CN104778482B

CN104778482B - The hyperspectral image classification method that dimension about subtracts is cut based on the semi-supervised scale of tensor

Info

Publication number: CN104778482B
Application number: CN201510224055.5A
Authority: CN
Inventors: 张向荣; 焦李成; 莫玉; 冯婕; 侯彪; 马文萍; 白静; 李阳阳; 郭智
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2015-05-05
Filing date: 2015-05-05
Publication date: 2018-03-13
Anticipated expiration: 2035-05-05
Also published as: CN104778482A

Abstract

The present invention disclose it is a kind of the hyperspectral image classification method that dimension about subtracts is cut based on the semi-supervised scale of tensor, mainly solving the problems, such as that high spectrum image dimension is too high causes computationally intensive and existing method loss spatial information.Implementation step is：By high-spectral data set representations into full wave subdata cube set；Mark training set, test set and total training set have been selected from subdata cube set；Be configured with mark training set class between, the sample similarity matrix of dissimilarity matrix and total training set in class；Object function is cut by the semi-supervised scale of three above matrix construction tensor；Projection matrix is solved to object function；There to be a mark training set and test set projects to lower dimensional space and obtains new having mark training set and test set；There are mark training set and test set input supporting vector machine to be classified new, obtain the classification information of test set.The present invention can obtain higher classification accuracy rate, available for map making, vegetation investigation.

Description

Hyperspectral image classification method based on tensor semi-supervised scale tangent dimension reduction

Technical Field

The invention belongs to the technical field of image processing, relates to dimension reduction of high-dimensional data, and is used for classifying hyperspectral remote sensing images.

Background

The emerging hyperspectral remote sensing image processing in recent years is the leading edge technology of remote sensing. The hyperspectral remote sensing image processing technology utilizes an imaging spectrometer to simultaneously image earth surface objects at dozens or hundreds of wave bands with nanometer-level spectral resolution, thereby obtaining continuous spectral information of the earth surface objects, enabling synchronous acquisition of spatial information, radiation information and spectral information of the earth surface objects to be possible, and the most remarkable characteristic is 'map-in-one', and the development of the technologies enables human beings to make a qualitative leap in the aspects of earth observation and information acquisition capability.

Common hyperspectral image data in research comprises Indian pins data obtained by an unloaded visible light/infrared imaging spectrometer AVIRIS of a NASA jet propulsion laboratory and University of Pavia data obtained by a ROSIS spectrometer.

The hyperspectral image classification is a process of classifying each pixel in the hyperspectral image into a corresponding category by combining the characteristics of the hyperspectral image. Although the images obtained by the hyperspectral remote sensing technology contain abundant spectral information, spatial information and radiation information, which makes the classification easier, the classification of the hyperspectral images still faces huge difficulties and challenges: (1) the data volume is large, the storage, the display and the like are difficult, the wave band number is high, and the calculation amount is large; (2) dimension disasters, redundant information brought by too high dimension can reduce the classification precision; (3) the number of wave bands is large, the correlation is high, and therefore the requirement for the number of training samples is increased, and the reliability of the classification model parameters is reduced to a certain extent because of insufficient samples. Therefore, to obtain a high classification accuracy, the dimensionality of the hyperspectral image is reduced to reduce the data size.

There are many dimension reduction methods, and there are supervised dimension reduction methods, unsupervised dimension reduction methods, and semi-supervised dimension reduction methods, for example, principal component analysis PCA and local linear embedding LLE methods belong to the unsupervised method, linear discriminant analysis LDA belongs to the supervised method, and semi-supervised discriminant analysis SDA belongs to the semi-supervised method, depending on the utilization of the marked samples. The supervised dimensionality reduction method is to train by using labeled data and obtain a low-dimensional space according to category information. In contrast to supervised dimensionality reduction methods, unsupervised dimensionality reduction methods do not have class information, but rather select low-dimensional feature vectors that best embody the data structure by finding the inherent structural features of the data. The semi-supervised method combines the characteristics of the supervised method and the unsupervised method, takes the category information into consideration, simultaneously excavates the structural information of the data, maximizes the utilization of resources and further obtains better low-dimensional space.

