CN103927522B - A kind of face identification method based on manifold self-adaptive kernel - Google Patents

Abstract

The present invention relates to a kind of face identification method based on manifold self-adaptive kernel, the detailed process is：Facial image is expressed as by vector form using the method for expressing based on profile；Calculate figure Laplace operator；Calculate nonparametric kernel matrix K；Above-mentioned calculated figure Laplace operator L and nonparametric kernel matrix K are calculated, you can obtain the manifold self-adaptive kernel function being closely related with human face data；The optimization object function of core NMF is built, Lagrangian is set up, multiplying property is obtained and is updated rule；The low-rank approximation technique of method realizes the nuclear matrix calculating process in core NMF；The W and V of optimization are calculated, then test facial image z new for a width_test, obtain by the low-dimensional character representation after core NMF dimensionality reductions；Step h, sets up the optimization object function of SVM；Calculate optimization solution α.The face recognition accuracy rate of manifold self-adaptive kernel NMF of the present invention is better than existing algorithm, and dimension dimensionality reduction can effectively strengthen the performance of face recognition algorithms as a kind of Preprocessing Algorithm.

Description

A kind of face identification method based on manifold self-adaptive kernel

Technical field

The present invention relates to area of pattern recognition, more particularly to a kind of face identification method based on manifold self-adaptive kernel.

Background technology

An entirety generally as is regarded human face region using the method based on global characteristics or subspace in the prior art, Using face as certain technical characteristic as Expressive Features.

Chinese patent《Face identification method and face identification system》, publication number：CN101763507A, by face sample graph As being divided into multiple mutually overlapping and subregions not of uniform size, the face sample image is the fixed size by pre-processing Facial image；Extract the textural characteristics of the subregion；Effective texture is chosen from the textural characteristics according to presetting rule Feature, and obtain the projection properties value of effective textural characteristics；Recognition of face is carried out according to the projection properties value of all subregion.

Data processing algorithm in above-mentioned face recognition process, is non-optimal way, and computation complexity is big, as a result accuracy rate It is not high.

In view of drawbacks described above, creator of the present invention passes through prolonged research and practice obtains this creation finally.

The content of the invention

It is an object of the invention to provide a kind of face identification method based on manifold self-adaptive kernel, it is used to overcome above-mentioned skill Art defect.

To achieve the above object, the present invention provides a kind of face identification method based on manifold self-adaptive kernel, the specific mistake Cheng Wei：

Step a, vector form, i.e. X=[x are expressed as using the method for expressing based on profile by facial image₁, x₂, L, x_n], wherein x_iRepresent the i-th width facial image；

Step b, calculates figure Laplace operator L；

Step c, calculates nonparametric kernel matrix K；

Step d, above-mentioned calculated figure Laplace operator L and nonparametric kernel matrix K is calculated, you can obtain and people The manifold self-adaptive kernel function that face data are closely related；

Step e, builds the optimization object function of core NMF, sets up Lagrangian, obtains multiplying property and updates rule；

Step f, usesThe low-rank approximation technique of method realizes the nuclear matrix calculating process in core NMF；

Step g, calculates the W and V of optimization, then test facial image z new for a width_test, obtain and dropped by core NMF Low-dimensional character representation after dimension；

Step h, sets up the optimization object function of SVM；Optimization solution α is calculated, then SVM is to facial image using following formula Classified and adjudicated.

Further, in above-mentioned steps b, if G represents a non-directed graph with n summit, wherein i vertex representation people Face image x_i, for each data point x_i, find its p nearest-neighbors point set N (x_i)；If x_iIt is x_jP- nearest-neighbors or Person x_jIt is x_iP- nearest-neighbors, then build a line between them, side right weight determines according to following formula；

Then figure Laplace operator L=D-W, wherein D are a diagonal matrix, and its value is D_ii=∑_jW_ij, D_iiDescribe Data point x_iThe local density of surrounding.

Further, in above-mentioned steps c, similarity matrix E is built using following formula；

Then, similar paired constraint set S and dissimilar paired constraint set D is given, a similitude square is constructed Battle array E represents the paired constraint between data, i.e.,：

One core K_{I, j}Should as much as possible with side information E_{I, j}Alignment is kept, i.e.,：The alignment E of each core_{I, j}K_{I, j}Should Work as maximization.

