CN112052888A - Domain adaptive mode identification method based on coupled projection and embedded subspace - Google Patents

Domain adaptive mode identification method based on coupled projection and embedded subspace Download PDF

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CN112052888A
CN112052888A CN202010881620.6A CN202010881620A CN112052888A CN 112052888 A CN112052888 A CN 112052888A CN 202010881620 A CN202010881620 A CN 202010881620A CN 112052888 A CN112052888 A CN 112052888A
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王磊
孟令臣
李丹萍
裴庆祺
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Abstract

The invention provides a field self-adaptive mode identification method based on coupled projection and embedding subspace, which aims to solve the problems of heavy burden of a projection matrix and heterogeneous problem between a source domain and a target domain in the prior art and improve the average identification accuracy. The implementation steps are as follows: acquiring a source domain training set, a target domain training set and a test set; constructing a domain self-adaptive objective function based on coupled projection and an embedded subspace; calculating a kernel matrix, a source domain kernel matrix and a target domain kernel matrix; optimizing a domain self-adaptive objective function; constructing a classifier model; training a classifier model; and acquiring a field self-adaptive mode identification result. The invention can be used in the fields of image recognition, text recognition and the like.

Description

Domain adaptive mode identification method based on coupled projection and embedded subspace
Technical Field
The invention belongs to the technical field of pattern recognition, relates to a field self-adaptive pattern recognition method, and particularly relates to a field self-adaptive pattern recognition method based on coupled projection and embedded subspace, which can be used in the fields of image recognition, text recognition and the like.
Background
One of the mainstream implementation methods of pattern recognition is a statistical machine learning model, which relies heavily on the following assumptions: the data used for training and testing are from the same or similar distributions. However, in the real world, this assumption is difficult to achieve. Therefore, classifier models do not generally perform well in recognition tasks due to the bias between the distribution of training data and test data, and this domain difference is a major obstacle to training predictive models across domains. For example, the pose, occlusion, or illumination of a training object on a labeled image, once changed, may not be well generalized to a test image. In machine learning, this problem is called domain bias. Failure to process the domain offset can result in a significant degradation of recognition performance. Moreover, models trained with only a limited number of labeled samples are generally not robust to pattern recognition tasks, and it is impractical to manually label a sufficient number of training samples for various application domains. However, if the tagged data can be extracted from another sufficiently tagged source domain (which describes the content associated with the target domain), an efficient model can be built using this data. Therefore, how to implement the cross-domain knowledge transfer to reduce domain bias is a challenging and practical problem, and domain adaptation is one of the important technologies to solve the problem.
Domain adaptation solves the problem of data coming from two related but different domains. Domain-adaptive aims at learning a domain-invariant model across source and target domains, enabling knowledge transfer from labeled source domains to unlabeled target domains by exploring domain-invariant structures, bridging different domains with substantial distribution differences. The goal of domain adaptation is to implement knowledge transfer between different domains, reducing the degradation of recognition performance due to domain bias, but to account for differences between domains, it is necessary to account for differences in feature space, edge probability distribution, and conditional probability distribution.
In a patent document filed by the research of the computational technology of the Chinese academy of sciences, namely a method and a system for identifying a field adaptive mode (an authorization publication number: CN103729648.B application number: 201410006653.0), a method for identifying a field adaptive mode is disclosed: target-localized source domain sample method (TSL). The method converts source domain samples to a target domain by representing the source domain samples as a linear combination of the target domain samples, trains a supervision model by using the converted samples, and performs pattern recognition on the target domain by using the trained supervision model. The method has the disadvantages that 1, the public subspace in the method is learned in advance and is independent of the self-adaptive reconstruction process, so that the identification accuracy is reduced; 2. the self-adaptive reconstruction frame in the method field is based on low-rank representation, the low-rank representation requires strong subspace independence, the reconstruction coefficient can possibly obtain trivial solution under the condition that the total data volume is insufficient, and the identification accuracy is further reduced.
A Visual self-adaptation (LSDT) method based on hidden Sparse space field migration Learning is proposed in a paper 'LSDT: needle Sparse Domain Transfer Learning for Visual adaptation' (IEEE Transactions on Image Processing,2016, vol.25(3), pp.1177-1191) published by Zhang et al. The LSDT obtains a quite good identification effect in the field self-adaptation, but the method has the disadvantages that a single projection is used, the functional burden of the projection is too much, the solved projection matrix is difficult to consider all aspects, and the heterogeneous problem between a source domain and a target domain cannot be solved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a field adaptive mode identification method based on coupled projection and an embedding subspace, aims to solve the problem that the constraint of the prior art on a projection matrix is too heavy and the heterogeneous problem between a source domain and a target domain by constructing the coupled projection and introducing the embedding subspace, and improves the identification accuracy.
