CN105868713B - A kind of Concurrent Feature fusion facial expression recognizing method based on core LDA - Google Patents
A kind of Concurrent Feature fusion facial expression recognizing method based on core LDA Download PDFInfo
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Abstract
The present invention relates to a kind of, and the Concurrent Feature based on core LDA merges facial expression recognizing method, pass through the combining form Parallel Fusion by two groups of feature vectors Jing Guo different expression using plural number, constitute complex eigenvector, and core Fisher is identified into criterion and introduces complex space, the defect of linear problem can only be analyzed to solve tradition LDA on the basis of complex space, Scatter Matrix in class is redefined simultaneously, passes through regulatable parameterTo solve small sample problem and eigenmatrix imbalance problem.Method of the invention has improvement in varying degrees than Traditional parallel Feature fusion and serial nature fusion method, traditional LDA is not only solved the problem of the fields such as facial expression recognition can not handle nonlinear characteristic, method solves small sample problem simultaneously to a certain extent, and the experiment on the database of human face expression feature database achieves higher discrimination.
Description
Technical field
The invention belongs to data identifications；Data indicate；Record carrier；The technical field for recording the processing of carrier, especially relates to
And a kind of small sample problem and eigenmatrix imbalance problem of being solved by regulatable parameter is to improve face identification rate
Concurrent Feature based on core LDA merges facial expression recognizing method.
Background technique
Feature extraction is one of the link of most critical in Expression Recognition, and extracting has the feature for identifying meaning to Accurate classification
Human face expression, solving practical problems play an important role, and more in place, then Expression Recognition is more accurate for feature extraction.Expression Recognition
Technology can be applied to all trades and professions, such as be applied to police criminal detection field, can assist micro- expression judgement to target object
Make more structurally sound data supporting.
With deepening continuously for correlative study, Feature Fusion gradually receives concern in the industry.Feature Fusion
Not only manifold effective authentication information had been merged, but also has eliminated the information of most of redundancy, to realize being effectively compressed, saving for information
About information storage space, be conducive to accelerate arithmetic speed and carry out information real-time processing.
Currently used Feature fusion is mainly serial fusion method.Serial fusion method is first by two or more sets
Feature vector generates a joint vector according to end to end mode, then carries out feature to this new feature vector again and mentions
It takes, this method remains manifold authentication information, has certain advantage, but will lead to the dimension of new feature after merging simultaneously
Number sharply increases, to increase the difficulty of subsequent step such as feature extraction and identification, makes to screen speed and accuracy rate is greatly reduced.
Researcher carries out a large amount of linguistic term to traditional serial fusion method as a result, wherein the researchs such as Yang Jian mention
A kind of method of Concurrent Feature fusion is gone out, the principle of this method is to utilize complex vector by two or more sets spies on sample space
Collection constitutes complex eigenvector space altogether, i.e., the feature of the real vector space is extended to complex vector space.Concurrent Feature is melted
The method of conjunction extracts effective diagnostic characteristics with linear discriminant criterion (LDA), LDA be currently used feature extracting method it
One, but what is substantially extracted due to it is linear character, handles Shortcomings to nonlinear characteristic.Therefore, related researcher
The LDA method based on core is proposed, that is, is based on Kernel discriminant analysis method (KDA), this method is by being mapped to a height for sample
Dimension space utilizes Fisher method Extraction and discrimination feature in the higher dimensional space, obtains the nonlinear characteristic of original image, in practice it has proved that
Core method of discrimination has significant advantage to nonlinear problem is solved, however practice also shows nuclear space during using KDA
Dimension is many to the improved method of small sample commonly greater than the number of training sample, i.e. small sample problem, such as to Fisher criterion
It is local weighted, redefine class scatter matrix, solve small sample problem etc. with kernel, even, merged based on Concurrent Feature
Characterization method not only there is small sample problem due to using Fisher to identify criterion, while that there is also fusions is special
The unbalanced problem of matrix is levied, so that Scatter Matrix in class is not only influenced by small sample problem and is lost scattered information in class, can also
Deviation and greater variance are generated because of eigenmatrix imbalance, influences experiment effect.
