CN110781926A - Support vector machine multi-spectral-band image analysis method based on robust auxiliary information reconstruction - Google Patents
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Abstract
The invention provides a multi-spectral-segment image analysis method of a support vector machine based on robust auxiliary information reconstruction, which comprises the following steps: selecting training samples from an original multi-spectral image data set, respectively calculating a kernel matrix and a robust constraint matrix of all input multi-spectral image samples and auxiliary image data, defining intermediate variables, and optimally solving a quadratic programming problem corresponding to an objective function to obtain optimal variables; based on the current optimal variable, optimizing and solving a reconstruction coefficient matrix; repeating until the model is converged, and outputting a robust classifier model; and verifying the classification effect, predicting the label of the test sample possibly with noise, and comparing the label with the real label. The invention considers the difficult situation that noise possibly exists in the original multi-spectral-band data sample and the auxiliary image data, and makes up the defect that the existing method lacks an effective solving strategy.
Description
Technical Field
The invention belongs to the technical field of multi-spectral-segment image analysis and processing, and particularly relates to a multi-spectral-segment image analysis method of a support vector machine based on robust auxiliary information reconstruction.
Background
With the rapid development of machine learning, more and more means are provided for multi-spectral-segment image analysis processing technology. Image classification, one of the important analytical methods, has been receiving continuous attention. Conventional multi-spectral image classification methods often employ supervised methods to obtain a better classification result, i.e., based on a set of samples and their corresponding labels, the conventional supervised methods may train a classification model and then use it to classify unknown test samples. However, the multispectral image sometimes suffers from problems that the image resolution is not high enough, the spectral information is not as good as that of the hyperspectral image, and the like, and especially under the condition that the number of marked samples is small, if additional images with higher resolution and more spectral dimensions are obtained as auxiliary information, the image classification and analysis results are more accurate.
A Support Vector Machine (SVM) is one of the most popular classifiers at present, and has a good classification effect on multi-dimensional data with less labeled data. However, in reality, the success of existing methods of SVM is often achieved when training and testing data are considered clean and noiseless. In practice, the training set can be designed according to specific requirements, but it is difficult or even impossible to determine what the test data is, with or without noise. The existing methods lack a clear strategy to address the potential noise in the data and therefore the practical performance of these methods will suffer. In addition, in the existing method, auxiliary data is often used as a new feature expression and is directly superposed on the original data feature expression in the training and testing processes, and the feature dimension of multi-spectral-segment image data is increased so as to improve the classification precision. However, in practical situations, it is difficult to acquire corresponding auxiliary image data for a large amount of test data, and when the test data cannot acquire the auxiliary image data, many existing methods cannot use the auxiliary image data any more, and the auxiliary image data that can be acquired by the training sample is wasted. Meanwhile, the acquired auxiliary image data are always accurate and noise-free, and if the auxiliary image data have noise, the addition of the auxiliary image data may not ensure that correct judgment is made, so that the expression of the model is influenced. In addition, when only a part of the training samples have auxiliary information, the existing method can only utilize the part of the existing auxiliary information, and does not consider that the possible auxiliary information expression of the rest training samples can be learned by using the existing auxiliary information.
Therefore, there is a need for a multi-spectral-band image classification analysis method that can generate auxiliary information and is robust to noise present in data samples and auxiliary image information, and the model of the method can make better use of the existing auxiliary information as much as possible while tolerating greater data noise, thereby achieving better classification effect. A robust multi-spectral-band image analysis method of a support vector machine by using auxiliary information is developed day by research teams of the applicant, and the robustness of a model is enhanced by adding a robust regularization function to an improved support vector machine classification method in consideration of the disturbance of noise to original image sample data and auxiliary image data. But practice has shown that the auxiliary information is not necessarily complete and further improvements are needed.
Disclosure of Invention
In order to solve the technical problem, the invention provides a support vector machine multi-spectral-segment image analysis method based on robust auxiliary information reconstruction, which can reconstruct unknown image auxiliary information by using the existing auxiliary image information, considers the disturbance of noise to the original image sample data and the auxiliary image data, adds a robust regularization function into an improved support vector machine classification method, and simultaneously considers the mutual expression characteristics among the auxiliary information to enhance the robustness of a model.