The technical idea of the invention is as follows: in the process of learning projection, coupling projection is constructed, projection of a source domain and projection of a target domain are jointly learned, meanwhile, an embedding subspace is introduced, re-representation of a sample is optimized in the embedding subspace, data in the embedding subspace is required to be capable of carrying out sparse reconstruction on the data of the target domain, and then kernel method expansion is further achieved through a nonlinear transformation function.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) obtaining a source domain training set XSTarget domain training set XTAnd test set Xtest：
Setting the number of image categories as m, and selecting n contained in each categorySLabeling the images, and forming a source domain training set X by each image and the corresponding label thereofS(ii) a Selecting n contained in each categoryTMarking the images of which the number is less than half, and forming a target domain training set X by each image and the corresponding labelTN is to beSThe rest of the image is taken as test set XtestWherein m is more than or equal to 5, nS≥10，nT≥10；
(2) Constructing a domain self-adaptive target function Q based on coupled projection and an embedded subspace:
(2a) construction of coupled projections [ P ]1,P2]And by projection of P1Training set X of source domainSProjecting into the embedding subspace to obtain XSRe-representation in embedding subspace as BSSimultaneously by projection P2Training set X of target domainTProjecting into the embedding subspace to obtain XTRe-representation in embedding subspace as BTThe above process is realized by the following formula:
Figure BDA0002651248820000031
wherein min (-) represents the minimum value operation,
Figure BDA0002651248820000032
denotes Frobenius norm operation, lambda2And λ3Represents the adjusting parameter and has a value range of [10 ]-2,102]B denotes the re-representation of the training set X in the embedding subspace, X ═ XS,XT],B＝[BS,BT],(·)TDenotes a fetch-transpose operation, K denotes a kernel matrix, Φ denotes a coefficient group, Φ ═ Φ1,Φ2]，Φ1Representing a projection P1Of (2) an optimal solution P1 *Training set X by source domainSRepresenting the desired coefficient,. phi2Representing a projection P2Of (2) an optimal solution P2 *Training set X by target domainTThe coefficients required to represent the desired coefficients are,
Figure BDA0002651248820000033
(2b) pair B in embedding subspaceSAnd BTOptimizing and learning BTAnd BSSparse reconstruction coefficient matrix Z of BTCan be covered by BT、BSAnd Z is represented by and1and D, norm sparsity constraint Z, wherein the process is realized by the following formula:
Figure BDA0002651248820000034
wherein λ1Represents the adjusting parameter and has a value range of [10 ]-2,102]Z represents BSAnd BTSparse reconstruction coefficient matrix between, | · | | non-woven phosphor1Represents a 1 norm operation;
(2c) coupled projection [ P ]1,P2]Carrying out orthogonal constraint, wherein the constraint condition s.t. is as follows:
Figure BDA0002651248820000035
wherein I represents an identity matrix;
(2d) combining (2a), (2b), and (2c) to obtain a domain-adaptive objective function Q:
Figure BDA0002651248820000041
Figure BDA0002651248820000042
(3) calculating a kernel matrix K and a source domain kernel matrix KSAnd a target domain kernel matrix KT：
Transposing the training set X, and calculating a kernel matrix K which is X according to the transposing result of XTX, source domain kernel matrix KS＝XTXSAnd a target domain kernel matrix of KT＝XTXT；
(4) Optimizing a domain self-adaptive objective function Q:
(4a) the number of initialization iterations is t, and the maximum number of iterations is tmax，tmaxNot less than 100, the t-th iteration of Z is ZtThe t-th iteration of phi is phitThe re-representation of the training set X in the embedding subspace is B ═ Φ (Φ)t)TK, and let t equal to 0, Zt＝Z，Φt＝Φ；
(4b) Adopting ADMM alternating direction multiplier method, and representing B pairs of sparse reconstruction coefficient matrix Z in embedding subspace through training set XtUpdating to obtain an updated sparse reconstruction coefficient matrix Zt；
(4c) Adopting eigenvalue decomposition method, and passing through kernel matrix K and target domain kernel matrix KTAnd an updated sparse reconstruction coefficient matrix ZtFor coefficient group phitUpdating to obtain updated domain adaptive objective function Qt；
(4d) Judging t as tmaxIf yes, obtaining an optimized sparse reconstruction coefficient matrix of
Figure BDA0002651248820000043
Coefficient set is
Figure BDA0002651248820000044
Of a domain adaptive objective function Q*Otherwise, let t be t +1, and execute step (4 b);
