CN110020674B - Cross-domain self-adaptive image classification method for improving local category discrimination - Google Patents

Cross-domain self-adaptive image classification method for improving local category discrimination Download PDF

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CN110020674B
CN110020674B CN201910190041.4A CN201910190041A CN110020674B CN 110020674 B CN110020674 B CN 110020674B CN 201910190041 A CN201910190041 A CN 201910190041A CN 110020674 B CN110020674 B CN 110020674B
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宋士吉
陈一鸣
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Abstract

The invention relates to a cross-domain self-adaptive image classification method for improving local category discrimination, and belongs to the technical field of image processing. According to the cross-domain self-adaptive image classification method, when an image content classification model is trained, images of a training set and a testing set are different in tone, angle, definition and the like, and data representing image information obeys different probability distribution. The method has the advantages that the distributed and shared characteristics of the two images are learned, common points among the images with the same content and differences among the images with different contents are mined in other images with similar styles of each image, the aggregation of the images with the same content is stronger, the mutual interference among the images with different contents is reduced, the local category distinguishing degree of the image data set is improved, and the image classification accuracy is improved.

Description

Cross-domain self-adaptive image classification method for improving local category discrimination
Technical Field
The invention relates to a cross-domain self-adaptive image classification method for improving local category discrimination, and belongs to the technical field of image processing.
Background
In a general image classification problem, training set and test set images generally exhibit the same style. These images may be captured or drawn collectively in the same environment by the same equipment in a short time, or collected and collated by the collector intentionally according to some criteria. After the images are subjected to the data processing, the data obey the same probability distribution. In this case, the classifier is trained by using known image content classification information (i.e., labels) in the training set, so that the image content in the test set can be accurately identified and classified. However, when solving the actual problem, the image set involved in the problem, i.e., the target domain data set, often has insufficient content tags that can be used directly because of problems such as tag production cost. To cope with this, another set of labeled image sets with a style not identical to the target image style may be used as the training set, i.e., the source domain data set. The images of the source domain and the target domain are subjected to different probability distributions after being digitized. In this case, the classifier of the training set (source domain) cannot be directly used for classification of the test set (target domain) data. The core of the cross-domain image classification problem is to solve the problem that the image styles of the training set and the test set are inconsistent.
In recent years, researchers have proposed a variety of models and algorithms that enable cross-domain image classification. Since each image is composed of a large number of pixel points, the dimension of the image itself is often as high as 1e6, a commonly used method is to find a low-dimensional subspace, so that the images of the source domain and the target domain are subjected to the same or similar distribution after being subjected to dimension reduction mapping to the subspace, wherein the migration component analysis method proposed by Pan et al in 2011 and the joint distribution adaptation algorithm proposed by Long et al in 2013 are representative. The core idea is to search an optimal low-dimensional mapping to minimize the sample probability distribution difference in the low-dimensional space. The distance measurement method of probability distribution used in these two methods is the Maximum Mean Distance (MMD). The MMD is defined as the distance maximum of two expected values distributed under a certain function class mapping. And minimizing the MMD in the low-dimensional subspace to obtain the optimal low-dimensional invariant feature representation of the image, and eliminating the difference between the source domain image and the target domain image after dimension reduction.
Minimizing MMD, while having good results in terms of distribution alignment, can only numerically translate two different sets of images into the same distribution, according to the mathematical definition of MMD, without retaining sufficient information of the images themselves. This causes part of information that is useful for image classification to be lost in the low-dimensional subspace, resulting in a reduction in classification accuracy. Therefore, how to perfect an objective function in an algorithm based on MMD optimization is an important problem to protect key content information of an image while ensuring the cross-domain characteristics of the obtained features.
In the related algorithm of the classification problem, there are a lot of methods for improving the image classification degree of data distribution. Typical methods such as Linear Discriminant Analysis (LDA) simultaneously maximize the dispersion between data classes and minimize the dispersion within data classes in the form of rayleigh quotient, thereby realizing the aggregation of homogeneous data and the separation of heterogeneous data. Similarly, Yan et al, 2007, proposed an edge Fisher analysis (MFA) method that improves the class clustering operation of LDA on the global data distribution to be performed in the local neighborhood of each data point, i.e., maximizes the dispersion between each data point and the heterogeneous points in its neighborhood, and minimizes the dispersion between each data point and the homogeneous points in its neighborhood. Compared with LDA, MFA does not need the hypothesis that various data distributions obey Gaussian distribution, does not need prior information of the distribution, has better generalization capability, and can effectively solve the problem of data multimodal distribution. However, this method has not been applied to the problem of cross-domain adaptation of images.
Disclosure of Invention
The invention aims to provide a cross-domain self-adaptive image classification method for improving local category discrimination, which optimizes the local dispersion characteristics of a plurality of image samples and enhances the content discrimination of an image in a local adjacent range so as to be beneficial to the prediction of image content classification labels.
The invention provides a cross-domain self-adaptive image classification method for improving local category discrimination, which comprises the following steps:
(1) the method comprises the steps of scanning a plurality of images line by line, sequentially arranging pixels obtained by line scanning into column vectors according to a scanning sequence, and dividing the column vectors by Euclidean norms of the column vectors to obtain a plurality of image column vectors with Euclidean norms of 1;
(2) dividing a plurality of image column vectors obtained in the step (1) into a source domain training set { ZS,YSAnd target domain test set ZT}，
Figure BDA0001994113080000021
Wherein Z isSIs a set of a plurality of image column vectors in a source domain training set, YSIs a set of content classification labels for a plurality of images in a source domain training set, nSThe number of image column vectors in the training set for the source domain,
Figure BDA0001994113080000022
is ZSThe ith image column vector, i.e., the ith image sample in the source domain training set,
Figure BDA0001994113080000023
is a content classification label for the ith image, i.e.