These vector-based methods require vectorization of the image, and therefore they rely only on spectral characteristics and ignore spatial distributions. In order to solve the defects, the academic world introduces a tensor-based hyperspectral image representation, and the spatial and inter-spectral structures are analyzed simultaneously, so that a good result is obtained.

Dacheng Tao et al in the article "General transducer characterization and gaborFeatures for gap Recognition" (PAMI 2007) proposed the method of Tensor LDA for Gait Recognition, which mainly generalizes the method of LDA to Tensor computation. This method, while utilizing tagged information, is unable to handle heterovariance and polymorphic data.

Disclosure of Invention

The invention aims to provide a novel hyperspectral image classification method based on tensor semi-supervised scale tangent dimension reduction, which is used for better mining the internal structure of data by utilizing a small amount of marked samples and a large amount of unmarked data, solving the problems that image vectorization, space information loss and incapability of processing heterovariance and polymorphic data are required in the prior art and improving the classification precision.

The technical idea of the invention is as follows: by learning the features in the image, the commonality and the heterology between different data are represented properly, the dimensionality reduction of the hyperspectral image is realized by utilizing a tensor correlation calculation method, the dimensionality disaster is overcome, the essential rule of an object is sought by finding valuable intrinsic low-dimensional structure information embedded in high-dimensional data, and the original data is represented more compactly by mapping and projecting to a low-dimensional feature space. The method comprises the following implementation steps:

(1) inputting a hyperspectral data set A epsilon R^m×n×DThe data set comprises c types of ground objects, wherein m multiplied by n represents the size of an image space, namely the number of pixel points, and D represents the total wave band number of the data set;

(2) taking 5 × 5 neighborhood blocks by taking each pixel point of A as a center to obtain Q sub-data cubes with full wave bands, and making each sub-data cube as a sub-data cubeExpressing a sample by a third-order tensor to obtain a sample setWherein c is_aRepresenting the a sample, Q represents the total number of samples, and Q is m multiplied by n;

(3) from a set of samplesRandomly selecting N marked samples to form a marked training sample setThe corresponding class label vector is noted as:the other Q-N unmarked samples form a test sample set,y_u∈R^5×5×DTherein, x_tT-th sample, l, representing a labeled training set_tDenotes the class label to which the t-th labeled training sample belongs, y_uThe u-th sample representing the test set;

(4) h unlabeled samples are selected from Q-N unlabeled samples and form a total training set together with N labeled samplesWherein s is_kRepresenting the kth training sample of the total training set, wherein N + η is the number of samples of the total training set, and Q-N is more than or equal to 1 and less than or equal to η;

(5) constructing an inter-class dissimilarity matrix B with a labeled training set X:

wherein, V_pIndicating that the p-th class is labeledSet of training samples, V_p' denotes a set of all samples except the p-th type sample in the labeled training sample set, n_pIndicates the number of samples in the p-th labeled training set, n_c(j)Indicates the number of samples, χ, to which the jth labeled training sample belongs_iThe ith labeled training sample, χ, representing the p-th class_jRepresents V_p' the j-th labeled training sample, U₁Projection matrix, U, representing the horizontal direction of a full-band sub-data cube₁＝1_5×5，U₂Projection matrix, U, representing the vertical direction of a full-band sub-data cube₂＝1_5×5，U₁And U₂Each element of (a) has a value of 1,representing tensor and matrixPerforming modulo 1 and modulo 2 product, T represents transposition, (. epsilon.) epsilon.R^5×5×DA tensor is represented which is,the first and second stages, representing the product of the two tensors, are compressed to obtain a matrix of size dxd,(·)∈R^5×5×Drepresenting a third order tensor, (.)₍₃₎∈R^D ^×(5×5)The representation tensor (-) is expanded into a matrix according to mode 3;