(5) constructing a classifier W model:
by means of2Linear regression with norm regularization constructs classifier W, whose objective function is j (W):
Figure BDA0002651248820000045
wherein the content of the first and second substances,
Figure BDA0002651248820000046
and
Figure BDA0002651248820000047
respectively represent XSAnd XTIs re-represented by YSAnd YTRespectively represent XSAnd XTCorresponding label set, alpha represents the constraint parameter of the classifier;
(6) training a classifier W model:
mixing XSAnd XTIs re-represented
Figure BDA0002651248820000051
And
Figure BDA0002651248820000052
linear regression as input to classifier W to obtain XSAnd XTCorresponding label set YSAnd YTSimultaneously calculate
Figure BDA0002651248820000053
And
Figure BDA0002651248820000054
the respective values of the respective values are,
Figure BDA0002651248820000055
Figure BDA0002651248820000056
and will be
Figure BDA0002651248820000057
And YS、YTAnd substituting the constraint parameter alpha into a classifier target function J (W) to obtain a trained classifier W:
Figure BDA0002651248820000058
(7) obtaining a field self-adaptive mode identification result:
test set XtestLinear regression as input to the trained classifier W to obtain XtestTag set Y oftestAnd is combined with YtestImparting XtestObtaining a recognition result of the field adaptive pattern recognition for each test sample in (1), wherein Y istestThe calculation formula of (2) is as follows:
Ytest＝WTΦXTXtest。
compared with the prior art, the invention has the following advantages:
firstly, the method constructs coupled projection for the source domain and the target domain, jointly learns the projection of data in the source domain and the target domain, can maintain the global structure and the local structure of the data, enhances the edge judgment information of the data, solves the problem that the single projection in the prior art is difficult to solve the problem of heterogeneity among different domains, and has higher average accuracy when pattern recognition is carried out;
secondly, the embedding subspace is introduced, so that the re-representation of the sample is optimized in the embedding subspace, the data embedded in the subspace is required to be capable of carrying out sparse reconstruction on the target domain data, a common hidden structure of the source domain data and the target domain data is found out, the problem of heavy burden of a projection function in the prior art can be solved on the premise of keeping the advantages of a sparse representation method, and the identification accuracy of the method is further improved.
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FIG. 1 is a flow chart of an implementation of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the present invention includes the steps of:
step 1) obtaining a source domain training set XSTarget domain training set XTAnd test set Xtest：
Setting the number of image categories as m, and selecting n contained in each categorySLabeling the images, and forming a source domain training set X by each image and the corresponding label thereofS(ii) a Selecting n contained in each categoryTMarking the images of which the number is less than half, and forming a target domain training set X by each image and the corresponding labelTN is to beSThe rest of the image is taken as test set XtestWherein m is more than or equal to 5, nS≥10，nT≥10；
Step 2), constructing a domain self-adaptive target function Q based on coupled projection and an embedded subspace:
step 2a) construction of a coupled projection [ P ]1,P2]And by projection of P1Training set X of source domainSProjecting into the embedding subspace to obtain XSRe-representation in embedding subspace as BSSimultaneously by projection P2Training set X of target domainTProjecting into the embedding subspace to obtain XTRe-representation in embedding subspace as BTThe above process is realized by the following formula:
Figure BDA0002651248820000061
wherein min (-) represents the minimum value operation,
Figure BDA0002651248820000062
denotes Frobenius norm operation, lambda2And λ3Represents the adjusting parameter and has a value range of [10 ]-2,102]，BRepresenting a re-representation of the training set X in the embedding subspace, X ═ XS,XT],B＝[BS,BT],(·)TDenotes a fetch-transpose operation, K denotes a kernel matrix, Φ denotes a coefficient group, Φ ═ Φ1,Φ2]，Φ1Representing a projection P1Of (2) an optimal solution P1 *Training set X by source domainSRepresenting the desired coefficient,. phi2Representing a projection P2Of (2) an optimal solution P2 *Training set X by target domainTThe coefficients required to represent the desired coefficients are,
Figure BDA0002651248820000063