Figure BDA0001994113080000024
Representing an object described by an image, with dimension 1;
Figure BDA0001994113080000025
wherein Z isTIs an objectSet of multiple image column vectors in a domain test set, nTThe number of image column vectors in the test set for the target domain,
Figure BDA0001994113080000026
is ZTA jth image column vector, namely a jth image sample in the target domain test set;
(3) respectively calculating a plurality of source domain training set samples of the step (2)
Figure BDA0001994113080000031
First column vector of
Figure BDA0001994113080000032
Figure BDA0001994113080000033
Wherein
Figure BDA0001994113080000034
K (·,) is a kernel function selected arbitrarily among a Gaussian kernel function, a hyperbolic tangent kernel function or a linear kernel function, and superscript T represents matrix transposition; using first column vectors respectively
Figure BDA0001994113080000035
Representing a plurality of images in a source domain training set and comparing the plurality of images
Figure BDA0001994113080000036
Sequentially arranged in rows to obtain a source domain training set matrix XS(ii) a Respectively calculating a plurality of target domain samples of the step (2)
Figure BDA0001994113080000037
Second column vector of
Figure BDA0001994113080000038
Figure BDA0001994113080000039
Wherein
Figure BDA00019941130800000310
Using second column vectors respectively
Figure BDA00019941130800000311
Representing a plurality of images in a target domain test set and combining the plurality of images
Figure BDA00019941130800000312
Sequentially arranging the target domain test set matrixes according to rows to obtain a target domain test set matrix XT(ii) a Training set matrix X according to source domainSAnd a target domain test set matrix XTObtaining a whole-body data set matrix X, X ═ XS,XT]；
(4) Setting a projection matrix ATUsing projection matrix ATPerforming linear mapping on the plurality of image column vectors obtained in the step (3), namely performing linear mapping on the plurality of image column vectors
Figure BDA00019941130800000313
And
Figure BDA00019941130800000314
respectively linear mapping to obtain projection column vector
Figure BDA00019941130800000315
And
Figure BDA00019941130800000316
(5) taking the projection column vector obtained after the linear mapping in the step (4) as an image data point sample, and establishing an optimization model of cross-domain self-adaptive image classification features, wherein an objective function of the optimization model comprises the following steps:
a. the square MMD of the maximum mean distance sample estimation value between the probability distribution of the image samples in the source domain training set and the probability distribution of the image samples in the target domain testing set2(S, T) is minimum:
Figure BDA00019941130800000317
wherein, Tr represents the trace of the matrix, i.e. the sum of diagonal elements of the matrix, M is the maximum mean distance matrix:
Figure BDA00019941130800000318
wherein 1 represents an all-1 matrix;
b. according to the types of the content classification labels in the step (2), enabling the square sum of the maximum mean distance sample estimation values between the sample probability distribution of each type of image samples in the source domain training set and the sample probability distribution of each type of image samples in the target domain testing set
Figure BDA0001994113080000041
To a minimum:
Figure BDA0001994113080000042
wherein C represents the number of image sample classes,
Figure BDA0001994113080000043
indicating that the data point is temporarily assigned at the current step
Figure BDA0001994113080000044
The prediction content classification label of (1) dimension,
Figure BDA0001994113080000045
representing the number of image samples in the source domain training set with a content classification label c,
Figure BDA0001994113080000046
representing the number of image samples with a current predicted content classification label of c in the target domain test set, McIs the maximum mean distance matrix of the image samples with content classification label c:
Figure BDA0001994113080000047
wherein e isScIs of length nSIs a column vector composed of 0 and 1, e is a column vector composed of e when the content classification label of the corresponding image in the source domain training set is cScThe value of the element in (e) is 1, and when the content classification label of the corresponding image in the source domain training set is not c, eScThe value of the element in (A) is 0; e.g. of the typeTcIs of length nTIs composed of 0 and 1, eTcThe element value of (1) represents that the corresponding image in the target domain test set has the current prediction content classification label of c, eTcThe value of the element in the target domain is 0, which indicates that the classification label of the corresponding image in the target domain test set in the current prediction content is not c;
c. minimizing the weighted square sum of the Euclidean distance between the projection column vectors of every two image samples with the same content label in the source domain training set and the Euclidean distance between the projection column vectors of every two image samples with the same content label in the target domain testing set:
Figure BDA0001994113080000048
in the first row of the above-mentioned formula,
Figure BDA0001994113080000049
and
Figure BDA00019941130800000410
the weighting coefficients for the distance between every two image samples with the same content label inside the source domain training set and the target domain test set respectively,
Figure BDA00019941130800000411
indicating if the image sample is
Figure BDA00019941130800000412
Is a sample of an image
Figure BDA00019941130800000413
Like k-neighbors of, then get ηijIf the image sample is 1
Figure BDA00019941130800000414
Not of image samples
Figure BDA00019941130800000415
Like k-neighbors of, then get ηijWhen the value of k is 0, the value of k is determined according to the precision of image processing; alpha is alphacIs a positive coefficient, alpha, associated with a class in the source domain training setcIs determined according to the accuracy of the image processing, in one embodiment of the invention, αcIs 0.01;
Figure BDA0001994113080000051
if the image sample
Figure BDA0001994113080000052
Is a sample of an image
Figure BDA0001994113080000053
Like k-neighbors of, then get ηklIf the image sample is 1
Figure BDA0001994113080000054
Not of image samples
Figure BDA0001994113080000055
Like k-neighbors of, then get ηkl＝0；βcIs a positive coefficient, β, associated with the class in the target domain test setcThe value of (a) is determined according to the precision of image processing;
in the first term of the second line of the above formula, WSIs formed by weight coefficients
Figure BDA0001994113080000056
The weight matrix of the composition is formed,
Figure BDA0001994113080000057
is a diagonal matrix with diagonal elements in the diagonal matrix of
Figure BDA0001994113080000058
RSIs an intra-class dispersion matrix of a source domain training set,
Figure BDA0001994113080000059
in the second term of the second line of the above formula, WTIs formed by weight coefficients
Figure BDA00019941130800000510
The weight matrix of the composition is formed,
Figure BDA00019941130800000511
is a diagonal matrix with diagonal elements in the diagonal matrix of