(6) constructing an intra-class dissimilarity matrix W with a labeled training set X:

wherein, χ_hRepresents V_pThe h-th labeled training sample in the training set;

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

wherein m is_i'j'Represents a sample c_i'And c_j'Similarity therebetween, χ_i'Denotes the ith' training sample, χ, in S_j'Represents the jth training sample in S;

(8) constructing a tensor semi-supervised scale cutting objective function by an inter-class dissimilarity matrix B of the marked training set, an intra-class dissimilarity matrix W of the marked training set and a similarity matrix M:

where parameter β is a fine tuning parameter whose value is artificially specified as 0.001, U₃For the projection matrix in the direction of the required feature dimension, tr represents the trace of the matrix;

(9) solving the tensor semi-supervised scale cutting objective function to obtain a projection matrix of the characteristic dimension direction

(10) Respectively will have a training set of marksAnd test setIs projected toThe formed low-dimensional space is used for obtaining a new marked training set after projectionAnd a new test setWhereinFor the new feature tensor for the t-th labeled training sample,for the new feature tensor for the u-th test sample,representing tensor and matrixPerforming mould 3 product;

(11) new labeled training setCategory label setAnd a new test setInputting the data into a Support Vector Machine (SVM) for classification to obtain a classification result of the test setWherein l_u' denotes a class label to which the u-th test sample belongs. Compared with the prior art, the invention has the following advantages:

firstly, the invention reduces the dimension of the hyperspectral image data by adopting a dimension reduction algorithm and then classifies the hyperspectral image data, thereby greatly reducing the calculated amount and improving the classification speed.

Secondly, based on the characteristics that in a small-range space region, the ground object type corresponding to the hyperspectral image is single, and the pixels have great similarity, each sample is expressed into a sub-data cube with a full wave band, tensor calculation is utilized, vectorization processing of the image is avoided, and regional space correlation and inter-spectrum correlation can be utilized to the maximum extent;

thirdly, compared with the existing tensor LDA method, each class of data is not required to meet Gaussian equal variance distribution, and the dissimilarity matrix is constructed by calculating the dissimilarity between samples, so that the influence of class centers is eliminated.

Fourthly, the method fully utilizes the information provided by the marked samples to search a projection space capable of better keeping the separability of the classes, and simultaneously, as the geometric structure information of the data mined by the unmarked samples is utilized, the essential geometric characteristics of the data can be reflected;

a contrast experiment shows that the method effectively reduces the complexity of calculation and improves the classification accuracy of the hyperspectral remote sensing image.

Drawings

FIG. 1 is a flow chart of an implementation of the present invention;

FIG. 2 is an Indian Pines image used in the simulation of the present invention;

FIG. 3 is a diagram of the classification results of Indian Pines images according to the present invention and the prior art method.

Detailed description of the preferred embodiments

The technical solution and effects of the present invention will be further described with reference to the accompanying drawings.

Referring to fig. 1, the implementation steps of the invention are as follows:

step 1, inputting a hyperspectral data set A epsilonR^m×n×DThe data set comprises 16 types of ground objects, wherein m × n represents the size of an image space, namely the number of pixel points, D represents the total wave band number of the data set, and R represents a real number domain;

and 2, selecting a marked training set X, a test set Y and a total training set S.

2a) Taking 5 × 5 neighborhood blocks by taking each pixel point of A as a center to obtain Q sub-data cubes with full wave bands, expressing each sub-data cube as a sample by using a third-order tensor to obtain a sample setWherein c is_aRepresenting the a sample, Q represents the total number of samples, and Q is m multiplied by n;

2b) from a set of samplesRandomly selecting N marked samples to form a marked training sample setThe corresponding class label vector is noted as:the other Q-N unmarked samples form a test sample set,y_u∈R^5×5×DTherein, x_tT-th sample, l, representing a labeled training set_tDenotes the class label to which the t-th labeled training sample belongs, y_uThe u-th sample representing the test set;

2c) h unlabeled samples are selected from Q-N unlabeled samples and form a total training set together with N labeled samplesWherein s is_kShow general trainingThe kth training sample of the training set, N + η is the number of samples of the total training set, and Q-N is more than or equal to 1 and less than or equal to η.