to ensure that the data is not distorted during projection and to maintain as much information as possible, a training set X of source and target domains is requiredSAnd XTThe sample in (1) is projected to be close to BSAnd BTRespectively, while requiring B to be representedSAnd BTAfter back-projecting the re-represented samples in (1) back to the original space, as close to X as possibleSAnd XTThe respective original samples;
step 2B) for B in the embedding subspaceSAnd BTOptimizing and learning BTAnd BSSparse reconstruction coefficient matrix Z of BTCan be covered by BT、BSAnd Z is represented by and1and D, norm sparsity constraint Z, wherein the process is realized by the following formula:
Figure BDA0002651248820000071
wherein λ1Represents the adjusting parameter and has a value range of [10 ]-2,102]Z represents BSAnd BTSparse reconstruction coefficient matrix between, | · | | non-woven phosphor1Represents a 1 norm operation;
in order to realize sparse optimization of sample re-representation in the embedding subspace, the data embedded in the subspace is required to be capable of carrying out sparse reconstruction on the target domain data, so that the method can ensureThe advantage of sparse expression is retained, and l is adopted to make the target function Q approximate to a convex function and easy to solve1Norm sparsity constraint Z;
step 2c) coupled projection [ P ]1,P2]Carrying out orthogonal constraint, wherein the constraint condition s.t. is as follows:
Figure BDA0002651248820000072
wherein I represents an identity matrix;
to prevent coupled projection [ P1,P2]Degenerated to 0, requiring projection P in constraints1Orthogonal normalization, therefore, requires
Figure BDA0002651248820000073
Requiring projection P simultaneously2Orthogonal normalization, therefore, requires
Figure BDA0002651248820000074
Step 2d) combining (2a), (2b) and (2c) to obtain a domain adaptive objective function Q:
Figure BDA0002651248820000075
Figure BDA0002651248820000076
step 3) calculating a kernel matrix K and a source domain kernel matrix KSAnd a target domain kernel matrix KT：
Transposing the training set X, and calculating a kernel matrix K which is X according to the transposing result of XTX, source domain kernel matrix KS＝XTXSAnd a target domain kernel matrix of KT＝XTXT；
Step 4), optimizing a domain self-adaptive objective function Q:
step 4a) the number of initialization iterations ist, maximum number of iterations is tmax，tmaxNot less than 100, the t-th iteration of Z is ZtThe t-th iteration of phi is phitThe re-representation of the training set X in the embedding subspace is B ═ Φ (Φ)t)TK, and let t equal to 0, Zt＝Z，Φt＝Φ；
Step 4B) adopting an ADMM alternative direction multiplier method, and representing B pairs of sparse reconstruction coefficient matrixes Z in the embedding subspace through the training set XtUpdating to obtain an updated sparse reconstruction coefficient matrix ZtThe method comprises the following concrete implementation steps:
step 4b1) initializing auxiliary variables as E, and Lagrange multipliers as Y respectively1And Y2The penalty parameter is mu, and the maximum penalty parameter is mumax＝106The iteration step is rho 1.1, and the iteration number of the ADMM algorithm is tinMaximum number of iterations tinmax，tinmaxT-th of not less than 20, EinThe sub-iteration is
Figure BDA0002651248820000081
Y1And Y2T th of (1)inThe sub-iterations are respectively
Figure BDA0002651248820000082
And
Figure BDA0002651248820000083
t of ZinThe sub-iteration is
Figure BDA0002651248820000084
T of μinThe sub-iteration is
Figure BDA0002651248820000085
And let tin＝0，
Figure BDA0002651248820000086
Step 4b2) on auxiliary variables
Figure BDA0002651248820000087
Updating to obtain updated auxiliary variable
Figure BDA0002651248820000088
Figure BDA0002651248820000089
Wherein, (.)-1Representing an inverse matrix, NSRepresenting a source domain training set XSNumber of samples in (1), NTRepresenting a target domain training set XTThe number of all samples in;
step 4b3) by means of updated auxiliary variables
Figure BDA00026512488200000810
For sparse reconstruction coefficient matrix
Figure BDA00026512488200000811
Updating to obtain an updated sparse reconstruction coefficient matrix
Figure BDA00026512488200000812
Figure BDA00026512488200000813
Wherein the content of the first and second substances,
Figure BDA00026512488200000814
the value of the variable when the expression reaches the minimum value;
step 4b4) determining tin＝tinmaxIf yes, obtaining an updated sparse reconstruction coefficient matrix
Figure BDA00026512488200000815
Otherwise, step 4b5 is executed);
step 4b5) by means of updated auxiliary variables
Figure BDA00026512488200000816
And updatingThe post-sparse reconstruction coefficient matrix
Figure BDA00026512488200000817
For lagrange multiplier
Figure BDA00026512488200000818
And