The technical scheme adopted by the invention provides a multi-spectral-segment image analysis method of a support vector machine based on robust auxiliary information reconstruction, which comprises the following steps:
step 1, selecting n image samples and labels from an original multispectral image data set as training samples to obtain auxiliary image data
l is an auxiliary imageNumber of data, where l < n, corresponding auxiliary image data, reconstructing the unknown training auxiliary image data
Then, the reconstruction coefficient matrix V ═ V is recorded
1,…,v
n]，v
1,…,v
nA vector of reconstructed coefficients for the respective assistance data;
step 2, calculating kernel matrixes K and K of all input multispectral image samples and auxiliary image data respectively
*；
Step 3, respectively calculating a robust constraint matrix H of each image sample and auxiliary image data
s；
Step 4, calculating the matrix
And
where ρ and λ are respectively predetermined hyper-parameters, defining intermediate variables, including μ ═ α
T,β
T]
Tα and β are Lagrange multipliers, and the quadratic programming problem corresponding to the objective function is solved in an optimized mode to obtain the optimal variable mu;
step 5, based on the current mu, optimizing and solving a reconstruction coefficient matrix V;
step 6, repeating the steps 3 to 5 until the model is converged, and outputting a robust classifier model;
and 7, verifying the classification effect, predicting the label of the test sample possibly with noise, and comparing the label with the real label.
In step 4, moreover, the objective function is as follows,
1
T(α+β-C
1)＝0
y
Tα＝0
0≤α≤C
3
β≥0
wherein the content of the first and second substances,
representing the product of the vector element correspondences, α and β are lagrange multipliers, y ═ y
1,…,y
n]Is the label of the training sample, 1 represents the vector with all 1 elements, the top right-hand label T represents the transpose of the matrix, C
1And C
3Is a pre-set hyper-parameter.
In step 4, an intermediate variable μ ═ α is defined
T,β
T]
TAnd
the simplification results in the following objective function,
1
T(α+β-C
1)＝0
y
Tα＝0
0≤α≤C
3
β≥0
and (4) optimizing and solving a quadratic programming problem corresponding to the objective function by using a quadratic programming toolkit to obtain an optimal variable mu.
In step 5, the reconstruction coefficient matrix V is optimized and solved in the following manner,
let the intermediate variable matrix
Solving the following objective function using the alternating direction multiplier method
Wherein, C
1And C
2Is a preset hyper-parameterThe number of the first and second groups is,
is a row vector of length l with elements of 1,
the elements of length n-l are all row vectors of 1.
In step 6, the difference between the two iterations of the objective function value is less than 10
-3The model is considered to converge.
The invention has the beneficial effects that:
(1) aiming at the problem of multi-spectral image classification analysis, auxiliary image data such as high spectral band or high image resolution and the like are considered and used simultaneously in the training process, and the discrimination capability of image data representation and analysis models is enhanced.
(2) The unknown training assistance image data is reconstructed taking into account the training assistance image data that can be acquired using the existing part.
(3) The difficult situation that noise possibly exists in the original multi-spectral-band data sample and the auxiliary image data is considered, and the defect that an effective solution strategy is lacked in the existing method is overcome;
(4) the robustness of the model is theoretically considered, so that the final classifier has better stability and robustness for the classification of the image data with noise;
(5) the method has the characteristics of high adaptability and easy solving of an optimization problem, and can effectively solve the problem of image with noise and the problem of non-image data classification.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Detailed Description
In order to facilitate the understanding and practice of the present invention for those of ordinary skill in the art, the following detailed description is to be read in connection with the accompanying drawings and examples, it being understood that the examples described herein are for purposes of illustration and explanation only and are not intended to be limiting.