And 3, constructing an inter-class dissimilarity matrix B and an intra-class dissimilarity matrix W of the labeled training set X.

3a) Forming the p-th type labeled sample in the labeled training set X into a homogeneous sample set1,2, c, wherein χ_iI-th labeled training sample, n, representing the p-th class_pA set of representations V_pThe number of marked training samples;

3b) all samples except the p-th type sample in the marked training sample set form a different type sample setWherein x_jRepresents V_p' the jth labeled training sample, n_c(j)Representing the number of samples of the class to which the jth marked training sample belongs;

3c) calculating homogeneous sample set V_pMarked sample and heterogeneous sample set V in (1)_pThe dissimilarity between the labeled samples in' yields an inter-class dissimilarity matrix B for each class_p：

U₁Projection matrix, U, representing the horizontal direction of a full-band sub-data cube₁＝1_5×5，U₂Projection matrix, U, representing the vertical direction of a full-band sub-data cube₂＝1_5×5，U₁And U₂Each element of (a) has a value of 1,representing tensor and matrixPerforming modulo 1 and modulo 2 product, T represents transposition,the first and second stages of the product of the two tensors are compressed to obtain a matrix of size DxD, (. epsilon. R)^5×5×DRepresenting a third order tensor, (.)₍₃₎∈R^D×(5×5)The representation tensor (-) is expanded into a matrix in mode 3_，T represents transposition;

3d) calculating homogeneous sample set V_pThe dissimilarity among the marked samples in (1) to obtain an intra-class dissimilarity matrix W of each class_p：

χ_hRepresents V_pThe h-th labeled training sample in the training set;

3e) inter-class dissimilarity matrix B for each class of labeled training samples of step 3c)_pAnd summing to obtain an inter-class dissimilarity matrix B with a labeled training set:

3f) for each class of labeled training samples of step 3d), an intra-class dissimilarity matrix W_pAnd summing to obtain an inter-class dissimilarity matrix W with a labeled training set:

and 4, constructing an unsupervised sample similarity matrix M according to the total training set S.

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

wherein m is_i'j'Represents a sample c_i'And c_j'Similarity therebetween, χ_i'Denotes the ith' training sample, χ, in S_j'Representing the jth training sample in S, wherein delta is a kernel parameter;

4b) calculating an unsupervised sample similarity matrix M according to the total training set S:

step 5, constructing a tensor semi-supervised scale cutting objective function by the inter-class dissimilarity matrix B of the marked training set, the intra-class dissimilarity matrix W of the marked training set and the similarity matrix M:

step 6, solving the tensor semi-supervised scale tangent objective function to obtain a projection matrix U in the characteristic dimension direction₃。

6a) The tensor semi-supervised scale cut objective function is transformed into the form:

whereinIs a parameter for the adjustment of the position of the object,is (B + W + β X M)^-B maximum eigenvalue corresponding to (B + W + β XM)^-Represents inverting B + W + β × M;

6b) setting the value of the characteristic dimension d after dimensionality reduction, and performing the above-mentioned operation on the obtained valueSingular value decomposition is carried out on the items to obtain d maximum eigenvalues and eigenvectors u corresponding to the d maximum eigenvalues₁,u₂,...,u_dWherein the value of D is an integer, and D is more than 0 and less than or equal to D;

6c) using feature vectors u₁,u₂,...,u_dForming a projection matrix in the direction of the feature dimension

Step 7, respectively projecting the marked training set X and the marked testing set Y to a projection matrix U^* ₃And (4) obtaining a projected new marked training set X 'and a new testing set Y' from the formed low-dimensional space.