Summary of the invention
Present invention solves the technical problem that be, in the prior art, though serial fusion method remains manifold identification
Information has certain advantage, but will lead to simultaneously merge after the dimension of new feature sharply increase, to increase subsequent step such as
The difficulty of feature extraction and identification makes to screen speed and accuracy rate is greatly reduced, and uses Concurrent Feature fusion method with linearly
Identify criterion (LDA) come during extracting effective diagnostic characteristics, the dimension of nuclear space commonly greater than training sample number, i.e.,
Small sample problem, even, since the method uses Fisher to identify criterion, therefore it is uneven also to exist simultaneously fusion feature matrix
The problem of weighing apparatus, makes Scatter Matrix in class not only be influenced by small sample problem and lose scattered information in class, can also be because of eigenmatrix
It is uneven and the problem of generate deviation and greater variance, seriously affect experiment effect, and then provide a kind of optimization based on core
The Concurrent Feature of LDA merges facial expression recognizing method.
The technical scheme adopted by the invention is that a kind of Concurrent Feature based on core LDA merges facial expression recognizing method,
It the described method comprises the following steps:
Step 1.1: face characteristic being extracted using Gabor filter from any human face expression feature database, obtains several
Global characteristics vector β on direction；It is extracted using local feature of the PCA algorithm to face, obtains local feature vectors α,
α and β is merged by Concurrent Feature information, obtains matrix X；
Step 1.2: when carrying out Fusion Features, when there are larger in quantitative relation for two groups of feature vectors of same sample
When difference, by discrete matrix S in classωIt redefines to solve small sample problem, i.e.,
Wherein, Si=Si+ kI, k are control parameter, 0≤k≤1, SiIt is the covariance matrix of single sample class；Control k's
Value is to increase SωSmall feature vector value, reduce big feature vector value so that SωDeviation it is minimum；
Step 1.3: matrix X being transformed in feature space F by Nonlinear Mapping Φ, i.e., Φ: xi∈X→Φ(xi)∈
F；In feature space F, linear Fisher Discrimination Functions are
Wherein, ω ∈ F, and
WithCorresponding within-class scatter matrix and between class scatter matrix in respectively feature space F,Indicate the sample average in i-th of classification in feature space F,It indicates
The mean value of all samples in feature space F；
Step 1.4: formula (II) and formula (III) being introduced into complex space, obtain the class scatter matrix of complex spaceIn class
Scatter Matrix
Wherein,P(ωi) be the i-th class training sample prior probability；
Step 1.5: by theory of reproducing kernel space, solution vector ω can be unfolded in feature space F by all training sample data,
Wherein, core discriminant vector ζ=(ζ1,ζ2,…,ζn)T, Φ=(Φ (x1),Φ(x2),…,Φ(xn)), ζ is in Φ
The best core discriminant vectors of discriminant vectors ω；
Step 1.6: after formula (IV), formula (V) and formula (VI) are substituted into formula (I), by matrixing, obtaining
Wherein, K () is inner product kernel function,
μ0=E [Φ (x1)HΦ(xk),...,Φ(xn)HΦ(xk)|ωi]H, k=1,2 ..., n；P is core class scatter square
Battle array, Q are Scatter Matrix in core class；
Step 1.7: after formula (VII) and formula (VIII) are substituted into formula (I), obtaining the linear Fisher mirror in feature space F
Other function is
Step 1.8: by formula (VIII) and
To
Step 1.9: J (ζ) acquirement maximum value when what value of ζ is sought, it is rightIt is solved using Lagrange algorithm,
It obtains P ζ=λ Q' ζ, acquires one group of base feature vector, obtain best projection direction ζ, i.e., when taking best projection direction ζ, J (ζ)
Obtain maximum value；
Step 1.10: matrix X being projected into corresponding feature space using best projection direction ζ, obtains all samples
Optimal classification characteristic Y: yi=ζHxi, yi∈Y；
Step 1.11: with yiIt is characterized the face that value identifies any human face expression feature database.