Figure BDA00026512488200000819
updating to obtain updated Lagrange multiplier
Figure BDA00026512488200000820
And
Figure BDA00026512488200000821
Figure BDA00026512488200000822
Figure BDA00026512488200000823
step 4b6) for penalty parameters
Figure BDA00026512488200000824
Updating to obtain updated punishment parameter
Figure BDA00026512488200000825
And let tin＝tin+1, perform step 4b 2):
Figure BDA0002651248820000091
step 4c), a characteristic value decomposition method is adopted, and a kernel matrix K and a target domain kernel matrix K are passedTAnd an updated sparse reconstruction coefficient matrix ZtFor coefficient group phitUpdating to obtain updated domain adaptive objective function QtIn particularThe implementation steps are as follows:
step 4c1), performing eigenvalue decomposition on the kernel matrix K to obtain a matrix V and a diagonal matrix S, wherein the eigenvalue decomposition formula of K is as follows:
K＝VSV-1；
step 4c2), calculating an auxiliary matrix theta, and performing eigenvalue decomposition on theta to obtain a matrix U and a diagonal matrix M, wherein the calculation formula of theta is as follows:
Figure BDA0002651248820000092
θ＝UMU-1；
step 4c3) for ΦtUpdating to obtain updated domain adaptive objective function QtWherein phitIs updated as a result of
Figure BDA0002651248820000093
U (: ω), ω represents the eigenvectors corresponding to the d minimum eigenvalues;
step 4d) judging t ═ tmaxIf yes, obtaining an optimized sparse reconstruction coefficient matrix of
Figure BDA0002651248820000094
Coefficient set is
Figure BDA0002651248820000095
Of a domain adaptive objective function Q*Otherwise, let t be t +1 and execute step 4 b);
step 5), constructing a classifier W model:
by means of2Linear regression with norm regularization constructs classifier W, whose objective function is j (W):
Figure BDA0002651248820000096
wherein the content of the first and second substances,
Figure BDA0002651248820000097
and
Figure BDA0002651248820000098
respectively represent XSAnd XTIs re-represented by YSAnd YTRespectively represent XSAnd XTCorresponding label set, alpha represents the constraint parameter of the classifier;
step 6) training a classifier W model:
mixing XSAnd XTIs re-represented
Figure BDA0002651248820000099
And
Figure BDA00026512488200000910
linear regression as input to classifier W to obtain XSAnd XTCorresponding label set YSAnd YTSimultaneously calculate
Figure BDA00026512488200000911
And
Figure BDA00026512488200000912
the respective values of the respective values are,
Figure BDA00026512488200000913
Figure BDA00026512488200000914
and will be
Figure BDA00026512488200000915
And YS、YTAnd substituting the constraint parameter alpha into a classifier target function J (W) to obtain a trained classifier W:
Figure BDA0002651248820000101
step 7) obtaining a field self-adaptive mode identification result:
test set XtestLinear regression as input to the trained classifier W to obtain XtestTag set Y oftestAnd is combined with YtestImparting XtestObtaining a recognition result of the field adaptive pattern recognition for each test sample in (1), wherein Y istestThe calculation formula of (2) is as follows:
Ytest＝WTΦXTXtest。
the effect of the present invention will be further explained with the simulation experiment.
1. Simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the Qinghua same party H110-4S-R2 PC, the processor are Intel i 57000 CPU and the memory 8 GB.
The software platform of the simulation experiment of the invention is as follows: windows 10 operating system and MATLAB 2016 a.
The simulation experiment of the invention adopts two common reference data sets for testing: the CMU PIE data set and the COIL-20 data set.
The CMU PIE data set contains 41368 pictures of a 32 x 32 face with resolution, including 68 photographs of a person in multiple groups of poses, light intensities, and expressions. The 5 subsets are selected according to different postures, P1 (left), P2 (upper), P3 (lower), P4 (front) and P5 (right), and the 5 subsets are related but distributed differently.
The COIL-20 dataset contains 1440 pictures of 20 classes of objects, each object taken from 5 angles (72 ° apart). The size of each picture is 32 x 32, 256 levels of gray. The experiment divides the data into two subsets C1, C2, C1 containing 720 pictures with shooting angles in 1 and 3 quadrants, and C2 containing all 720 pictures with shooting angles in 2 and 4 quadrants.
2. Simulation experiment contents:
simulation experiment 1:
by adopting the method, the TSC (target scoped source domain sample) method and the LSDT (hidden sparse domain transfer learning method) in the prior art, 10 simulation experiments are carried out on the CMU PIE data set, and the average accuracy of the 10 simulation experiments is taken as the final accuracy.