7a) The original labeled training setProjection to the projection matrixIn the space of the formation, a new marked training set is obtainedWherein,a new feature tensor for the tth labeled training sample;

7b) original test setProjection to the projection matrixIn the space formed by stretching, a new test set is obtainedA new feature tensor for the u-th test sample;

step 8, new marked training setCategory label setAnd a new test setInputting the data into a Support Vector Machine (SVM) for classification to obtain a classification result of the test setWherein l_u' denotes a class label to which the u-th test sample belongs.

The effect of the invention can be further illustrated by the following simulation experiment:

1. simulation conditions are as follows:

the image used in the simulation experiment was an Indian Pines image taken by the AVIRIS of the NASA jet propulsion laboratory in the united states space agency, NASA, on north of indiana, 6 months 1992, as shown in fig. 2. The general 16 types of feature information are shown in fig. 2, and the class name and the number of samples of each type of feature information are shown in table 1.

TABLE 1 Indian Pines dataset Categories case

Categories	Category name	Number of
			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

The image size in fig. 2 is 145 × 145, 220 bands, and 200 bands for removing noise and absorption by the atmosphere and water. The simulation experiment of the invention is realized on MATLAB 2011b on AMD (TM) A8CPU, main frequency 1.90GHz, memory 8G and Windows7(64bit) platforms.

2. Emulated content and analysis

The invention and the existing two methods are used for dimensionality reduction of the hyperspectral image Indian Pines, and the two existing methods are respectively as follows: scaling down the dimension SC, tensor linear discriminant analysis TLDA.

The three dimensionality-reduced images obtained by the method and the existing three dimensionality reduction method of SC and TLDA are classified, wherein a kernel parameter gamma of a classifier SVM is obtained by a quintuple cross validation method, a penalty factor C is set to be 100, a kernel parameter sigma of a similarity matrix M is set to be 1, a weight parameter β is set to be 0.001, and the number η of unmarked training samples is fixed to be 2000.

Simulation 1, selecting 10 samples from each of 16 types of data shown in table 1 as marked samples, using the remaining samples in the 16 types of data as unmarked samples, performing 20 dimensionality reduction classification experiments on the 16 types of data by using the method of the invention and the existing two methods, and taking the average value of 20 classification results as the final classification accuracy, wherein the results are shown in table 2.

TABLE 2 Overall Classification accuracy of different methods on Indian Pines datasets

As can be seen from Table 2, the present invention is very superior to the two prior methods based on vectors; when the feature dimension is larger than 10, the classification accuracy of the method reaches more than 60 percent, which is obviously higher than that of the existing method;

as can be seen from table 2, after the dimension is greater than 25, the result of the present invention tends to be stable, so that only 25-dimensional features need to be adopted to obtain a higher recognition rate, thereby greatly reducing the amount of calculation.

Simulation 2, selecting 10 pixels from each type of pixels of 16 types of data shown in table 1 as marked pixels, using the remaining pixels of the whole Indian Pines image as unmarked pixels, classifying all the pixels of the whole Indian Pines image by the above three methods, setting the characteristic dimension after dimensionality reduction to be 25 in each method, and the result is shown in fig. 3, wherein a graph (3a) is a classification result graph of the invention, a graph (3b) is a classification result graph of the existing SC + SVM, and a graph (3c) is a classification result graph of the existing TLDA + SVM,

as can be seen from the three graphs of fig. 3a, 3b and 3c, the result graph of the present invention is smoother and better classified than that obtained by the two existing methods.

In conclusion, the dimensionality reduction is carried out on the hyperspectral image, and then SVM classification is used, so that on one hand, vectorization of the image is avoided by using tensor correlation operation, and spatial information is fully utilized; on the other hand, the geometric structure information of the data is fully mined by utilizing the information with the mark and the information without the mark, the classification precision is improved, and the method has the advantages compared with the existing method.