Preferably, in the step 1.1, the local feature using the PCA face extracted includes mouth feature, eye spy
Sign, nose feature.
Preferably, in the step 1.1, X=α+i β or X=β+i α.
Preferably, in the step 1.1, global characteristics vector β is generally the vector on 4~8 directions.
Preferably, in the step 1.2, increase control parameter k to control the value of k to increase SωSmall characteristic value, reduction
Big characteristic value, so that SωDeviation it is minimum.
The present invention provides a kind of optimizations, and the Concurrent Feature based on core LDA merges facial expression recognizing method, pass through by
Two groups of feature vectors Jing Guo different expression constitute complex eigenvector using the combining form Parallel Fusion of plural number, and by core
Fisher identifies criterion and introduces complex space, so that lacking for linear problem can only be analyzed by solving tradition LDA on the basis of complex space
It falls into, while Scatter Matrix in class is redefined, small sample problem is solved by regulatable parameter k and eigenmatrix is uneven
Problem.Method of the invention has improvement in varying degrees than Traditional parallel Feature fusion and serial nature fusion method,
Traditional LDA is not only solved the problem of the fields such as facial expression recognition can not handle nonlinear characteristic, method is simultaneously one
Determine solve small sample problem in degree, the experiment on the database of human face expression feature database achieves higher discrimination.
Detailed description of the invention
Fig. 1 is the classification and recognition when present invention selects different k under JAFFE database；
Fig. 2 is the classification and recognition when present invention selects different k under Yale database.
Specific embodiment
The present invention is described in further detail below with reference to embodiment, but protection scope of the present invention is not limited to
This.
The Concurrent Feature that the present invention relates to a kind of based on core LDA merges facial expression recognizing method, the method includes with
Lower step:
Step 1.1: face characteristic being extracted using Gabor filter from any human face expression feature database, obtains several
Global characteristics vector β on direction；It is extracted using local feature of the PCA algorithm to face, obtains local feature vectors α,
α and β is merged by Concurrent Feature information, obtains matrix X；
Step 1.2: when carrying out Fusion Features, when there are larger in quantitative relation for two groups of feature vectors of same sample
When difference, by discrete matrix S in classωIt redefines to solve small sample problem, i.e.,
Wherein, Si=Si+ kI, k are control parameter, 0≤k≤1, SiIt is the covariance matrix of single sample class；Control k's
Value is to increase SωSmall feature vector value, reduce big feature vector value so that SωDeviation it is minimum；
Step 1.3: matrix X being transformed in feature space F by Nonlinear Mapping Φ, i.e., Φ: xi∈X→Φ(xi)∈
F；In feature space F, linear Fisher Discrimination Functions are
Wherein, ω ∈ F, and
WithCorresponding within-class scatter matrix and between class scatter matrix in respectively feature space F,Indicate the sample average in i-th of classification in feature space F,It indicates
The mean value of all samples in feature space F；
Step 1.4: formula (II) and formula (III) being introduced into complex space, obtain the class scatter matrix of complex spaceIn class
Scatter Matrix
Wherein,m0 Φ=E { Φ (xi)}；P(ωi) be the i-th class training sample prior probability；
Step 1.5: by theory of reproducing kernel space, solution vector ω can be unfolded in feature space F by all training sample data,
Wherein, core discriminant vector ζ=(ζ1,ζ2,…,ζn)T, Φ=(Φ (x1),Φ(x2),…,Φ(xn)), ζ is in Φ
The best core discriminant vectors of discriminant vectors ω；
Step 1.6: after formula (IV), formula (V) and formula (VI) are substituted into formula (I), by matrixing, obtaining
Wherein,
K(·,·)
For inner product kernel function,μ0=E [Φ (x1)HΦ
(xk),...,Φ(xn)HΦ(xk)|ωi]H, k=1,2 ..., n；P is core class scatter matrix, and Q is Scatter Matrix in core class；
Step 1.7: after formula (VII) and formula (VIII) are substituted into formula (I), obtaining the linear Fisher mirror in feature space F
Other function is
Step 1.8: by formula (VIII) and
To
Step 1.9: J (ζ) acquirement maximum value when what value of ζ is sought, it is rightIt is asked using Lagrange algorithm
Solution, obtains P ζ=λ Q' ζ, acquires one group of base feature vector, obtain best projection direction ζ, i.e., when taking best projection direction ζ, J
(ζ) obtains maximum value；
Step 1.10: matrix X being projected into corresponding feature space using best projection direction ζ, obtains all samples
Optimal classification characteristic Y: yi=ζHxi, yi∈Y；
Step 1.11: with yiIt is characterized the face that value identifies any human face expression feature database.
