^{\′}}){\×}_1{U}_1^T{\×}_2{U}_2^T\right)\right)\right)$

Step 5, by having dissimilarity matrix B between the class of mark training set, having dissimilarity matrix W and the semi-supervised scale of similarity matrix M structure tensor in the class of mark training set to cut objective function:

$U_3^{*}=\underset{U_3}{\arg \max }\frac{\mathrm{tr}\left(U_3^T{\mathrm{BU}}_3\right)}{\mathrm{tr}\left(U_3^T(W+\mathrm{\βM})U_3\right)}$

Wherein, parameter beta be one fine setting parameter, its value by people for being appointed as 0.001, U ₃for the projection matrix on required feature dimensions direction, the mark of tr representing matrix;

Step 6, cuts objective function to the semi-supervised scale of tensor and solves, and obtains the projection matrix U in feature dimensions direction ₃.

6a) semi-supervised for tensor scale is cut objective function and is transformed into following form:

Wherein an adjustment parameter, for (B+W+ β × M) ^-the eigenvalue of maximum that B is corresponding, (B+W+ β × M) ^-represent and B+W+ β × M is inverted;

6b) arrange dimension about subtract after the value of intrinsic dimensionality d, and by above-mentioned objective function item carries out svd, draws d eigenvalue of maximum and the proper vector u corresponding to this d eigenvalue of maximum ₁, u ₂..., u _d, wherein the value of d is integer, and 0 < d≤D;

6c) use proper vector u ₁, u ₂..., u _dprojection matrix on constitutive characteristic dimension direction

Step 7, will have mark training set X and test set Y to project to by projection matrix U respectively ^* ₃the lower dimensional space opened, to obtain after projecting new mark training set X' and new test set Y'.

7a) original there is mark training set project to by projection matrix space in, obtain new having mark training set wherein, be t the new characteristic tensor having mark training sample;

7b) by original test set project to by projection matrix in the space of opening, obtain new test set it is the new characteristic tensor of u test sample book;

Step 8, has mark training set by new category label collection with new test set be input in supporting vector machine SVM and classify, obtain the classification results of test set wherein, l _u' represent category label belonging to u test sample book.

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

1. simulated conditions:

The image adopted in emulation experiment is the Indian Pines image that the unloaded visible ray/Infrared Imaging Spectrometer AVIRIS of NASA NASA jet propulsion laboratory obtains in June, 1992 in the northwestward, Indiana, as shown in Figure 2.Have 16 class terrestrial object informations in Fig. 2, class name and the number of samples of every class terrestrial object information are as shown in table 1.

Table 1 Indian Pines categories of datasets situation

Classification	Item name	Number
			1	Alfafa	54
2	Corn-notill	1434
			3	Corn-min	834
4	Corn	234
			5	Grass/Pasture	497
6	Grass/Trees	747
			7	Grass/Pasture-mowed	26
8	Hay-windrowed	489
			9	Oats	20
10	Soybeans-notill	968
			11	Soybeans-min	2468
12	Soybeans-clean	614
			13	Wheat	212
14	Woods	1294
			15	Building-Grass-Trees-Drives	380
16	Stone-steel Towers	95

In Fig. 2, image size is 145 × 145, totally 220 wave bands, and the wave band removing noise and air and waters absorption also has 200 wave bands.Emulation experiment of the present invention is at AMD (TM) A8CPU, dominant frequency 1.90GHz, and the MATLAB 2011b on internal memory 8G, Windows7 (64bit) platform realizes.

2. emulate content and analysis

Use the present invention and existing two kinds of methods to carry out dimension to high spectrum image Indian Pines about to subtract, existing two kinds of methods respectively: scale cuts dimensionality reduction SC, tensor linear discriminant analysis TLDA.

Classify to about subtracting three dimensionality reduction images that method obtains with the present invention and existing SC, TLDA tri-kinds of dimensions, wherein the nuclear parameter γ of sorter SVM adopts five retransposing verification methods to obtain, and penalty factor is set to 100.The nuclear parameter σ of similarity matrix M is set to 1, and weight parameter β is set to 0.001, and Using Non-labeled Training Sample number η is fixed as 2000.

Emulation 1,10 samples are selected as there being marker samples from each class 16 class data shown in table 1, using the residue sample in these 16 class data as unmarked sample, by the present invention and existing two kinds of methods, 20 dimensionality reduction classification experiments are carried out to 16 class data, get the mean value of 20 subseries results, as final classification accuracy rate, result is as shown in table 2.