The CMU PIE data set selects 5 subsets according to different postures, wherein the P1, P2, P3, P4 and P5 are related but distributed differently. Two subsets are selected in turn as source domain and target domain respectively, for a total of 20 combinations. When P1 and P4 are used as source domains, 40 samples of each class are randomly selected for training, and when P2, P3 and P5 are used as source domains, 20 samples of each class are randomly selected. When any subset is used as the target domain, 4 samples per class are randomly selected for training, and the rest are used for testing.
In the simulation experiment 1 of the present invention, in the process of identifying samples in the CMU PIE dataset, the parameters are set as follows:
regulating parameter lambda1＝1，λ2＝100，λ3The constraint parameter α is 0.001, 1.
The average accuracy results for each method on the CMU PIE data set are shown in table 1.
As can be seen from table 1, the average accuracy of the present invention on each task is higher than that of the prior art on the CMU PIE data set, and the following conclusion is reached: by constructing the coupled projection and introducing the embedding subspace, the problems that in the prior art, a single projection matrix is difficult to solve the problem of heterogeneity between a source domain and a target domain and the problem of overload of the projection matrix are solved, so that the method has better identification accuracy during identification.
TABLE 1 average accuracy (%), on CMU PIE data set, for each method
Figure BDA0002651248820000111
Figure BDA0002651248820000121
Simulation experiment 2:
by adopting the method, a target-scoped source domain sample method TSC and a hidden sparse domain migration learning method LSDT in the prior art, 20 simulation experiments are carried out on the COIL-20 data set, and the average accuracy of the 20 simulation experiments is taken as the final accuracy.
Experiments separated the COIL-20 dataset into two subsets C1, C2, C1 containing 720 pictures taken at angles in 1, 3 quadrants, and C2 containing all 720 pictures taken at angles in 2, 4 quadrants. Thus, C1 and C2 are structured into two related but differently distributed domains. The two domains are alternately used as a source domain and a target domain, and 2 groups of experimental configurations are obtained. In the experiment, all samples of the subset used as the source domain participate in training, 270 samples are randomly selected as a training set by the subset used as the target domain, and the rest samples are used for testing.
In the simulation experiment 2, parameters are selected as follows in the process of identifying samples in the COIL-20 data set:
regulating parameter lambda1＝1，λ2＝100，λ3The constraint parameter α is 0.1.
The average accuracy results for each method on the COIL-20 dataset are shown in table 2.
As can be seen from Table 2, the average accuracy of the present invention on each task was higher than that of the prior art on the COIL-20 dataset, and the following conclusion was reached: by constructing the coupled projection and introducing the embedding subspace, the problems that a single projection matrix is difficult to solve the problem of heterogeneity between a source domain and a target domain and the problem that the projection matrix is overloaded in the prior art are solved, so that the method has a good identification effect during identification.
TABLE 2 mean accuracy (%), of each method on COIL-20 data set
Task TSC LSDT The invention
C1->C2 85.01 91.92 95.56
C2->C1 84.29 91.02 94.43
Average 85.65 91.47 95.45

Claims (3)

1. A field self-adaptive mode identification method based on coupled projection and embedding subspace is characterized by comprising the following steps:
(1) obtaining a source domain training set XSTarget domain training set XTAnd test set Xtest：
Setting the number of image categories as m, and selecting n contained in each categorySLabeling the images, and forming a source domain training set X by each image and the corresponding label thereofS(ii) a Selecting n contained in each categoryTMarking the images of which the number is less than half, and forming a target domain training set X by each image and the corresponding labelTN is to beSThe rest of the image is taken as test set XtestWherein m is more than or equal to 5, nS≥10，nT≥10；
(2) Constructing a domain self-adaptive target function Q based on coupled projection and an embedded subspace:
(2a) construction of coupled projections [ P ]1,P2]And by projection of P1Training set X of source domainSProjecting into the embedding subspace to obtain XSRe-representation in embedding subspace as BSSimultaneously by projection P2Training set X of target domainTProjecting into the embedding subspace to obtain XTRe-representation in embedding subspace as BTThe above process is realized by the following formula:
Figure FDA0002651248810000011
wherein min (-) represents the minimum value operation,
Figure FDA0002651248810000012
denotes Frobenius norm operation, lambda2And λ3Represents the adjusting parameter and has a value range of [10 ]-2,102]B denotes the re-representation of the training set X in the embedding subspace, X ═ XS,XT],B＝[BS,BT],(·)TDenotes a fetch-transpose operation, K denotes a kernel matrix, Φ denotes a coefficient group, Φ ═ Φ1,Φ2]，Φ1Representing a projection P1Of (2) an optimal solution P1 *Training set X by source domainSRepresenting the desired coefficient,. phi2Representing a projection P2Of (2) an optimal solution P2 *Training set X by target domainTThe coefficients required to represent the desired coefficients are,
Figure FDA0002651248810000013
(2b) pair B in embedding subspaceSAnd BTOptimizing and learning BTAnd BSSparse reconstruction coefficient matrix Z of BTCan be covered by BT、BSAnd Z is represented by and1and D, norm sparsity constraint Z, wherein the process is realized by the following formula:
Figure FDA0002651248810000014
wherein λ1Represents the adjustment parameter, and has a value range of[10-2,102]Z represents BSAnd BTSparse reconstruction coefficient matrix between, | · | | non-woven phosphor1Represents a 1 norm operation;
(2c) coupled projection [ P ]1,P2]Carrying out orthogonal constraint, wherein the constraint condition s.t. is as follows:
Figure FDA0002651248810000021
wherein I represents an identity matrix;
(2d) combining (2a), (2b), and (2c) to obtain a domain-adaptive objective function Q:
Figure FDA0002651248810000022
Figure FDA0002651248810000023
(3) calculating a kernel matrix K and a source domain kernel matrix KSAnd a target domain kernel matrix KT：
Transposing the training set X, and calculating a kernel matrix K which is X according to the transposing result of XTX, source domain kernel matrix KS＝XTXSAnd a target domain kernel matrix of KT＝XTXT；
(4) Optimizing a domain self-adaptive objective function Q:
(4a) the number of initialization iterations is t, and the maximum number of iterations is tmax，tmaxNot less than 100, the t-th iteration of Z is ZtThe t-th iteration of phi is phitThe re-representation of the training set X in the embedding subspace is B ═ Φ (Φ)t)TK, and let t equal to 0, Zt＝Z，Φt＝Φ；
(4b) Adopting ADMM alternating direction multiplier method, and representing B pairs of sparse reconstruction coefficient matrix Z in embedding subspace through training set XtUpdating to obtain updated dataThe post-sparse reconstruction coefficient matrix Zt；
(4c) Adopting eigenvalue decomposition method, and passing through kernel matrix K and target domain kernel matrix KTAnd an updated sparse reconstruction coefficient matrix ZtFor coefficient group phitUpdating to obtain updated domain adaptive objective function Qt；
(4d) Judging t as tmaxIf yes, obtaining an optimized sparse reconstruction coefficient matrix of
Figure FDA0002651248810000024
Coefficient set is
Figure FDA0002651248810000025
Of a domain adaptive objective function Q*Otherwise, let t be t +1, and execute step (4 b);
(5) constructing a classifier W model:
by means of2Linear regression with norm regularization constructs classifier W, whose objective function is j (W):
Figure FDA0002651248810000031
wherein the content of the first and second substances,
Figure FDA0002651248810000032
and
Figure FDA0002651248810000033
respectively represent XSAnd XTIs re-represented by YSAnd YTRespectively represent XSAnd XTCorresponding label set, alpha represents the constraint parameter of the classifier;
(6) training a classifier W model:
mixing XSAnd XTIs re-represented
Figure FDA0002651248810000034
And
Figure FDA0002651248810000035
linear regression as input to classifier W to obtain XSAnd XTCorresponding label set YSAnd YTSimultaneously calculate
Figure FDA0002651248810000036
And
Figure FDA0002651248810000037
the respective values of the respective values are,
Figure FDA0002651248810000038
Figure FDA0002651248810000039
and will be
Figure FDA00026512488100000310
And YS、YTAnd substituting the constraint parameter alpha into a classifier target function J (W) to obtain a trained classifier W:
Figure FDA00026512488100000311
(7) obtaining a field self-adaptive mode identification result:
test set XtestLinear regression as input to the trained classifier W to obtain XtestTag set Y oftestAnd is combined with YtestImparting XtestObtaining a recognition result of the field adaptive pattern recognition for each test sample in (1), wherein Y istestThe calculation formula of (2) is as follows:
Ytest＝WTΦXTXtest。