In the present invention, when carrying out Concurrent Feature fusion, two groups of characteristic values of same sample may deposit in quantitative relation
In bigger difference: big characteristic value is bigger than normal, and small characteristic value is less than normal, eigenmatrix may be made unbalance after fusion.For this reason, it may be necessary to
By to discrete matrix S in classωIt redefines to solve small sample problem, i.e.,
In the present invention, equipped with two groups of feature sets A, B on sample space Ω, the corresponding feature vector of A is α ∈ A, and B is corresponding
Feature vector be β ∈ B.γ=α+i β indicates the combination of feature vector, and wherein i is imaginary unit, i.e., on sample space Ω
May be defined as C={ α+i β | α ∈ A, β ∈ B } by combined feature space, i.e. matrix X in the present invention, if two groups of features to
The dimension of amount α and β differs, then the feature vector of low-dimensional spot patch foot, which is that n ties up complex vector space, n=max
{dimA,dimB}.Define inner product (X, Y)=XHY, wherein X, Y ∈ C, H are conjugate transposition symbol, claim the multiple sky for defining inner product
Between be the unitary space.Correspondingly, it is assumed that have L known mode class, class scatter matrix in the unitary space, Scatter Matrix and totality in class
Scatter Matrix respectively indicates are as follows:
St=Sb+Sω=E { (X-m0)(X-m0)H}
Wherein, P | ωi| it is the prior probability of the i-th class training sample, mi=E | X | ωi| for the equal of the i-th class training sample
Value,For the mean value of all training samples.
In the present invention, byAnd X, Y ∈ C, C=α+i β | α ∈ A, β ∈
B }, analogize discrete matrix S in the class known in step 1.2ωWith the covariance matrix S of single sample classiIt is and local feature
Vector α and the relevant rectangle of global characteristics vector β.
In the present invention, thus, it is possible to increase within class scatter matrix S by adjusting parameter kωSmall characteristic value, reduction
Its big characteristic value inhibits deviation, to achieve the purpose that improve discrimination.
In the present invention, xiIt is the sample vector in matrix X.
In the present invention, Q is nonnegative definite matrix, and the product of parameter k and unit matrix I are positive definite, then Q+kI is exactly positive definite,
So formulaMiddle ζ has solution, and unrelated with the singularity of Scatter Matrix Q in core class, and the singularity for solving Q is asked
Topic is inhibiting S to be resolved the problem of small sampleωAlso the spy that may be present in fusion is balanced while deviation
Levy the problems such as vector is uneven.
In the present invention, in order to give full expression to expression information, local message is extracted using PCA algorithm, using Gabor filter
The Global Information for extracting human face expression, is first carried out PCA algorithm and obtains local feature vectors α, change by α and via Gabor
To global characteristics vector β merge to obtain matrix X by Concurrent Feature information, analyze the dimension size and training sample of α and β
Divergence in the core class of complex space is calculated to redefine Scatter Matrix in class in number, the value for obtaining adjusting controllable parameter k
Matrix and core class scatter matrix solve Generalized Characteristic Equation P ζ=λ Q' ζ, find one group of base feature vector, obtain best projection
Direction ζ.X is projected into a t dimension space, obtains the optimal classification feature of all samples: Yi=ζHXi。
In the step 1.1, the local feature using the PCA face extracted includes mouth feature, eye feature, nose spy
Sign.
In the step 1.1, X=α+i β or X=β+i α.