Further, in above-mentioned steps c, the optimization problem in following formula is solved using global optimization approach obtain The nonparametric kernel matrix K of optimization,

Wherein, C is the positive parameter traded off between a control side information and regularization term, l (E_{I, j}K_{I, j}) it is an experience Loss function；It is normalized figure Laplace operator, it is defined as follows：

One nonparametric kernel matrix K can be expressed as K=V relative to n data^TV>0, wherein, V=[v₁, L, v_n]^TIt is Data point X=[x₁, L, x_n]^TEmbeded matrix；Thus, being defined as follows can describe to be embedded in v_iAnd v_jBetween local correlations core Matrix regularization term：

It is above-mentioned to merge, obtain nonparametric kernel matrix K.

Further, in above-mentioned steps e, by above-mentioned calculated figure Laplace operator L and nonparametric kernel matrix K generation Enter following formula, you can obtain the manifold self-adaptive kernel function being closely related with human face data；

In formula, K represents nonparametric kernel matrix；

Step e, builds the optimization object function of core NMF according to following formula first,

The constraints of above formula is：W >=0, V >=0；In formula, input data matrix X=[x₁, L, x_n] it is a m- dimension data Vector set, then in nonlinear mapping functionIn the presence of, the image data in feature space F accordingly becomes

Further, in above-mentioned steps e, the Lagrangian that foundation is shown below,

Wherein, α and β are the Lagrange coefficient more than or equal to zero；

The partial derivative of above formula is made to be respectively zero, the multiplying property that can be shown below updates rule, kernel function therein is Manifold self-adaptive kernel function；

Further, in above-mentioned steps f,

Make the multiplying property in above-mentioned formula update rule nuclear matrix K to be replaced with following formula, utilizeThe low-rank of method is near The nuclear matrix calculating process in core NMF is realized like technology；

K is positive definite nuclear matrix, E_ij=k (x_i, z_j),Λ_kThe characteristic vector and characteristic value and W of W are contained respectively_ij=k (z_i, z_j)。

Further, in above-mentioned steps g, the W and V of optimization are calculated, then test facial image z new for a width_test, It is by the low-dimensional character representation after core NMF dimensionality reductions：

Wherein,Represent V^TPseudo inverse matrix.

Further, in above-mentioned steps h, the optimization object function of SVM is set up according to following formula；

In formula,It is a mapping function without explicitly knowing concrete form, its computational methods can be by core letter NumberTo realize；＜ w, x ＞ represent the inner product between vectorial w and x, l (；) represent that loss function is right Afterwards rapid solving is carried out using stochastic gradient descent method come the optimization object function to SVM.

Further, in above-mentioned steps h,

Optimization solution α is calculated, then SVM is that facial image is classified and adjudicated using following formula：

Wherein, k (x_i, x) represent the manifold self-adaptive kernel function for above calculating.

Compared with prior art the beneficial effects of the present invention are：The recognition of face of manifold self-adaptive kernel NMF of the present invention Accuracy rate is better than existing algorithm, and dimension dimensionality reduction can effectively strengthen face recognition algorithms as a kind of Preprocessing Algorithm Performance.NMF is a kind of method for expressing based on part, and LDA and PCA are all based on the method for expressing of the overall situation, thus NMF can It is the characteristics of being made up of the part such as eyes, nose and mouth to be well adapted for face；As a kind of nonlinear dimension dimension-reduction algorithm, So as to preferably overcome PCA, LDA and NMF facial image complex nonlinear structure cannot be effectively processed as linear algorithm Deficiency.

Manifold self-adaptive kernel function preferably make use of in face image data manifold structure, manifold self-adaptive kernel letter Number achieves good recognition performance；The present invention is with being based onThe low-rank approximation method of method has the less time Complexity；SVM run times based on stochastic gradient descent method are few.

Specific embodiment

Hereinafter, the technical characteristic above-mentioned and other to the present invention and advantage are described in more detail.

The detailed process of face identification method of the present invention based on manifold self-adaptive kernel be：

Step a, vector form, i.e. X=[x are expressed as using the method for expressing based on profile by facial image₁, x₂, L, x_n], wherein x_iRepresent the i-th width facial image；

Step b, calculates figure Laplace operator L；

If G represents a non-directed graph with n summit, wherein i vertex representation facial image x_i, for each number Strong point x_i, find its p nearest-neighbors point set N (x_i)；If x_iIt is x_jP- nearest-neighbors or x_jIt is x_iP- nearest-neighbors, A line is then built between them, and side right weight determines according to formula (1)；

Then figure Laplace operator L=D-W, wherein D are a diagonal matrix, and its value is D_ii=∑_jW_ij, D_iiDescribe Data point x_iThe local density of surrounding.

