Application of tensor ELM based on LDA and SSA in HSI classification

Abstract

The application discloses application of a tensor ELM based on LDA and SSA in HSI classification, and comprises the following steps: step 1: inputting test tensor samples, training tensor samples, label samples and parameters; step 2: data processing part; step 4: obtaining tensor sample output of a hidden layer; step 5: initialization process, for each mode i; step 8: obtaining initial value of W (i) Step 16: obtaining final optimized classification result of a prediction test sample: test tensor sample A i After singular spectrum analysis denoising and a hidden layer of an extreme learning machine, output tensor B i of the hidden layer is obtained, and then, Γ i ∈R C×1 is obtained, and the serial number of the maximum element in Γ i is the classification result of the test tensor sample A i . The application can effectively utilize spatial sequence information of a hyperspectral image, can fuse spatial and spectral information into a tensor, can optimize the spatial and spectral information together, and can propose a tensor ELM model, so that the classification precision is higher and the calculation speed is faster in actual classification and other applications.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of HSI classification, and particularly relates to application of a tensor ELM based on LDA and SSA in HSI classification. BACKGROUND

[0002] Due to different reflection abilities of different ground objects to the same band, the pixel value of each band of the hyperspectral image is the emissivity of the ground object to the band. Since each pixel of the ground surface image taken from high altitude may cover a very broad area, most of the pixels are mixed pixels, so that the hyperspectral image pixel contains more noise signals. Secondly, the image data of super high dimension makes the processing process extremely prone to "dimension disaster", and the conventional feature extraction and classification method is difficult to apply. Finally, the mutual interference between adjacent band information and the small band difference significantly increase the redundancy of the remote sensing image, intensify the difficulty of noise suppression in the feature extraction process, and also seriously test the fitting ability of the classifier classification surface.

[0003] For the fusion of spatial and spectral information, the traditional method mainly performs fixed feature extraction mode in the spatial domain. One of such methods is to sequentially pass a fixed size spatial window over the hyperspectral image, calculate the influence degree of each window pixel on the middle pixel according to the distance of the window pixel from the middle pixel, and perform weighted summation processing on the pixels in the window to obtain the value of the new middle pixel. This method leads to the loss of the inherent structural information of the hyperspectral image.

[0004] Another such method is a rolling guided filter. First, the hyperspectral image is processed for detail texture, at this time a grain noise filtered image J1 is generated, then the J1 image is iterated, and the image is processed for boundary recovery through a guided filter-like idea, and then the iterated image is processed continuously, and the clarity of the boundaries of different categories of images is higher and higher, and the texture of small areas is also removed. This method has high time complexity, and it takes several minutes to run a hyperspectral image. Inspired by the tensor learning method, some methods regard the pixel and its neighboring pixels as a three-dimensional tensor to solve this problem, thereby proposing a tensor optimization classification method. Most tensor methods physically construct tensors, and ignore the characteristics of following a pre-defined logical arrangement. Therefore, we propose an application of a tensor ELM based on LDA and SSA in HSI classification to solve the problems mentioned in the background. SUMMARY

[0005] The purpose of the application is to provide an application of a tensor ELM based on LDA and SSA in HSI classification to solve the problems mentioned in the background.

[0006] To achieve the above object, the application provides the following technical scheme: an application of tensor ELM based on LDA and SSA in HSI classification, comprising the following steps:

[0007] Step 1: input test tensor sample A ∈ R H×L×ω×(N-J) , training tensor sample χ ∈ R H×L×ω×J , label sample Γ ∈ R c×1×1×J and parameters λ, a, c, tol;

[0008] Step 2: data processing part;

[0009] Step 3: one-dimensional singular spectrum analysis is used to remove noise in the hyperspectral pixel tensor;

[0010] Step 4: random initialization weight and sigmoid activation function processing of the limit learning machine are performed on the hyperspectral pixel tensor, and the output of the hidden layer tensor sample is obtained;

[0011] Step 5: initialization process, for each mode i;

[0012] Step 6: the mean of the other two modes of Γ except the i th th mode is calculated;

[0013] Step 7: the mean of the other two modes of χ except the i th th mode is calculated;

[0014] Step 8: the initial value of W (i) is obtained by using the method of multi-classification ridge regression