Figure BDA00019941130800000512
RTIs an intra-class dispersion matrix of the target domain,
Figure BDA00019941130800000513
the definition of the matrix R in the third row of the above equation is:
Figure BDA00019941130800000514
wherein 0 represents a matrix with elements all 0;
d. maximizing the weighted square sum of the Euclidean distance between the projection column vectors of every two image samples with different content labels in the source domain training set and the Euclidean distance between the projection column vectors of every two image samples with different content labels in the target domain testing set:
Figure BDA00019941130800000515
in the first row of the above-mentioned formula,
Figure BDA00019941130800000516
and
Figure BDA00019941130800000517
weighting coefficients for the distance between the image samples with different content labels inside the source domain training set and the target domain testing set respectively,
Figure BDA00019941130800000518
if the image sample
Figure BDA00019941130800000519
Is a sample of an image
Figure BDA00019941130800000520
Of different classes of neighbors, then
Figure BDA00019941130800000530
If the image sample
Figure BDA00019941130800000521
Not of image samples
Figure BDA00019941130800000522
Of different classes of neighbors, then
Figure BDA00019941130800000523
Figure BDA00019941130800000524
Indicating points
Figure BDA00019941130800000525
Is a point
Figure BDA00019941130800000526
The different kinds of neighboring points of (a),
Figure BDA00019941130800000527
indicating points
Figure BDA00019941130800000528
Is not a point
Figure BDA00019941130800000529
Different classes of neighbors of (1);
in the first term of the second line of the above formula, USIs formed by weight coefficients
Figure BDA0001994113080000061
The weight matrix of the composition is formed,
Figure BDA0001994113080000062
is a diagonal matrix having diagonal elements of
Figure BDA0001994113080000063
PSIs an inter-class dispersion matrix of the source domain training set,
Figure BDA0001994113080000064
in the second term of the second row, UTIs formed by weight coefficients
Figure BDA0001994113080000065
The weight matrix of the composition is formed,
Figure BDA0001994113080000066
is a diagonal matrix having diagonal elements of
Figure BDA0001994113080000067
PTIs the inter-class dispersion matrix of the target domain test set,
Figure BDA0001994113080000068
the definition of matrix P in the third row of the above equation is:
Figure BDA0001994113080000069
e. making the projection matrix A in step (4)TThe regularization term of (d) is minimum:
Figure BDA00019941130800000610
wherein,
Figure BDA00019941130800000611
is the sum of the squares of all elements in the matrix a, λ is a positive coefficient, and the value of λ is taken according to the image classification accuracy, and in one embodiment of the method, the value is 1;
according to the objective function, an optimization model of cross-domain self-adaptive image classification features is obtained as follows:
Figure BDA00019941130800000612
(6) and solving the optimization model of the cross-domain self-adaptive image classification characteristics, and initializing to obtain the following optimization model in the first iteration of solving the optimization model:
Figure BDA00019941130800000613
wherein I is an identity matrix, and the optimization model is solved by the following formula to obtain an intermediate optimal solution A*：
Figure BDA00019941130800000614
Where Θ is the diagonal matrix and the diagonal elements of the diagonal matrix are matrices
Figure BDA00019941130800000615
Relative to the matrix
Figure BDA00019941130800000616
Solving the matrix for the generalized eigenvalues of
Figure BDA00019941130800000617
Relative to the matrix
Figure BDA00019941130800000618
N of (A) to (B)S+nTA sum of generalized eigenvalues and nS+nTN corresponding to each generalized eigenvalueS+nTA generalized characteristic column vector from nS+nTM minimum generalized eigenvalues are selected from the generalized eigenvalues and are arranged in the order from small to large, m generalized eigenvalue column vectors respectively corresponding to the m generalized eigenvalues obtained by selection are sequentially arranged in rows in the same order as the m generalized eigenvalues, and a matrix A is obtained*，A*Is a first intermediate optimal solution of the above-mentioned optimization model;
(7) according to the first intermediate optimal solution A obtained in the step (6)*For the original image column vector
Figure BDA0001994113080000071
And
Figure BDA0001994113080000072
linear mapping is carried out to obtain the column vector of the image sample
Figure BDA0001994113080000073
And
Figure BDA0001994113080000074
using column vectors
Figure BDA0001994113080000075
Making training set, and aligning column vector by using nearest neighbor method
Figure BDA0001994113080000076
Predicting image content labels to obtain predicted content labels of a group of target domain test set samples
Figure BDA0001994113080000077
(8) Substituting the predicted content label obtained in the step (7) into the complete optimization model in the step (5), solving the optimization model, and solving the intermediate optimal solution A of the optimization model by using the following formula*：
Figure BDA0001994113080000078
Where Θ is the diagonal matrix and the diagonal elements of the diagonal matrix are matrices
Figure BDA0001994113080000079
Relative to matrix XPXTThe generalized eigenvalues of (a); solving the matrix
Figure BDA00019941130800000710
Relative to matrix XPXTN of (A) to (B)S+nTA generalized eigenvalue and nS+nTN corresponding to each generalized eigenvalueS+nTA generalized characteristic column vector from nS+nTM minimum generalized eigenvalues are selected from the generalized eigenvalues and are arranged in the order from small to large, m generalized eigenvalue column vectors respectively corresponding to the m generalized eigenvalues obtained by selection are sequentially arranged in rows in the same order as the m generalized eigenvalues, and a projection matrix A is obtained*，A*Is a second intermediate optimal solution of the above-mentioned optimization model;
(9) replacing the first intermediate optimal solution in the step (7) with the second intermediate optimal solution obtained in the step (8), repeating the steps (7) and (8), and predicting the content label of the step (7) obtained by N times of circulation
Figure BDA00019941130800000711
Making a judgment if the predicted content label obtained in N cycles
Figure BDA00019941130800000712
If the two are identical, ending the iteration and labeling the predicted content obtained in the step (7) in the last iteration
Figure BDA00019941130800000713
As a prediction result, namely an image classification result, the cross-domain self-adaptive image classification for improving the local category discrimination is realized; if obtained in N cyclesContent measurement label
Figure BDA00019941130800000714
And (3) if the two solutions are not identical, returning to the step (7), replacing the first intermediate optimal solution in the step (7) with the second intermediate optimal solution obtained in the step (8), repeating the steps (7) and (8), determining the value of N according to the image classification precision, and in one embodiment of the method, setting the value of N to be 10.