In the present invention, if two assemblage characteristic spaces on sample space Ω are respectively defined as C1=α+i β | α ∈ A, β ∈
B }, C2=β+i α | and α ∈ A, β ∈ B }, if matrix H (α, β)=(α+i β) (α+i β)H, H (α, β)=(β+i α) (β+i α)H,Wherein, α, β are the real vector of n dimension, if, α=(α1,...,αn)T, β=(b1,...,bn)T, then
Therefore
Therefore,
Therefore obtain X=α+i β or X=β+i α.
In the step 1.1, global characteristics vector β is generally the vector on 4~8 directions.
In the present invention, global characteristics vector β is generally the vector on 4~8 directions, and direction is divided equally, with Gabor as
The global characteristics on six direction are extracted, six direction is respectively 0, π/6,2 π/6,3 π/6,4 π/6,5 π/6.
In the step 1.2, increase control parameter k to control the value of k to increase SωSmall characteristic value, reduce big feature
Value, so that SωDeviation it is minimum.
In the present invention, the two expression libraries JAFFE and Yale are selected；For without loss of generality, classifier is (close based on K using KNN
Adjacent rule).Wherein, JAFFE Facial expression database is made of the 213 width images of 10 people, everyone shows 7 kinds of expressions；And Yale
Expression library includes 4 kinds of expressions of 15 people, and totally 165 width image, is 320 × 243 8 gray level images.
In the present invention, selects everyone 6 kinds of expressions each one secondary total 60 secondary from JAFFE, 10 people, 4 kinds of tables are selected from Yale
Secondary total 40 width of feelings each one, using the preceding M width image of every kind of expression as training sample, rear (10-M) width is as test sample.This
Sample, training sample and test sample form typical high dimensional and small sample size problem.Circulation 5 times, takes the average value conduct of institute's espressiove
Experimental result.
K is changed between [0,1], be can be consecutive variations and is also possible to Discrete Change.It can be seen that from Fig. 1 and Fig. 2
As M >=4 due to there is enough training samples, k value very little also can guarantee variance and deviation balance, work as M=2, when 3, due to
Lack of training samples, discrete matrix S in classωIt will appear great number variance.Therefore, control parameter must just be increased to increase the small of it
Characteristic value, reduce big characteristic value and inhibit its deviation, to control the variance of kernel, can be only achieved relatively good identification
Rate.It tests while knowing constantly to increase with the increase discrimination of k value, peak value is obtained after increasing to certain value, and identifying
The discrimination variation nearby of rate highest point is slow.
Present invention demonstrates that different expression library or with sample values different in the same library in the case where discrimination highest point institute it is right
The k answered is not identical, and the present invention is more suitable in small sample operation, when sample is smaller, is solved using regulatable parameter k
Certainly small sample problem and eigenmatrix imbalance problem effect are more preferable.
In the present invention, a facial expression image conduct in every kind of expression of a people is taken in two databases of JAFFE and Yale
Test sample, remaining is as training sample.Circulation 5 times is averaged as discrimination, and k used is under JAFFE database
K value used is 0.85 under 0.9, Yale database, obtains following verification result:
The discrimination (%) of distinct methods under 1 JAFFE database of table
| It is angry | Happily | It is frightened | It is sad | It is surprised | Detest | Average recognition rate | |
| Serial nature fusion | 84.5 | 85.3 | 84.6 | 85.3 | 85.1 | 84.7 | 84.9 |
| Concurrent Feature fusion | 89.5 | 90.7 | 90.2 | 90.4 | 90.8 | 89.7 | 90.2 |
| The present invention | 93.3 | 93.7 | 93.1 | 93.6 | 93.5 | 93.0 | 93.4 |
The nicety of grading (%) of distinct methods classifier under 2 Yale database of table
| Happily | It is neutral | It is sad | It is surprised | Average recognition rate | |
| Serial nature fusion | 89.9 | 87.6 | 88.6 | 89.8 | 88.9 |
| Concurrent Feature fusion | 92.3 | 91.5 | 92.7 | 91.5 | 92.1 |
| The present invention | 95.6 | 95.1 | 96.3 | 96.8 | 95.9 |
From Table 1 and Table 2, method discrimination obtained in three kinds of methods of serial nature fusion is minimum, this
It is to extract to generate larger characteristic dimension due to Gabor characteristic, in the case where no dimensionality reduction, spy will be made by serial nature fusion
Sign dimension sharply increases.The average recognition rate that traditional LDA Concurrent Feature merges in two sample databases is respectively 90.2% He
92.1%, and method proposed by the invention, 93.4% and 95.90% discrimination has been respectively obtained, institute of the present invention is demonstrated
It is proposed the validity of Parallel Fusion method.