Step c, calculates nonparametric kernel matrix K；

Step c1, similarity matrix E is built using formula (2)；

In recognition of face, the paired constraint set D of some similar paired constraint set S and some dissmilarities is easy to Obtain, these information are also commonly known as " side information ".

Then, set S and D are given, constructs a similarity matrix E to represent the paired constraint between data, i.e.,：

One core K_{I, j}Should as much as possible with side information E_{I, j}Alignment is kept, i.e.,：The alignment E of each core_{I, j}K_{I, j}Should Work as maximization.

Step c2, is solved to obtain the nonparametric of optimization using global optimization approach to the optimization problem in formula (3) Nuclear matrix K.

Wherein, C is the positive parameter traded off between a control side information and regularization term, l (E_{I, j}K_{I, j}) it is an experience Loss function；It is normalized figure Laplace operator, it is defined as follows：

One nonparametric kernel matrix K can be expressed as K=V relative to n data^TV>0, wherein, V=[v₁, L, v_n]^TIt is Data point X=[x₁, L, x_n]^TEmbeded matrix；Thus, being defined as follows can describe to be embedded in v_iAnd v_jBetween local correlations core Matrix regularization term：

Step d, formula (6) is substituted into by above-mentioned calculated figure Laplace operator L and nonparametric kernel matrix K, you can To the manifold self-adaptive kernel function being closely related with human face data；

In formula, K represents nonparametric kernel matrix；

Step e, builds the optimization object function of core NMF according to formula (7) first,

The constraints of above formula is：W >=0, V >=0；In formula, input data matrix X=[x₁, L, x_n] it is a m- dimension data Vector set, then in nonlinear mapping functionIn the presence of, the image data in feature space F accordingly becomes

The Lagrangian as shown in formula (8) is set up,

Wherein, α and β are the Lagrange coefficient more than or equal to zero.

Make the partial derivative of above formula (8) be respectively zero, can obtain the multiplying property as shown in (9) and (10) and update rule, it is therein Kernel function is manifold self-adaptive kernel function.

Step f, makes the nuclear matrix K in above-mentioned formula (9) and (10) be replaced with (11), to utilizeMethod Low-rank approximation technique efficiently realize the nuclear matrix calculating process in core NMF；

K is positive definite nuclear matrix, E_ij=k (x_i, z_j),Λ_kThe characteristic vector and characteristic value and W of W are contained respectively_ij=k (z_i, z_j)。

Step g, calculates the W and V of optimization, then test facial image z new for a width_test, it is by core NMF dimensionality reductions Low-dimensional character representation afterwards is

Wherein,Represent V^TPseudo inverse matrix.

Step h, the optimization object function of SVM is set up according to formula (13)；

In formula,It is a mapping function without explicitly knowing concrete form, its computational methods can be by core letter NumberTo realize；＜ w, x ＞ represent the inner product between vectorial w and x, l (；) represent that loss function is right Afterwards rapid solving is carried out using stochastic gradient descent method come the optimization object function to SVM；

Optimization solution α is calculated, then SVM is that facial image is classified and adjudicated using following formula：

Wherein, k (x_i, x) represent the manifold self-adaptive kernel function for above calculating.

The computation complexity analysis of above-mentioned algorithm：Assuming that the dimension of original facial image be h, then construct p- nearest-neighbors and Time complexity needed for calculating figure Laplace operator is O ((h+k) n²)；Nonparametric kernel matrix K is solved using interior point method Computation complexity is O (n^6.5)；The computation complexity for calculating manifold self-adaptive kernel function is O (n³)；Using fusion The approximate required computation complexity of low-rank that method calculates nuclear matrix is O (m²N), wherein m represents nuclear moment rank of matrix；Training Time complexity required for SVM is O (d/ λ ε).

Therefore the total time complexity of face recognition algorithms of the present invention based on manifold self-adaptive kernel NMF is O ((h+k) n²) +O(n^6.5)+O(n³)+O(m²n)+O(d/λε).It can be seen that amount of calculation the best part is to calculate initial nonparametric kernel function K, it is Avoiding him influences the calculating performance of whole face recognition algorithms.

The advantage of the algorithm is：It is in order to obtain the only O of the iterations required for accuracy rate ε (1/ λ ε) and required Total operation time be O (d/ λ ε), wherein d is maximum non-zero characteristics number in each sample data.Therefore the algorithm is maximum excellent Gesture is run time unrelated with the size of sample data set, so being particularly suitable for the solution of large-scale dataset.