The overall classification accuracy of table 2 distinct methods on Indian Pines data set

As can be seen from Table 2, the present invention has an enormous advantage compared with two kinds of existing methods based on vector; When intrinsic dimensionality is greater than 10, the classification accuracy rate of the inventive method reaches more than 60%, apparently higher than existing method;

As can also be seen from Table 2, after dimension is greater than 25, result of the present invention tends towards stability, and therefore only needs employing 25 dimensional feature, namely can obtain higher discrimination, thus greatly reduce calculated amount.

Emulation 2, from each class pixel of 16 class data shown in table 1, select 10 conducts have marker image vegetarian refreshments, the residual pixel point of view picture Indian Pines image is as unmarked pixel, classify with all pixels of above-mentioned three kinds of methods to view picture Indian Pines image, intrinsic dimensionality in each method after dimensionality reduction is set to 25, result as shown in Figure 3, wherein scheming (3a) is classification results figure of the present invention, figure (3b) is the classification results figure of existing SC+SVM, the classification results figure that figure (3c) is existing TLDA+SVM

As can be seen from figure (3a), scheme (3b) and scheme (3c) these three figure, result figure of the present invention is more level and smooth than what obtained by existing two kinds of methods, and classification results is better.

To sum up, the present invention carries out dimension to high spectrum image and about subtracts rear use svm classifier, uses the related operation of tensor to avoid image vector on the one hand, takes full advantage of spatial information; On the other hand, utilize and have mark and unmarked information, the geometry information of abundant mining data, improves nicety of grading, has advantage compared with the existing methods.

Claims (3)

1. cut based on the semi-supervised scale of tensor the hyperspectral image classification method that dimension about subtracts, comprise the following steps:

(1) high-spectral data collection A ∈ R is inputted ^{m × n × D}, this data set comprises c class atural object, and wherein m × n represents the number of image space size and pixel, and D represents total wave band number of data set, and R represents real number field;

(2) centered by each pixel of A, get the neighborhood block of 5*5, obtain Q and have full wave subdata cube, each subdata cube represents as a sample three rank tensors, obtains sample set wherein χ _arepresent a sample, Q represents the total number of sample, Q=m × n;

(3) from sample set middle Stochastic choice is N number of has marker samples to be configured with mark training sample set corresponding class mark vector is designated as: all the other Q-N unmarked composition of sample test sample book collection y _u∈ R ^{5 × 5 × D}, wherein, χ _tindicate t sample of mark training set, l _trepresent that t has the category label of mark belonging to training sample, y _urepresent u sample of test set;

(4) from Q-N unmarked sample, select η unmarked sample, with N number of have together with marker samples form total training set wherein, s _krepresent a kth training sample of total training set, N+ η is the number of samples of total training set, 1≤η≤Q-N;

(5) dissimilarity matrix B between the class marking training set X is configured with:

$B=\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{i\&Element;V_p}{\mathrm{\&Sigma;}}\underset{j\&Element;V_P^{\&prime;}}{\mathrm{\&Sigma;}}\frac{1}{n_p{n}_{c\left(j\right)}}{\mathrm{mat}}_3\left(\left(({\mathrm{\&chi;}}_i-{\mathrm{\&chi;}}_j){\&times;}_1{U}_1^T{\&times;}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\&chi;}}_i-{\mathrm{\&chi;}}_j){\&times;}_1{U}_1^T{\&times;}_2{U}_2^T\right)\right)$

Wherein, V _prepresent that p class has the set of mark training sample, V ' _prepresent the set be made up of all samples in the set of mark training sample except p class sample, n _prepresent that p class has the number of samples in mark training set, n _{c (j)}represent that jth has the number of samples of class belonging to mark training sample, χ _irepresent that i-th of p class has mark training sample, χ _jrepresent V ' _pin jth have mark training sample, U ₁represent the projection matrix of all band subdata cube horizontal direction, U ₁=1 _{5 × 5}, U ₂represent the projection matrix of all band subdata cube vertical direction, U ₂=1 _{5 × 5}, U ₁and U ₂the value of each element be 1, represent tensor and matrix carry out mould 1, mould 2 amasss, T represents transposition, () ∈ R ^{5 × 5 × D}represent a tensor, expression is contractd to the first long-pending rank of two tensors and second-order, and obtaining a size after contracing is the matrix of D × D, () ∈ R ^{5 × 5 × D}represent three rank tensors, () ₍₃₎∈ R ^{d × (5 × 5)}represent that tensor () is launched into a matrix by mode 3 _;