[0015] Step 9: the F-norm of the initialization is calculated

[0016] Step 10: the initialization process ends;

[0017] Step 11: the following is the main part of optimization;

[0018] Step 12: when the number of iterations does not reach 50 times, or the results of the previous and subsequent two optimizations do not satisfy the following steps are executed:

[0019] Step 13: the joint divergence matrix M (i) is obtained according to the formula joint lda formula, i = 1, 2, 3;

[0020] Step 14: the weight W (i) of the output layer is obtained according to singular value decomposition and the following formulas (1)-(6), i = 1, 2, 3;

[0021] Definition: So we have the following formula:

[0022]

[0023] According to formula (2), we get formula (3);

[0024]

[0025] Let B (i) =(H (i) ) -1 E (i) We define the optimization formula described in formula (3) as follows:

[0026]

[0027] Solving the optimization formula (4), we get The analytical solution of:

[0028]

[0029] According to formula (5), the analytical solution W t (i) ,i=1,2,3;

[0030]

[0031] Step 15: According to formula, Get the normalized analytical solution of the hidden layer output after the tth iteration

[0032] Step 16: After the main part of the optimization is completed, the final optimized Predict the classification result of the test sample: test tensor sample A i After singular spectrum analysis denoising, the output tensor B of the hidden layer of the extreme learning machine is obtained i Then according to And get Γ i ∈R C×1 The serial number of the maximum element in Γ i Is the classification result of the test tensor sample A i .

[0033] Compared with the prior art, the beneficial effects of the present application are: the application provides an application of a tensor ELM based on LDA and SSA in HSI classification, and the application can effectively utilize the spatial sequence information of hyperspectral images, and can fuse spatial and spectral information into a tensor, and can optimize them together, and can propose a tensor ELM model, and in actual classification and other applications, the classification accuracy is higher.

[0034] The present application can effectively improve the quality of spectral classification in constructing a tensor odorant type discriminant analysis model. High-quality spectral feature extraction can effectively improve the classification accuracy.

[0035] The present application has a faster calculation speed. The traditional filtering technology is used for spatial information extraction of hyperspectral images, which is a time-consuming process. The present application can significantly reduce the time complexity because the spatial information is fused into a tensor for optimization. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The present application is a flowchart. DETAILED DESCRIPTION

[0037] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0038] Please refer to Figure 1 , the implementation is as follows: an application of a tensor ELM based on LDA and SSA in HSI classification, comprising the following steps:

[0039] Step 1: input test tensor sample A ∈ R H×L×ω×(N-J) , training tensor sample χ ∈ R H×L×ω×J , label sample Γ ∈ R c×1×1×J and parameters λ, a, c, tol;

[0040] Step 2: data processing part;

[0041] Step 3: one-dimensional singular spectrum analysis to remove noise in the hyperspectral pixel tensor;

[0042] Step 4: performing random initialization weight and sigmoid activation function processing of the limit learning machine on the hyperspectral pixel tensor to obtain the tensor sample output of the hidden layer;

[0043] Step 5: initialization process, for each mode i;

[0044] Step 6: calculate the mean of the other two modes of Γ except the i th th mode;

[0045] Step 7: calculate the mean of the other two modes of χ except the i th th mode;

[0046] Step 8: using the method of multi-classification ridge regression, obtain W(i) the initial value W0 of W (i) ;

[0047] Step 9: Calculate the F-norm of the initialization

[0048] Step 10: The initialization process is over.

[0049] Step 11: The following is the main part of the optimization.

[0050] Step 12: When the number of iterations does not reach 50 times, or the results of the previous two optimizations do not meet The following steps are performed:

[0051] Step 13: According to the formula joint lda formula, obtain the joint divergence matrix M (i) i = 1, 2, 3;

[0052] Step 14: According to the singular value decomposition and the following formula (1)-(6), obtain the weight W of the output layer (i) i = 1, 2, 3;

[0053] Definition: Then we have the following formula:

[0054]

[0055] According to formula (2), we get formula (3);

[0056]

[0057] Let B (i) = (H (i) ) -1 E (i) We define the optimization formula described in formula (3):

[0058]

[0059] Solve the optimization formula (4), we get The analytical solution of W

[0060]

[0061] According to formula (5), we get the analytical solution W t (i) i = 1, 2, 3;

[0062]

[0063] Step 15: According to the formula Get the normalized analytical solution of the hidden layer output after the tth iteration

[0064] Step 16: after the main part of optimization, get the final optimized Predict the classification result of the test sample: test tensor sample A i After singular spectrum analysis denoising, the output tensor B of the hidden layer of the extreme learning machine is obtained i Then, according to And get Γ i ∈R C×1 , the serial number of the maximum element in Γ i is the classification result of the test tensor sample A i .