The cross-domain self-adaptive image classification method for improving the local category discrimination, provided by the invention, has the characteristics and advantages that:
according to the cross-domain self-adaptive image classification method for improving the local category discrimination, when an image content classification model is trained, images of a training set and a testing set are different in aspects of tone, angle, definition and the like, and data representing image information obeys different probability distribution. The method has the advantages that the distributed and shared characteristics of the two images are learned, common points among the images with the same content and differences among the images with different contents are mined in other images with similar styles of each image, the images with the same content are enabled to be more highly aggregated, mutual interference among the images with different contents is reduced, and therefore the local category distinguishing degree of the image data set is improved, and the classifying accuracy is further improved.
In conclusion, the image classification method can optimize the local dispersion characteristics of a plurality of image samples, enhance the content discrimination of the image in the local neighbor range and facilitate the prediction of the image content classification label; and the predicted image content label is updated iteratively, so that the accuracy and the reliability of image content classification are improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention provides a cross-domain self-adaptive image classification method for improving local category discrimination, a flow chart of which is shown in figure 1, and the method comprises the following steps:
(1) the method comprises the steps of scanning a plurality of images line by line, sequentially arranging pixels obtained by line scanning into column vectors according to a scanning sequence, and dividing the column vectors by Euclidean norms of the column vectors to obtain a plurality of image column vectors with Euclidean norms of 1;
(2) dividing a plurality of image column vectors obtained in the step (1) into a source domain training set { ZS,YSAnd target domain test set ZT}，
Figure BDA0001994113080000081
Wherein Z isSIs a set of a plurality of image column vectors in a source domain training set, YSIs a set of content classification labels for a plurality of images in a source domain training set, nSThe number of image column vectors in the training set for the source domain,
Figure BDA0001994113080000082
is ZSThe ith image column vector, i.e., the ith image sample in the source domain training set,
Figure BDA0001994113080000083
is a content classification label for the ith image, i.e.
Figure BDA0001994113080000084
Representing an object described by an image, with dimension 1;
Figure BDA0001994113080000085
wherein Z isTIs a set of a plurality of image column vectors in a target domain test set, nTThe number of image column vectors in the test set for the target domain,
Figure BDA0001994113080000086
is ZTThe jth image column vector is the jth image sample in the target domain test set, and the content classification label in the target domain test set is unknown;
(3) respectively calculating a plurality of source domain training set samples of the step (2)
Figure BDA0001994113080000091
First column vector of
Figure BDA0001994113080000092
Figure BDA0001994113080000093
Wherein
Figure BDA0001994113080000094
K (·,) is a kernel function selected arbitrarily among a Gaussian kernel function, a hyperbolic tangent kernel function or a linear kernel function, and superscript T represents matrix transposition; using first column vectors respectively
Figure BDA0001994113080000095
Representing a plurality of images in a source domain training set and comparing the plurality of images
Figure BDA0001994113080000096
Sequentially arranged in rows to obtain a source domain training set matrix XS(ii) a Respectively calculating a plurality of target domain samples of the step (2)
Figure BDA0001994113080000097
Second column vector of
Figure BDA0001994113080000098
Figure BDA0001994113080000099
Wherein
Figure BDA00019941130800000910
Using second column vectors respectively
Figure BDA00019941130800000911
Representing a plurality of images in a target domain test set and combining the plurality of images
Figure BDA00019941130800000912
Sequentially arranging the target domain test set matrixes according to rows to obtain a target domain test set matrix XT(ii) a Training set matrix X according to source domainSAnd a target domain test set matrix XTObtaining a whole-body data set matrix X, X ═ XS,XT]；
(4) Setting a projection matrix ATUsing projection matrix ATPerforming linear mapping on the plurality of image column vectors obtained in the step (3), namely performing linear mapping on the plurality of image column vectors
Figure BDA00019941130800000913
And
Figure BDA00019941130800000914
respectively linear mapping to obtain projection column vector
Figure BDA00019941130800000915
And
Figure BDA00019941130800000916
matrix ATThe value is undetermined;
(5) taking the projection column vector obtained after the linear mapping in the step (4) as an image data point sample, and establishing an optimization model of cross-domain self-adaptive image classification features, wherein an objective function of the optimization model comprises the following steps:
a. the square MMD of the maximum mean distance sample estimation value between the probability distribution of the image samples in the source domain training set and the probability distribution of the image samples in the target domain testing set2(S, T) is minimum:
Figure BDA00019941130800000917
wherein, Tr represents the trace of the matrix, i.e. the sum of diagonal elements of the matrix, M is the maximum mean distance matrix:
Figure BDA00019941130800000918
wherein 1 represents an all-1 matrix;
b. according to the types of the content classification labels in the step (2), the maximum average between the sample probability distribution of each type of image sample in the source domain training set and the sample probability distribution of each type of image sample in the target domain testing set is enabled to beSum of squares of the estimated values of the value distance samples