Said process is illustrated below by experiment：

Three famous face test databases are employed in experiment：Yale, ORL and CMU PIE.First to human face data Following pretreatment is carried out：Facial image is positioned first, then the position according to human eye carries out craft to facial image Alignment, shearing, it is 32 × 32 that facial image unification finally is zoomed into resolution ratio, and wherein the gray scale of each pixel is 256；Then Each facial image can be expressed as 1024 dimensional vectors in image space.

Face recognition experiment process is as follows：Face subspace is obtained using different dimension dimension-reduction algorithms first；Then Facial image is projected in these face subspaces；Facial image to be tested is entered using arest neighbors sorting algorithm finally Row classification judgement, distance metric therein uses Euclidean distance.

Yale face databases are the face test databases set up by the computer vision of Yale University and control centre, The database is that by 15 165 width Gray Face image constructions of people, wherein everyone is made up of 11 width facial images.These Facial image is different at illumination condition, human face expression (normal, glad, grieved, sleep, surprised and blink) aspect.In reality In testing, l (=2,3,4,5) the width facial image randomly choosed in everyone carrys out composing training collection, and will be remaining in everyone Other images are used as training set.

0RL face databases are that wherein everyone is by 10 width faces by 40 400 width Gray Face image constructions of people Image is constituted.These facial images were photographed in the different time, and expression (open or close eyes, smile or Do not smile) and facial detail (wear glasses or do not wear glasses) aspect it is different.These images have allowed maximum 20 when taking pictures That spends tilts or rotates.In an experiment, l (=2,3,4,5) the width facial image randomly choosed in everyone carrys out composing training collection, And using remaining other images in everyone as training set.

CMU PIE face databases contain the about 41368 width facial image altogether of 68 people, and these facial images are By 13 synchronized cameras and 21 flash lamps under the conditions of different postures, different illumination conditions and different human face expressions Take pictures.In this experiment, have selected 5 anterior postures (C05, C07, C09, C27, C29) and employ in different illumination With expression under face images, i.e.,：170 width facial images in everyone are used as actual test data source.Figure is in reality In testing, l (=5,10,20,30) width facial image that we are randomly choosed in everyone carrys out composing training collection, and by everyone Remaining other images are used as training set.

Recognition accuracy and corresponding optimization dimension of the table 1 on Yale face databases

Algorithm	2 width images	3 width images	4 width images	5 width images
					NN	45.3%	50.1%	53.1%	54.6%
PCA	45.8% (29)	50.2% (44)	53.3% (58)	54.8% (71)
					LDA	46.5% (9)	64.7% (13)	72.9% (14)	78.1% (14)
NMF	51.2% (30)	66.5% (50)	74.6% (70)	80.4% (75)
					MAKNMF	56.5% (20)	71.4% (40)	78.1% (50)	82.6% (50)

Recognition accuracy and corresponding optimization dimension of the table 2 on ORL face databases

Algorithm	2 width images	3 width images	4 width images	5 width images
					NN	66.5%	75.6%	82.3%	86.1%
PCA	66.7% (78)	75.7% (119)	82.5% (160)	86.7% (180)
					LDA	71.3% (22)	75.9% (39)	89.8% (39)	92.5% (39)
NMF	77.2% (40)	87.3% (42)	91.6% (43)	94.8% (45)
					MAKNMF	80.3% (43)	90.5% (45)	94.8% (50)	96.7% (60)

Recognition accuracy and corresponding optimization dimension of the table 3 on CMU PIE face databases

Algorithm	5 width images	10 width images	20 width images	30 width images
					NN	31.4%	44.7%	61.9%	72.6%
PCA	31.6% (300)	45.1% (600)	70.8% (800)	73.4% (900)
					LDA	68.9% (67)	77.8% (67)	84.7% (67)	92.4% (67)
NMF	70.1% (70)	79.5% (75)	85.8% (80)	93.7% (90)
					MAKNMF	79.3% (80)	87.6% (90)	90.2% (95)	94.3% (100)

In actual recognition of face test, l width image given for, in order to reduce the influence of random deviation, we Carry out 30 random divisions, and by the use of this 30 times average results of operation as final experimental result.In general, so dimension The performance of dimension-reduction algorithm changes with the dimension after yojan.Therefore, in test we report that the preferably identification of each algorithm is accurate Dimension after rate and corresponding dimensionality reduction.In addition, for benchmark test algorithm, using directly in 1024 original dimension facial images Space profit arest neighbors grader (NN) is identified, and the superiority of dimension dimension-reduction algorithm is illustrated with this.