(6) dissimilarity matrix W in the class marking training set X is configured with:

$W=\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{i\&Element;V_p}{\mathrm{\&Sigma;}}\underset{h\&Element;V_P}{\mathrm{\&Sigma;}}\frac{1}{n_p{n}_p}{\mathrm{mat}}_3\left(\left(({\mathrm{\&chi;}}_i-{\mathrm{\&chi;}}_h){\&times;}_1{U}_1^T{\&times;}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\&chi;}}_i-{\mathrm{\&chi;}}_h){\&times;}_1{U}_1^T{\&times;}_2{U}_2^T\right)\right)$

Wherein, χ _hrepresent V _ph in training set has mark training sample;

(7) the similarity matrix M of all samples in total training set S is constructed:

$M=\frac{1}{2}\underset{i^{\&prime;},j^{\&prime;}}{\overset{N+\mathrm{\&eta;}}{\mathrm{\&Sigma;}}}{m}_{i^{\&prime;}{j}^{\&prime;}}\left({\mathrm{mat}}_3(\left(({\mathrm{\&chi;}}_{i^{\&prime;}}-{\mathrm{\&chi;}}_{j^{\&prime;}}){\&times;}_1{U}_1^T{\&times;}_2{U}_2^T\right)\right){\mathrm{mat}}_3^T\left(\left(({\mathrm{\&chi;}}_{i^{\&prime;}}-{\mathrm{\&chi;}}_{j^{\&prime;}}){\&times;}_1{U}_1^T{\&times;}_2{U}_2^T\right))\right)$

Wherein, m _i'j'represent sample χ _i'and χ _j'between similarity, χ _i'represent the individual training sample of i-th in S ', χ _j'jth in expression S ' individual training sample;

(8) by having dissimilarity matrix B between the class of mark training set, having dissimilarity matrix W and the semi-supervised scale of similarity matrix M structure tensor in the class of mark training set to cut objective function:

$U_3^{*}=\underset{U_3}{\arg \max }\frac{\mathrm{tr}\left(U_3^T{\mathrm{BU}}_3\right)}{\mathrm{tr}\left(U_3^T(W+\mathrm{\&beta;M})U_3\right)}$

Wherein, parameter beta be one fine setting parameter, its value by people for being appointed as 0.001, U ₃for the projection matrix on required feature dimensions direction, the mark of tr representing matrix;

(9) cut objective function to the semi-supervised scale of tensor to solve, obtain the projection matrix in feature dimensions direction

(10) mark training set will be had respectively and test set project to by the lower dimensional space opened, obtain newly after projecting having mark training set with new test set wherein be t the new feature tensor having mark training sample, be the new feature tensor of u test sample book, represent tensor and matrix carry out mould 3 to amass;

(11) new there is mark training set category label collection with new test set be input in supporting vector machine SVM and classify, obtain the classification results of test set wherein, l ' _urepresent the category label belonging to u test sample book.

2. according to claim 1ly cut based on the semi-supervised scale of tensor the hyperspectral image classification method that dimension about subtracts, sample χ in required step (7) _i'and χ _j'between similarity m _i'j', by following formulae discovery:

Wherein, δ is nuclear parameter.

3. according to claim 1ly cut based on the semi-supervised scale of tensor the hyperspectral image classification method that dimension about subtracts, in described step (9), objective function cut to the semi-supervised scale of tensor and solve, carry out as follows:

9a) semi-supervised for tensor scale is cut objective function and is transformed into following form:

Wherein an adjustment parameter, for (B+W+ β × M) ^-the eigenvalue of maximum that B is corresponding, (B+W+ β × M) ^-represent and B+W+ β × M is inverted;

9b) arrange dimension about subtract after the value of intrinsic dimensionality d, and by above-mentioned objective function item carries out svd, draws d eigenvalue of maximum and the proper vector u corresponding to this d eigenvalue of maximum ₁, u ₂..., u _d, wherein the value of d is integer, and 0 < d≤D;

9c) use proper vector u ₁, u ₂..., u _dprojection matrix on constitutive characteristic dimension direction

$U_3^{*}=[u_1,u_2,...,u_d]\&Element;R^{D\&times;d}.$