Figure BDA0001994113080000101
To a minimum:
Figure BDA0001994113080000102
wherein C represents the number of image sample classes,
Figure BDA0001994113080000103
indicating that the data point is temporarily assigned at the current step
Figure BDA0001994113080000104
The prediction content classification label of (1) dimension,
Figure BDA0001994113080000105
representing the number of image samples in the source domain training set with a content classification label c,
Figure BDA0001994113080000106
representing the number of image samples with a current predicted content classification label of c in the target domain test set, McIs the maximum mean distance matrix of the image samples with content classification label c:
Figure BDA0001994113080000107
wherein e isScIs of length nSIs a column vector composed of 0 and 1, e is a column vector composed of e when the content classification label of the corresponding image in the source domain training set is cScThe value of the element in (e) is 1, and when the content classification label of the corresponding image in the source domain training set is not c, eScThe value of the element in (A) is 0; e.g. of the typeTcIs of length nTIs composed of 0 and 1, eTcThe element value of (1) represents that the corresponding image in the target domain test set has the current prediction content classification label of c, eTcThe value of the element in (1) is 0, which represents the target domain measurementThe classification label of the corresponding image in the trial set in the current prediction content is not c;
c. minimizing the weighted square sum of the Euclidean distance between the projection column vectors of every two image samples with the same content label in the source domain training set and the Euclidean distance between the projection column vectors of every two image samples with the same content label in the target domain testing set:
Figure BDA0001994113080000108
in the first row of the above-mentioned formula,
Figure BDA0001994113080000109
and
Figure BDA00019941130800001010
the weighting coefficients for the distance between every two image samples with the same content label inside the source domain training set and the target domain test set respectively,
Figure BDA00019941130800001011
indicating if the image sample is
Figure BDA00019941130800001012
Is a sample of an image
Figure BDA00019941130800001013
Like k-neighbors of, then get ηijIf the image sample is 1
Figure BDA00019941130800001014
Not of image samples
Figure BDA00019941130800001015
Like k-neighbors of, then get ηijWhen the value of k is 0, the value of k is determined according to the precision of image processing; alpha is alphacIs a positive coefficient, alpha, associated with a class in the source domain training setcIs determined according to the accuracy of the image processing, in one embodiment of the invention, αcIs 0.01;
Figure BDA0001994113080000111
if the image sample
Figure BDA0001994113080000112
Is a sample of an image
Figure BDA0001994113080000113
Like k-neighbors of, then get ηklIf the image sample is 1
Figure BDA0001994113080000114
Not of image samples
Figure BDA0001994113080000115
Like k-neighbors of, then get ηkl＝0；βcIs a positive coefficient, β, associated with the class in the target domain test setcIs determined according to the accuracy of the image processing, in one embodiment of the invention, βcIs 0.01;
in the first term of the second line of the above formula, WSIs formed by weight coefficients
Figure BDA0001994113080000116
The weight matrix of the composition is formed,
Figure BDA0001994113080000117
is a diagonal matrix with diagonal elements in the diagonal matrix of
Figure BDA0001994113080000118
RSIs an intra-class dispersion matrix of a source domain training set,
Figure BDA0001994113080000119
in the second term of the second line of the above formula, WTIs formed by weight coefficients
Figure BDA00019941130800001110
The weight matrix of the composition is formed,
Figure BDA00019941130800001111
is a diagonal matrix with diagonal elements in the diagonal matrix of
Figure BDA00019941130800001112
RTIs an intra-class dispersion matrix of the target domain,
Figure BDA00019941130800001113
the definition of the matrix R in the third row of the above equation is:
Figure BDA00019941130800001114
wherein 0 represents a matrix with elements all 0;
d. maximizing the weighted square sum of the Euclidean distance between the projection column vectors of every two image samples with different content labels in the source domain training set and the Euclidean distance between the projection column vectors of every two image samples with different content labels in the target domain testing set:
Figure BDA00019941130800001115
in the first row of the above-mentioned formula,
Figure BDA00019941130800001116
and
Figure BDA00019941130800001117
weighting coefficients for the distance between the image samples with different content labels inside the source domain training set and the target domain testing set respectively,
Figure BDA00019941130800001118
if the image sample
Figure BDA00019941130800001119
Is a sample of an image
Figure BDA00019941130800001120
Of different classes of neighbors, then
Figure BDA00019941130800001121
If the image sample
Figure BDA00019941130800001122
Not of image samples
Figure BDA00019941130800001123
Of different classes of neighbors, then
Figure BDA00019941130800001124
Figure BDA0001994113080000121
Indicating points
Figure BDA0001994113080000122
Is a point
Figure BDA0001994113080000123
The different kinds of neighboring points of (a),
Figure BDA0001994113080000124
indicating points
Figure BDA0001994113080000125
Is not a point
Figure BDA0001994113080000126
Different classes of neighbors of (1);
in the first term of the second line of the above formula, USIs formed by weight coefficients
Figure BDA0001994113080000127
The weight matrix of the composition is formed,
Figure BDA0001994113080000128
is a diagonal matrix having diagonal elements of
Figure BDA0001994113080000129
PSIs an inter-class dispersion matrix of the source domain training set,
Figure BDA00019941130800001210
in the second term of the second row, UTIs formed by weight coefficients
Figure BDA00019941130800001211
The weight matrix of the composition is formed,
Figure BDA00019941130800001212