[0065] Specifically, in use, the tensor RR has no noise processing operation, and has no operation of narrowing the distance between samples of the same class and widening the distance between samples of different classes. In view of these shortcomings, the application integrates the idea of linear discriminant analysis into the tensor extreme learning machine, and uses 1-dimensional singular spectrum analysis to process the noise existing in the hyperspectral image.

[0066] The existing spectral classification method does not combine the waveband processing and spatial information processing together for feature extraction. The application overcomes the shortcomings, combines the ideas of tensor parallel factor decomposition and multi-classification ridge regression, and proposes a tensor optimization method, which can extract the spectrum as a whole. In actual engineering application, the redundancy is reduced, the image processing time is effectively reduced, high-quality features are obtained, and the classification accuracy is improved.

[0067] The existing spectral classification method does not evaluate the quality of the spectral waveband well. The application overcomes the shortcomings, and proposes an evaluation criterion combining tensor linear discriminant analysis, which can ensure that the distance between pixels of the same class is closer and the distance between pixels of different classes is farther in the spectral feature selection process, and selects the waveband with high quality.

[0068] The existing tensor spectral classification method does not consider the noise information existing in the spectrum, and the classification effect is reduced. The application overcomes the shortcomings, uses the idea of singular spectrum analysis, and proposes a method for removing noise in the waveband direction, so that the selected spectral waveband has more clear effective information among all spectral wavebands. And the method has low computational complexity, short running time, low dependence on device performance, and is more conducive to deployment in actual engineering application.

[0069] Finally, it should be noted that the above only describes the preferred embodiments of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art will appreciate that the technical solutions described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalent features, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. Application of LDA and SSA based tensor ELM in HSI classification, characterized in that, Specifically comprising the following steps: Step 1: input test tensor sample A ∈ R H×L×ω×(N-J) , training tensor sample χ ∈ R H×L×ω×J , label sample Γ ∈ R c×1×1×J and parameters λ, a, c, tol; Step 2: One-dimensional singular spectrum analysis removes noise in the hyperspectral pixel tensor; Step 3: Randomly initialize the weights of the extreme learning machine and perform sigmoid activation function processing on the hyperspectral pixel tensor to obtain the tensor sample output of the hidden layer; Step 4: For each mode i, compute the mean of the other two modes of Γ except the i th th mode; Step 5: For each mode i, compute the mean of the other two modes of χ except the i th th mode; Step 6: Using the method of multiclass ridge regression, obtain the initial value W0 (i) of W (i) ; Step 7: Compute the F-norm of the initialization Step 9: Obtain the joint scatter matrix M according to the formula Joint LDA formula (i) i = 1, 2, 3; Step 10: The weights W of the output layer are obtained according to singular value decomposition and the following equations (1)-(6) (i) i = 1,2,3; Definitions: So there is the following formula: According to formula (2), formula (3) is obtained; Let B (i) = (H (i) ) -1 E (i) , define the optimization formula described by equation (3): Solving the optimization equation (4), we get the analytical solution of According to equation (5), the analytical solution of the hidden layer output after the tth iteration is obtained t (i) i = 1, 2, 3; Step 11: Obtain the normalized hidden layer output after the tth iteration, Wt, according to the formula t (i) i = 1, 2, 3;​ Step 12: When the number of iterations does not reach 50 times, or the results of the previous two optimizations do not meet Continue to perform steps 9-step 10: Step 13: After the end of the main part of optimization, the final optimized W is obtained t (i) i = 1, 2, 3, the classification result of the prediction test sample: test tensor sample A i After singular spectrum analysis denoising, the hidden layer of the extreme learning machine, the output tensor B of the hidden layer is obtained i , then according to Γ i ∈R C×1 , the serial number of the largest element in Γ i is the classification result of the test tensor sample A i .

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