Referring to fig. 1, the method for analyzing a multi-spectral-band image of a support vector machine based on robust auxiliary information reconstruction provided by the embodiment of the present invention includes the following steps:
step 1: selecting a proportion of image samples { x ] from an image dataset
1,…,x
nN is the number of image samples, and auxiliary image data of different multi-spectral bands or higher resolution can be acquired
l is the number of auxiliary image data, where l < n, and the label y ═ y
1,…,y
n]As training samples, as input data for training the model. For reconstructing unknown training auxiliary image data
Learning to reconstruct unknown auxiliary data using existing data
Is a dictionary composed of existing privilege information, where ψ (-) is a function to assist image data
Mapping from the original feature space into the reconstructed kernel Hilbert space, v
jIs the jth auxiliary data
The reconstructed coefficient vector of (1). The reconstruction coefficient vector of all auxiliary data is written in matrix form, which can be expressed as a reconstruction coefficient matrix V ═ V
1,…,v
n]Wherein, of the first l auxiliary samples, the coefficient vector v of any ith auxiliary sample
iThe coefficient is a vector with the ith element being 1 and the rest being 0.
The training data is clean and free of noise. Random noise is present in the test data. For example, the ImageNet2012 match sheet classification dataset may be used to classify the target in-frame region in which the target is located as the auxiliary image data. 40% of the samples were selected as training image samples, 30% as validation set, and the rest as test set.
Step 2: calculating kernel matrices K and K of all training image samples and auxiliary image data respectively
*。
In an embodiment, each image sample x is computed using a Gaussian kernel function
iAnd x
jKernel function value of (1) between
e is the natural logarithm, x
iRepresents the ith training image sample, x
jRepresents the jth training image sample, phi (-) is a function, x
iMapping from the original feature space into the reconstructed kernel hilbert space,<,>representing the inner product, gamma is a preset hyper-parameter, and the value range is preferably [10 ]
-3,…,10
3]Adjusting; calculating each auxiliary data vector
And
kernel function value of (1) between
Wherein
Represents the ith auxiliary image sample,
representing the jth auxiliary image sample. Constructing kernel matrices K and K for image samples and auxiliary image data
*In which K is
ij＝k(x
i,x
j) The element representing the ith row and the jth column of the matrix K,
representative matrix K
*Row i and column j.
And step 3:computing a robust constraint matrix H for each image sample and the auxiliary image data separately
s，H
sThe ith row and the jth column of (1) are gradients of the ith training sample and the sth training sample kernel function and gradients of the jth training sample and the sth training sample kernel function, namely, the kernel functions are respectively corresponding to x
jAnd x
sThe partial derivatives are calculated and then the inner product between the two gradients is calculated, where i, j and s are all taken from 1 to n.
And 4, step 4: computing matrices
Matrix array
Wherein rho and lambda are respectively preset hyper-parameters, and the range of rho is [10 ]
-2,…,10
2]In the middle adjustment, λ is [10 ]
-5,…,10
1]Within-range adjustment, the upper right corner mark T represents the transposition operation, resulting in the following objective function:
1
T(α+β-C
1)＝0
y
Tα＝0
0≤α≤C
3
β≥0
wherein the content of the first and second substances,
representing the product of the vector element correspondences, α and β are lagrange multipliers, y ═ y
1,…,y
n]Is the label of the training sample, 1 represents the vector with all 1 elements, the top right-hand label T represents the transpose of the matrix, C
1And C
3Is a preset hyper-parameter, and the range is preferably [10 ]
-2,…,10
2]And (4) adjusting.
Define intermediate variable μ ═ α
T,β
T]
TAnd
to simplify the expression of the subsequent objective function, the following objective function is obtained:
1
T(α+β-C
1)＝0
y
Tα＝0
0≤α≤C
3
β≥0
the existing quadratic programming toolkit is used for optimizing and solving the quadratic programming problem corresponding to the objective function to obtain the optimal variable mu; .
And 5: based on the current optimal mu, order intermediate variable matrix
To solve the reconstruction coefficient matrix V, the following objective function is solved using in particular the Alternating Direction Multiplier Method (ADMM)
Wherein, C
1And C
2Is a preset hyper-parameter, and the range is preferably [10 ]
-2,…,10
2]And (4) adjusting.