is a diagonal matrix having diagonal elements of
Figure BDA00019941130800001213
PTIs the inter-class dispersion matrix of the target domain test set,
Figure BDA00019941130800001214
the definition of matrix P in the third row of the above equation is:
Figure BDA00019941130800001215
e. making the projection matrix A in step (4)TThe regularization term of (d) is minimum:
Figure BDA00019941130800001216
wherein,
Figure BDA00019941130800001217
is the sum of the squares of all elements in the matrix a, λ is a positive coefficient, and the value of λ is taken according to the image classification accuracy, and in one embodiment of the method, the value is 1;
according to the objective function, an optimization model of cross-domain self-adaptive image classification features is obtained as follows:
Figure BDA00019941130800001218
(6) and solving the optimization model of the cross-domain self-adaptive image classification characteristics, and initializing to obtain the following optimization model in the first iteration of solving the optimization model:
Figure BDA00019941130800001219
wherein I is an identity matrix, and the optimization model is solved by the following formula to obtain an intermediate optimal solution A*：
Figure BDA00019941130800001220
Where Θ is the diagonal matrix and the diagonal elements of the diagonal matrix are matrices
Figure BDA00019941130800001221
Relative to the matrix
Figure BDA00019941130800001222
Solving the matrix for the generalized eigenvalues of
Figure BDA00019941130800001223
Relative to the matrix
Figure BDA00019941130800001224
N of (A) to (B)S+nTA sum of generalized eigenvalues and nS+nTN corresponding to each generalized eigenvalueS+nTA generalized characteristic column vector from nS+nTM minimum generalized eigenvalues are selected from the generalized eigenvalues and are arranged in the order from small to large, m generalized eigenvalue column vectors respectively corresponding to the m generalized eigenvalues obtained by selection are sequentially arranged in rows in the same order as the m generalized eigenvalues, and a matrix A is obtained*，A*Is a first intermediate optimal solution of the above-mentioned optimization model;
(7) according to the first intermediate optimal solution A obtained in the step (6)*For the original image column vector
Figure BDA0001994113080000131
And
Figure BDA0001994113080000132
linear mapping is carried out to obtain the column vector of the image sample
Figure BDA0001994113080000133
And
Figure BDA0001994113080000134
using column vectors
Figure BDA0001994113080000135
Making training set, and aligning column vector by using nearest neighbor method
Figure BDA0001994113080000136
Predicting image content labels to obtain predicted content labels of a group of target domain test set samples
Figure BDA0001994113080000137
(8) Substituting the predicted content label obtained in the step (7) into the complete optimization model in the step (5), solving the optimization model, and solving the intermediate optimal solution A of the optimization model by using the following formula*：
Figure BDA0001994113080000138
Where Θ is the diagonal matrix and the diagonal elements of the diagonal matrix are matrices
Figure BDA0001994113080000139
Relative to matrix XPXTThe generalized eigenvalues of (a); solving the matrix
Figure BDA00019941130800001310
Relative to matrix XPXTN of (A) to (B)S+nTA generalized eigenvalue and nS+nTN corresponding to each generalized eigenvalueS+nTA generalized characteristic column vector from nS+nTM minimum generalized eigenvalues are selected from the generalized eigenvalues and are arranged in the order from small to large, m generalized eigenvalue column vectors respectively corresponding to the m generalized eigenvalues obtained by selection are sequentially arranged in rows in the same order as the m generalized eigenvalues, and a projection matrix A is obtained*，A*Is a second intermediate optimal solution of the above-mentioned optimization model;
(9) replacing the first intermediate optimal solution in the step (7) with the second intermediate optimal solution obtained in the step (8), repeating the steps (7) and (8), and predicting the content label of the step (7) obtained by N times of circulation
Figure BDA00019941130800001311
Making a judgment if the predicted content label obtained in N cycles
Figure BDA00019941130800001312
If the two are identical, ending the iteration and labeling the predicted content obtained in the step (7) in the last iteration
Figure BDA00019941130800001313
As a prediction result, namely an image classification result, the cross-domain self-adaptive image classification for improving the local category discrimination is realized; if predicted content label obtained in N cycles
Figure BDA00019941130800001314
And (3) if the two solutions are not identical, returning to the step (7), replacing the first intermediate optimal solution in the step (7) with the second intermediate optimal solution obtained in the step (8), repeating the steps (7) and (8), determining the value of N according to the image classification precision, and in one embodiment of the method, setting the value of N to be 10.

Claims (1)

1. A cross-domain self-adaptive image classification method for improving local category discrimination is characterized by comprising the following steps:
(1) the method comprises the steps of scanning a plurality of images line by line, sequentially arranging pixels obtained by line scanning into column vectors according to a scanning sequence, and dividing the column vectors by Euclidean norms of the column vectors to obtain a plurality of image column vectors with Euclidean norms of 1;
(2) dividing a plurality of image column vectors obtained in the step (1) into a source domain training set { ZS,YSAnd target domain test set ZT}，
Figure FDA0002781721920000011
Wherein Z isSIs a set of a plurality of image column vectors in a source domain training set, YSIs a set of content classification labels for a plurality of images in a source domain training set, nSThe number of image column vectors in the training set for the source domain,
Figure FDA0002781721920000012
is ZSThe ith image column vector, i.e., the ith image sample in the source domain training set,
Figure FDA0002781721920000013
is a content classification label for the ith image, i.e.