In the present invention, test method unrelated with people is taken again, is tested 5 times and is averaged.K value used in this experiment is same
Sample is respectively 0.9 and 0.85.
The discrimination (%) of different characteristic extracting method under 3 JAFFE database of table
| PCA | Gabor | Traditional parallel fusion | The present invention | |
| It is angry | 84.6 | 87.4 | 90.2 | 92.7 |
| Happily | 84.3 | 89.3 | 90.6 | 92.7 |
| It is frightened | 82.7 | 87.4 | 89.5 | 92.6 |
| It is sad | 84.7 | 86.7 | 91.5 | 91.8 |
| It is surprised | 82.9 | 86.9 | 90.4 | 93.4 |
| Detest | 83.7 | 87.2 | 89.6 | 93.9 |
| Average recognition rate | 83.8 | 84.2 | 90.3 | 92.9 |
The nicety of grading (%) of different characteristic extracting method under 4 Yale database of table
| PCA | Gabor | Traditional parallel fusion | The present invention | |
| Happily | 86.6 | 90.4 | 93.6 | 95.3 |
| It is neutral | 85.4 | 89.3 | 92.5 | 95.7 |
| It is sad | 86.8 | 89.5 | 92.4 | 94.8 |
| It is surprised | 86.9 | 90.4 | 91.8 | 95.3 |
| Average recognition rate | 86.4 | 89.9 | 92.6 | 95.3 |
It can be concluded that, compared with single human face expression PCA feature and Gabor characteristic recognition result, incited somebody to action from table 3 and table 4
Two kinds of features are merged using the Parallel Fusion strategy mentioned, and discrimination are improved, this is because both sides of Parallel Fusion
Method contains the local feature and global feature of human face expression, and it is superfluous to also prevent information while remaining its effective authentication information
It is remaining.And nonlinear characteristic of the method proposed by the present invention due to sufficiently having handled facial expression image, the identification on two databases
Rate reaches 92.9% and 95.3%, 2.6% and 2.7% has been respectively increased than conventional method, it was demonstrated that in nuclear space Concurrent Feature
The validity of convergence strategy.
The present invention solves in the prior art, though serial fusion method remains manifold authentication information, has one
Fixed advantage, but will lead to simultaneously merge after the dimension of new feature sharply increase, thus increase subsequent step such as feature extraction and
The difficulty of identification makes to screen speed and accuracy rate is greatly reduced, and uses Concurrent Feature fusion method linear discriminant criterion
(LDA) come during extracting effective diagnostic characteristics, the dimension of nuclear space commonly greater than the number of training sample, i.e. ask by small sample
Topic even since the method uses Fisher to identify criterion, therefore also exists simultaneously that fusion feature matrix is unbalanced to ask
Topic, makes Scatter Matrix in class not only be influenced by small sample problem and lose scattered information in class, can also be because of eigenmatrix imbalance
And the problem of generating deviation and greater variance, seriously affecting experiment effect, by by two groups of feature vectors Jing Guo different expression
Using the combining form Parallel Fusion of plural number, complex eigenvector is constituted, and core Fisher is identified into criterion and introduces complex space, thus
Tradition LDA is solved on the basis of complex space can only analyze the defect of linear problem, while redefine to Scatter Matrix in class, lead to
Regulatable parameter k is crossed to solve small sample problem and eigenmatrix imbalance problem.Method of the invention is than Traditional parallel spy
Sign fusion method and serial nature fusion method have improvement in varying degrees, not only solve traditional LDA and know in human face expression
Not Deng fields the problem of nonlinear characteristic can not be handled, method solves small sample problem to a certain extent simultaneously, in people
Experiment on the database in face expressive features library achieves higher discrimination.