2. the coupled projection and embedding subspace-based domain adaptive model of claim 1The formula identification method is characterized in that: adopting ADMM alternative direction multiplier method and adopting ADMM alternative direction multiplier method in the step (4B), and re-representing B pairs of sparse reconstruction coefficient matrixes Z in the embedding subspace through the training set XtUpdating to obtain an updated sparse reconstruction coefficient matrix ZtThe method comprises the following implementation steps:
(4b1) initializing auxiliary variables as E and Lagrange multipliers as Y respectively1And Y2The penalty parameter is mu, and the maximum penalty parameter is mumax＝106The iteration number of the ADMM algorithm is tinMaximum number of iterations tin max，tin maxNot less than 20, the iteration step is rho 1.1, t th of EinThe sub-iteration is
Figure FDA00026512488100000312
Y1And Y2T th of (1)inThe sub-iterations are respectively
Figure FDA00026512488100000313
And
Figure FDA00026512488100000314
t of ZinThe sub-iteration is
Figure FDA00026512488100000315
T of μinThe sub-iteration is
Figure FDA00026512488100000316
And let tin＝0，
Figure FDA00026512488100000317
Figure FDA00026512488100000318
(4b2) For auxiliary variable
Figure FDA0002651248810000041
Updating to obtain updated auxiliary variable
Figure FDA0002651248810000042
Figure FDA0002651248810000043
Wherein, (.)-1Representing an inverse matrix, NSRepresenting a source domain training set XSNumber of samples in (1), NTRepresenting a target domain training set XTThe number of all samples in;
(4b3) by updated auxiliary variables
Figure FDA0002651248810000044
For sparse reconstruction coefficient matrix
Figure FDA0002651248810000045
Updating to obtain an updated sparse reconstruction coefficient matrix
Figure FDA0002651248810000046
Figure FDA0002651248810000047
Wherein the content of the first and second substances,
Figure FDA00026512488100000420
the value of the variable when the expression reaches the minimum value;
(4b4) judging tin＝tinmaxIf yes, obtaining an updated sparse reconstruction coefficient matrix
Figure FDA0002651248810000048
Otherwise, performing step (4b 5);
(4b5) by updated auxiliary variables
Figure FDA0002651248810000049
And an updated sparse reconstruction coefficient matrix
Figure FDA00026512488100000410
For lagrange multiplier
Figure FDA00026512488100000411
And
Figure FDA00026512488100000412
updating to obtain updated Lagrange multiplier
Figure FDA00026512488100000413
And
Figure FDA00026512488100000414
Figure FDA00026512488100000415
Figure FDA00026512488100000416
(4b6) for penalty parameter
Figure FDA00026512488100000417
Updating to obtain updated punishment parameter
Figure FDA00026512488100000418
And let tin＝tin+1, step (4b2) is performed:
Figure FDA00026512488100000419
3. the coupled projection and embedding subspace-based domain adaptive mode identification method according to claim 1, wherein: the eigenvalue decomposition is adopted in the step (4c), and the kernel matrix K and the target domain kernel matrix K are passedTAnd an updated sparse reconstruction coefficient matrix ZtFor coefficient group phitUpdating to obtain updated domain adaptive objective function QtThe method comprises the following implementation steps:
(4c1) and carrying out eigenvalue decomposition on the kernel matrix K to obtain a matrix V and a diagonal matrix S, wherein the eigenvalue decomposition formula of K is as follows:
K＝VSV-1；
(4c2) calculating an auxiliary matrix theta, and performing eigenvalue decomposition on the theta to obtain a matrix U and a diagonal matrix M, wherein the calculation formula of the theta is as follows:
Figure FDA0002651248810000051
θ＝UMU-1；
(4c3) for phitUpdating to obtain updated domain adaptive objective function QtWherein phitIs updated as a result of
Figure FDA0002651248810000052
ω represents the eigenvector corresponding to the d smallest eigenvalues.
CN202010881620.6A 2020-08-26 2020-08-26 Domain adaptive mode identification method based on coupled projection and embedded subspace Pending CN112052888A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112766405A (en) * 2021-01-29 2021-05-07 重庆大学 Sensor data classification method based on multi-constraint subspace projection
CN116935121A (en) * 2023-07-20 2023-10-24 哈尔滨理工大学 Dual-drive feature learning method for cross-region spectral image ground object classification

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112766405A (en) * 2021-01-29 2021-05-07 重庆大学 Sensor data classification method based on multi-constraint subspace projection
CN112766405B (en) * 2021-01-29 2023-08-29 重庆大学 Sensor data classification method based on multi-constraint subspace projection
CN116935121A (en) * 2023-07-20 2023-10-24 哈尔滨理工大学 Dual-drive feature learning method for cross-region spectral image ground object classification
CN116935121B (en) * 2023-07-20 2024-04-19 哈尔滨理工大学 Dual-drive feature learning method for cross-region spectral image ground object classification

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