Figure FDA0002781721920000014
Representing an object described by an image, with dimension 1;
Figure FDA0002781721920000015
wherein Z isTIs a set of a plurality of image column vectors in a target domain test set, nTThe number of image column vectors in the test set for the target domain,
Figure FDA0002781721920000016
is ZTA jth image column vector, namely a jth image sample in the target domain test set;
(3) respectively calculating a plurality of source domain training set samples of the step (2)
Figure FDA0002781721920000017
First column vector of
Figure FDA0002781721920000018
Figure FDA0002781721920000019
Wherein
Figure FDA00027817219200000110
K (·,) is a kernel function selected arbitrarily among a Gaussian kernel function, a hyperbolic tangent kernel function or a linear kernel function, and superscript T represents matrix transposition; using first column vectors respectively
Figure FDA00027817219200000111
Representing a plurality of images in a source domain training set and comparing the plurality of images
Figure FDA00027817219200000112
Sequentially arranged in rows to obtain a source domain training set matrix XS(ii) a Respectively calculating a plurality of target domain samples of the step (2)
Figure FDA00027817219200000113
Second column vector of
Figure FDA00027817219200000114
Figure FDA00027817219200000115
Wherein
Figure FDA00027817219200000116
Using second column vectors respectively
Figure FDA00027817219200000117
To representThe target domain test collects a plurality of images and combines the plurality of images
Figure FDA00027817219200000118
Sequentially arranging the target domain test set matrixes according to rows to obtain a target domain test set matrix XT(ii) a Training set matrix X according to source domainSAnd a target domain test set matrix XTObtaining a whole-body data set matrix X, X ═ XS,XT]；
(4) Setting a projection matrix ATUsing projection matrix ATPerforming linear mapping on the plurality of image column vectors obtained in the step (3), namely performing linear mapping on the plurality of image column vectors
Figure FDA0002781721920000021
And
Figure FDA0002781721920000022
respectively linear mapping to obtain projection column vector
Figure FDA0002781721920000023
And
Figure FDA0002781721920000024
(5) taking the projection column vector obtained after the linear mapping in the step (4) as an image data point sample, and establishing an optimization model of cross-domain self-adaptive image classification features, wherein an objective function of the optimization model comprises the following steps:
a. the square MMD of the maximum mean distance sample estimation value between the probability distribution of the image samples in the source domain training set and the probability distribution of the image samples in the target domain testing set2(S, T) is minimum:
Figure FDA0002781721920000025
wherein, Tr represents the trace of the matrix, i.e. the sum of diagonal elements of the matrix, M is the maximum mean distance matrix:
Figure FDA0002781721920000026
wherein 1 represents an all-1 matrix;
b. according to the types of the content classification labels in the step (2), enabling the square sum of the maximum mean distance sample estimation values between the sample probability distribution of each type of image samples in the source domain training set and the sample probability distribution of each type of image samples in the target domain testing set
Figure FDA0002781721920000027
To a minimum:
Figure FDA0002781721920000028
wherein C represents the number of image sample classes,
Figure FDA0002781721920000029
indicating that the data point is temporarily assigned at the current step
Figure FDA00027817219200000210
The prediction content classification label of (1) dimension,
Figure FDA00027817219200000211
representing the number of image samples in the source domain training set with a content classification label c,
Figure FDA00027817219200000212
representing the number of image samples with a current predicted content classification label of c in the target domain test set, McIs the maximum mean distance matrix of the image samples with content classification label c:
Figure FDA00027817219200000213
wherein e isScIs of length nSIs a column vector composed of 0 and 1, e is a column vector composed of e when the content classification label of the corresponding image in the source domain training set is cScThe value of the element in (e) is 1, and when the content classification label of the corresponding image in the source domain training set is not c, eScThe value of the element in (A) is 0; e.g. of the typeTcIs of length nTIs composed of 0 and 1, eTcThe element value of (1) represents that the corresponding image in the target domain test set has the current prediction content classification label of c, eTcThe value of the element in the target domain is 0, which indicates that the classification label of the corresponding image in the target domain test set in the current prediction content is not c;
c. minimizing the weighted square sum of the Euclidean distance between the projection column vectors of every two image samples with the same content label in the source domain training set and the Euclidean distance between the projection column vectors of every two image samples with the same content label in the target domain testing set:
Figure FDA0002781721920000031
in the first row of the above-mentioned formula,
Figure FDA0002781721920000032
and
Figure FDA0002781721920000033
the weight coefficients of the distance between every two image samples with the same content label in the source domain training set and the target domain testing set respectively,
Figure FDA0002781721920000034
ηijif an image sample is represented by 1
Figure FDA0002781721920000035
Is a sample of an image
Figure FDA0002781721920000036
The same class of K-neighbors of (1), then eta is obtainedijIf the image sample is 1
Figure FDA0002781721920000037
Not of image samples
Figure FDA0002781721920000038
The same class of K-neighbors of (1), then eta is obtainedijWhen the value of K is 0, the value of K is determined according to the precision of image processing; alpha is alphacIs a positive coefficient, alpha, associated with a class in the source domain training setcThe value of (a) is determined according to the precision of image processing;
Figure FDA0002781721920000039
if the image sample
Figure FDA00027817219200000310
Is a sample of an image
Figure FDA00027817219200000311
The same class of K-neighbors of (1), then eta is obtainedklIf the image sample is 1
Figure FDA00027817219200000312
Not of image samples
Figure FDA00027817219200000313
The same class of K-neighbors of (1), then eta is obtainedkl＝0；βcIs a positive coefficient, β, associated with the class in the target domain test setcThe value of (a) is determined according to the precision of image processing;
in the first term of the second line of the above formula, WSIs formed by weight coefficients
Figure FDA00027817219200000314
The weight matrix of the composition is formed,
Figure FDA00027817219200000315
is a diagonal matrix with diagonal elements in the diagonal matrix of
Figure FDA00027817219200000316
RSIs an intra-class dispersion matrix of a source domain training set,
Figure FDA00027817219200000317
in the second term of the second line of the above formula, WTIs formed by weight coefficients
Figure FDA00027817219200000318
The weight matrix of the composition is formed,