Claims

1. A hyperspectral image classification method based on tensor semi-supervised scale tangent dimension reduction comprises the following steps:

(1) inputting a hyperspectral data set A epsilon R^m×n×DThe data set comprises c types of ground objects, wherein m multiplied by n represents the size of an image space, namely the number of pixel points, D represents the total wave band number of the data set, and R represents a real number domain;

(2) taking 5 × 5 neighborhood blocks by taking each pixel point of A as a center to obtain Q sub-data cubes with full wave bands, and representing each sub-data cube as a sample by using a third-order tensorObtaining a sample setWherein x_aRepresenting the a sample, Q represents the total number of samples, and Q is m multiplied by n;

(3) from a set of samplesRandomly selecting N marked samples to form a marked training sample setThe corresponding class label vector is noted as:the other Q-N unmarked samples form a test sample sety_u∈R⁵ ^×5×DTherein, x_tT-th sample, l, representing a labeled training set_tDenotes the class label to which the t-th labeled training sample belongs, y_uThe u-th sample representing the test set;

(4) η unlabeled samples are selected from the Q-N unlabeled samples, and the unlabeled samples and the N labeled samples form a total training setWherein s is_kRepresenting the kth training sample of the total training set, wherein N + η is the number of samples of the total training set, and Q-N is more than or equal to 1 and less than or equal to η;

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wherein, V_pRepresents a set of p-th-class labeled training samples, V'_pRepresenting a set of all samples in the set of labelled training samples except the class p sample, n_pIndicates the number of samples in the p-th labeled training set, n_c(j)Indicates the number of samples, χ, to which the jth labeled training sample belongs_iThe ith labeled training sample, χ, representing the p-th class_jRepresents V'_pJ-th labeled training sample of (1), U₁Projection matrix, U, representing the horizontal direction of a full-band sub-data cube₁＝1_5×5，U₂Projection matrix, U, representing the vertical direction of a full-band sub-data cube₂＝1_5×5，U₁And U₂Each element of (a) has a value of 1,representing tensor and matrixPerforming modulo 1 and modulo 2 product, T represents transposition, (. epsilon.) epsilon.R^5×5×DA tensor is represented which is,the first and second stages, representing the product of the two tensors, are compressed to obtain a matrix of size dxd,(·)∈R^5×5×Dto representA third order tensor, (.)₍₃₎∈R^D ^×(5×5)The expression tensor (-) is unfolded into a matrix according to the mode 3, and c is a penalty factor;

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wherein m is_i'j'Representing sample χ_i'Hexix-_j'Similarity therebetween, χ_i'Denotes the ith' training sample, χ, in S_j'Represents the jth training sample in S;

(11) new labeled training setCategory label setAnd a new test setInputting the data into a Support Vector Machine (SVM) for classification to obtain a classification result of the test setWherein l'_uIndicates the class label to which the u-th test sample belongs.

2. The method for classifying hyperspectral images by reduction of tangent dimension of tensor-based semi-supervised scale as claimed in claim 1, wherein the sample χ in step (7) is determined_i'Hexix-_j'Similarity m between_i'j'Calculated by the following formula:

where δ is the nuclear parameter.

3. The hyperspectral image classification method based on tensor semi-supervised scale tangent dimension reduction according to claim 1, wherein the tensor semi-supervised scale tangent objective function is solved in the step (9) according to the following steps:

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

whereinIs a parameter for the adjustment of the position of the object,is (B + W + β X M)^-Maximum eigenvalue corresponding to B，(B+W+β×M)^-Represents inverting B + W + β × M;

9b) setting the value of the characteristic dimension d after dimensionality reduction, and performing the above-mentioned operation on the obtained valueSingular value decomposition is carried out on the items to obtain d maximum eigenvalues and eigenvectors u corresponding to the d maximum eigenvalues₁,u₂,...,u_dWherein the value of D is an integer, and D is more than 0 and less than or equal to D;

9c) using feature vectors u₁,u₂,...,u_dForming a projection matrix in the direction of the feature dimension