Is a row vector of length l with elements of 1,
the elements of length n-l are row vectors of 1,
step 6, iterating and repeating the steps 4 and 5, wherein when the optimization changes of α and V are small, for example, the difference value of two iterations before and after the corresponding objective function value is less than 10
-3Considering the model to be converged and outputting a robust classifier model;
and 7: verifying the classification effect, predicting the label of the test sample possibly having noise, comparing with the real label, and calculating the overall classification precision (the ratio of the number of the predicted correct samples to the number of all samples).
The implementation platform of the embodiment of the invention is MATLAB software, and the bases of data reading and writing, basic mathematical operation, optimization solution and the like are known technologies in the technical field, and are not described herein again.
In specific implementation, the automatic operation of the process can be realized by adopting a software mode. The apparatus for operating the process should also be within the scope of the present invention.
It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description.
Claims (5)
1. A multi-spectral-segment image analysis method based on robust auxiliary information reconstruction for a support vector machine is characterized by comprising the following steps:
step 1, selecting n image samples and labels from an original multispectral image data set as training samples to obtain auxiliary image data
l is the number of auxiliary image data, where l < n, corresponding auxiliary image data, reconstructing the unknown training auxiliary image data
Then, the reconstruction coefficient matrix V ═ V is recorded
1，...，v
n]，v
1，...，v
nA vector of reconstructed coefficients for the respective assistance data;
step 2, respectively calculating allKernel matrices K and K for input of multispectral image samples and auxiliary image data
*；
Step 3, respectively calculating a robust constraint matrix H of each image sample and auxiliary image data
s；
Step 4, calculating the matrix
And
where ρ and λ are respectively predetermined hyper-parameters, defining intermediate variables, including μ ═ α
T，β
T]
Tα and β are Lagrange multipliers, and the quadratic programming problem corresponding to the objective function is solved in an optimized mode to obtain the optimal variable mu;
step 5, based on the current mu, optimizing and solving a reconstruction coefficient matrix V;
step 6, repeating the steps 4 to 5 until the model is converged, and outputting a robust classifier model;
and 7, verifying the classification effect, predicting the label of the test sample possibly with noise, and comparing the label with the real label.
2. The robust side information reconstruction based support vector machine multi-spectral band image analysis method according to claim 1, wherein: in step 4, the objective function is as follows,
1
T(α+β-C
1)＝0
y
Tα＝0
0≤α≤C
3
β≥0
wherein the content of the first and second substances,
representing the corresponding product of the vector elementsα and β are lagrange multipliers, y ═ y
1，...，y
n]Is the label of the training sample, 1 represents the vector with all 1 elements, the top right-hand label T represents the transpose of the matrix, C
1And C
3Is a pre-set hyper-parameter.
3. The method for analyzing multi-spectral-segment image of support vector machine based on robust auxiliary information reconstruction as claimed in claim 2, wherein in step 4, an intermediate variable μ ═ α is defined
T，β
T]
TAnd
the simplification results in the following objective function,
1
T(α+β-C
1)＝0
y
Tα＝0
0≤α≤C
3
β≥0
and (4) optimizing and solving a quadratic programming problem corresponding to the objective function by using a quadratic programming toolkit to obtain an optimal variable mu.
4. The robust side information reconstruction based support vector machine multi-spectral band image analysis method according to claim 3, wherein: in step 5, the implementation manner of the optimal solution of the reconstruction coefficient matrix V is as follows,
let the intermediate variable matrix
Solving the following objective function using the alternating direction multiplier method
Wherein, C
1And C
2Is a pre-set hyper-parameter,
is a row vector of length l with elements of 1,
the elements of length n-l are all row vectors of 1.
5. The robust side information reconstruction based support vector machine multi-spectral band image analysis method according to claim 1 or 2 or 3 or 4, wherein: in step 6, the difference value of the two iterations before and after the objective function value is less than 10
-3The model is considered to converge.
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