Claims (5)
1. a kind of Concurrent Feature based on core LDA merges facial expression recognizing method, it is characterised in that: the method includes following
Step:
Step 1.1: face characteristic being extracted using Gabor filter from any human face expression feature database, obtains several directions
On global characteristics vector β；Extracted using local feature of the PCA algorithm to face, obtain local feature vectors α, by α and
β is merged by Concurrent Feature information, obtains matrix X；
Step 1.2: special after two groups of feature vectors of same sample have fusion in quantitative relation when carrying out Fusion Features
When sign matrix is unbalance, by discrete matrix S in classωIt redefines to solve small sample problem, i.e.,
Wherein, Si=Si+ kI, k are control parameter, 0≤k≤1, SiIt is the covariance matrix of single sample class；Control k value with
Increase SωSmall feature vector value, reduce big feature vector value so that SωDeviation it is minimum；
Step 1.3: matrix X being transformed in feature space F by Nonlinear Mapping Φ, i.e., Φ: xi∈X→Φ(xi)∈F；?
In feature space F, linear Fisher Discrimination Functions are
Wherein, ω ∈ F, and
WithCorresponding within-class scatter matrix and between class scatter matrix in respectively feature space F,Table
Show the sample average in i-th of classification in feature space F,Indicate all in feature space F
The mean value of sample；Step 1.4: formula (II) and formula (III) being introduced into complex space, obtain the class scatter matrix of complex spaceWith
Scatter Matrix in class
Wherein,P(ωi) be the i-th class training sample prior probability；
Step 1.5: by theory of reproducing kernel space, solution vector ω can be unfolded in feature space F by all training sample data,
Wherein, core discriminant vector ζ=(ζ1,ζ2,…,ζn)T, Φ=(Φ (x1),Φ(x2),…,Φ(xn)), ζ be Φ in identify to
Measure the best core discriminant vectors of ω；
Step 1.6: after formula (IV), formula (V) and formula (VI) are substituted into formula (I), by matrixing, obtaining
Wherein,
K () is inner product kernel function,μ0=E [Φ (x1)H
Φ(xk),...,Φ(xn)HΦ(xk)|ωi]H, k=1,2 ..., n；P is core class scatter matrix, and Q is Scatter Matrix in core class；
Step 1.7: after formula (VII) and formula (VIII) are substituted into formula (I), the linear Fisher obtained in feature space F identifies letter
Number is
Step 1.8: by formula (VIII) and
To
Step 1.9: J (ζ) acquirement maximum value when what value of ζ is sought, it is rightIt is solved, is obtained using Lagrange algorithm
P ζ=λ Q' ζ, acquires one group of base feature vector, obtains best projection direction ζ, i.e., when taking best projection direction ζ, J (ζ) is obtained
Maximum value；
Step 1.10: matrix X being projected into corresponding feature space using best projection direction ζ, obtains the best of all samples
Characteristic of division Y:yi=ζHxi, yi∈Y；
Step 1.11: with yiIt is characterized the face that value identifies any human face expression feature database.
2. a kind of Concurrent Feature based on core LDA according to claim 1 merges facial expression recognizing method, feature exists
In: in the step 1.1, the local feature using the PCA face extracted includes mouth feature, eye feature, nose feature.
3. a kind of Concurrent Feature based on core LDA according to claim 1 merges facial expression recognizing method, feature exists
In: in the step 1.1, X=α+i β or X=β+i α.
4. a kind of Concurrent Feature based on core LDA according to claim 1 merges facial expression recognizing method, feature exists
In: in the step 1.1, global characteristics vector β is the vector on 4~8 directions.
5. a kind of Concurrent Feature based on core LDA according to claim 1 merges facial expression recognizing method, feature exists
In: in the step 1.2, increase control parameter k to control the value of k to increase SωSmall characteristic value, reduce big characteristic value so that
SωDeviation it is minimum.
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