Figure FDA00027817219200000319
is a diagonal matrix with diagonal elements in the diagonal matrix of
Figure FDA0002781721920000041
RTIs an intra-class dispersion matrix of the target domain,
Figure FDA0002781721920000042
the definition of the matrix R in the third row of the above equation is:
Figure FDA0002781721920000043
wherein 0 represents a matrix with elements all 0;
d. maximizing the weighted square sum of the Euclidean distance between the projection column vectors of every two image samples with different content labels in the source domain training set and the Euclidean distance between the projection column vectors of every two image samples with different content labels in the target domain testing set:
Figure FDA0002781721920000044
in the first row of the above-mentioned formula,
Figure FDA0002781721920000045
and
Figure FDA0002781721920000046
the weight coefficients of the distance between every two image samples with different content labels in the source domain training set and the target domain testing set respectively,
Figure FDA0002781721920000047
if the image sample
Figure FDA0002781721920000048
Is a sample of an image
Figure FDA0002781721920000049
Of different classes of neighbors, then
Figure FDA00027817219200000410
If the image sample
Figure FDA00027817219200000411
Not of image samples
Figure FDA00027817219200000412
Of different classes of neighbors, then
Figure FDA00027817219200000413
Figure FDA00027817219200000414
Figure FDA00027817219200000415
Indicating points
Figure FDA00027817219200000416
Is a point
Figure FDA00027817219200000417
The different kinds of neighboring points of (a),
Figure FDA00027817219200000418
indicating points
Figure FDA00027817219200000419
Is not a point
Figure FDA00027817219200000420
Different classes of neighbors of (1);
in the first term of the second line of the above formula, USIs formed by weight coefficients
Figure FDA00027817219200000421
The weight matrix of the composition is formed,
Figure FDA00027817219200000422
is a diagonal matrix having diagonal elements of
Figure FDA00027817219200000423
PSIs an inter-class dispersion matrix of the source domain training set,
Figure FDA00027817219200000424
in the second term of the second row, UTIs formed by weight coefficients
Figure FDA00027817219200000425
The weight matrix of the composition is formed,
Figure FDA00027817219200000426
is a diagonal matrix having diagonal elements of
Figure FDA00027817219200000427
PTClass being target domain test setThe matrix of the inter-dispersion is,
Figure FDA00027817219200000428
the definition of matrix P in the third row of the above equation is:
Figure FDA00027817219200000429
e. making the projection matrix A in step (4)TThe regularization term of (d) is minimum:
Figure FDA00027817219200000430
wherein,
Figure FDA0002781721920000051
is the sum of squares of all elements in the matrix A, lambda is a positive coefficient, and the value of lambda is 1 according to the image classification precision;
according to the objective function, an optimization model of cross-domain self-adaptive image classification features is obtained as follows:
Figure FDA0002781721920000052
(6) and solving the optimization model of the cross-domain self-adaptive image classification characteristics, and initializing to obtain the following optimization model in the first iteration of solving the optimization model:
Figure FDA0002781721920000053
wherein I is an identity matrix, and the optimization model is solved by the following formula to obtain an intermediate optimal solution A*：
Figure FDA0002781721920000054
Where Θ is the diagonal matrix and the diagonal elements of the diagonal matrix are matrices
Figure FDA0002781721920000055
Relative to the matrix
Figure FDA0002781721920000056
Solving the matrix for the generalized eigenvalues of
Figure FDA0002781721920000057
Relative to the matrix
Figure FDA0002781721920000058
N of (A) to (B)S+nTA sum of generalized eigenvalues and nS+nTN corresponding to each generalized eigenvalueS+nTA generalized characteristic column vector from nS+nTM minimum generalized eigenvalues are selected from the generalized eigenvalues and are arranged in the order from small to large, m generalized eigenvalue column vectors respectively corresponding to the m generalized eigenvalues obtained by selection are sequentially arranged in rows in the same order as the m generalized eigenvalues, and a matrix A is obtained*，A*Is a first intermediate optimal solution of the above-mentioned optimization model;
(7) according to the intermediate optimal solution A obtained in the step (6)*For the original image column vector
Figure FDA0002781721920000059
And
Figure FDA00027817219200000510
linear mapping is carried out to obtain the column vector of the image sample
Figure FDA00027817219200000511
And
Figure FDA00027817219200000512
using column vectors
Figure FDA00027817219200000513
Making training set, and aligning column vector by using nearest neighbor method
Figure FDA00027817219200000514
Predicting image content labels to obtain predicted content labels of a group of target domain test set samples
Figure FDA00027817219200000515
(8) Substituting the predicted content label obtained in the step (7) into the complete optimization model in the step (5), solving the optimization model, and solving the intermediate optimal solution A of the optimization model by using the following formula*：
Figure FDA00027817219200000516
Where Θ is the diagonal matrix and the diagonal elements of the diagonal matrix are matrices
Figure FDA00027817219200000517
Relative to matrix XPXTThe generalized eigenvalues of (a); solving the matrix
Figure FDA0002781721920000061
Relative to matrix XPXTN of (A) to (B)S+nTA generalized eigenvalue and nS+nTN corresponding to each generalized eigenvalueS+nTA generalized characteristic column vector from nS+nTM minimum generalized eigenvalues are selected from the generalized eigenvalues and are arranged in the order from small to large, m generalized eigenvalue column vectors respectively corresponding to the m generalized eigenvalues obtained by selection are sequentially arranged in rows in the same order as the m generalized eigenvalues, and a projection matrix A is obtained*，A*Is a second intermediate optimal solution of the above-mentioned optimization model;
(9) replacing the first intermediate optimal solution in the step (7) with the second intermediate optimal solution obtained in the step (8), repeating the steps (7) and (8), and predicting the content label of the step (7) obtained by N times of circulation
Figure FDA0002781721920000062
Making a judgment if the predicted content label obtained in the last N cycles
Figure FDA0002781721920000063
If the two are identical, ending the iteration and labeling the predicted content obtained in the step (7) in the last iteration
Figure FDA0002781721920000064
As a prediction result, namely an image classification result, the cross-domain self-adaptive image classification for improving the local category discrimination is realized; if predicted content label obtained in N cycles
Figure FDA0002781721920000065
And (4) if the image classification accuracy is not the same, returning to the step (7), replacing the first intermediate optimal solution in the step (7) with the second intermediate optimal solution obtained in the step (8), repeating the steps (7) and (8), and determining the value of N according to the image classification accuracy.
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