Table 1 gives recognition accuracy and corresponding optimization of the various dimension dimension-reduction algorithms on Yale face databases Dimension；Table 2 gives recognition accuracy and corresponding optimization dimension of the various dimension dimension-reduction algorithms on ORL face databases Number；Table 3 gives recognition accuracy and corresponding optimization dimension of the various dimension dimension-reduction algorithms on CMU PIE face databases Number.

Can be drawn the following conclusions from above-mentioned experimental result：

1) face recognition accuracy rate of manifold self-adaptive kernel NMF (MAKNMF) of the present invention is in three human face datas tested It is better than benchmark test algorithm (NN), PCA, LDA and NMF algorithm on storehouse.

2) recognition accuracy of LDA is better than PCA, main reason is that：PCA is a kind of unsupervised learning algorithm, he Valuable authentication information is not utilized in the process of dimension dimensionality reduction；And LDA is a kind of learning algorithm for having a supervision, he can be in dimension By different classes of data while identical category data are mutually flocked together during number dimensionality reduction using authentication information It is separated from each other and comes.

3) recognition accuracy of NMF algorithms is better than LDA and PCA, main reason is that：NMF is a kind of based on part Method for expressing, and LDA and PCA be all based on the overall situation method for expressing, thus NMF can be well adapted for face be by eye it is fine, The characteristics of part such as nose and mouth is constituted.Other NMF is constrained during dimension dimensionality reduction by applying nonnegativity condition, so that So that the submatrix after decomposing is with preferably openness；And its nonnegativity cannot be ensured through the matrix after PCA and LDA dimensionality reductions, And negative is without clearly explainable physical significance in facial image is represented.Thus PCA and LDA is achieved less than NMF Recognition accuracy.

4) recognition accuracy of manifold self-adaptive kernel NMF (MAKNMF) be better than PCA, LDA and NMF the reason for be： MAKNMF as a kind of nonlinear dimension dimension-reduction algorithm so that preferably overcome PCA, LDA and NMF as linear algorithm without Method effectively processes the deficiency of facial image complex nonlinear structure.In addition, PCA, LDA and NMF are only capable of finding global Euclidean Structure, and the inherent manifold structure being hidden in higher-dimension facial image cannot be effectively found, many studies have shown that：Manifold structure Discovery contribute to strengthen algorithm discriminating performance., by using manifold self-adaptive kernel function, he can not only be effective for MAKNMF Ground finds inherent manifold structure in higher-dimension facial image, and can make designed kernel function well with facial image number According to being closely related, with data adaptive well, thus the discriminating performance of MAKNMF algorithms is enhanced well.

5) recognition accuracy of MAKNMF, NMF, LDA and PCA algorithm be better than benchmark test algorithm (NN) identification it is accurate Rate, this explanation：Dimension dimensionality reduction can effectively strengthen the performance of face recognition algorithms as a kind of Preprocessing Algorithm.

In order to the recognition performance for testing different IPs function pair core NMF influences, the height on three face databases to commonly using This kernel function, Polynomial kernel function, Radial basis kernel function and it is proposed that manifold self-adaptive kernel function pair core NMF performance shadow Sound is tested, and wherein the parameter in gaussian kernel function, Polynomial kernel function, Radial basis kernel function is verified using right-angled intersection Method is set to optimal value.

From experimental result it can be seen that：Manifold auto-adaptive function will be substantially better than conventional gaussian kernel function, polynomial kernel Function and Radial basis kernel function.Main reason is that：These conventional gaussian kernel functions, Polynomial kernel function and radial direction base core letter Number is all the general kernel function unrelated with specific data, therefore they cannot be consistent with specific face image data Property.Manifold self-adaptive kernel function preferably make use of in face image data manifold structure, manifold self-adaptive kernel function takes Obtained good recognition performance.

It is based on to testThe low-rank approximation method of method can effectively improve the computational efficiency of core NMF, Table 4 gives useMethod operates the spent time to compare with direct in original nuclear matrix.Therefrom can be with bright It is aobvious to find out：The run time that the run time of method far smaller than will be operated directly to original matrix, i.e.,：Using It is based onThe low-rank approximation method of method has less time complexity.

Table 4 is usedMethod operates the spent time with direct in original nuclear matrix

Finally, the computational efficiency that whether SVM classifier can be effectively improved based on stochastic gradient descent method is carried out Test.Table 5 gives conventional SVM training methods and the run time of stochastic gradient descent method compares.It can be seen that：Base Interior point method, decomposition method and cutting plane algorithm are significantly less than in the SVM run times of stochastic gradient descent method.Main reason is that： The run time of stochastic gradient descent method is unrelated with the size of sample data set, it is possible in large-scale data facial image number According to collection on can obtain less run time.

SVM training time of the table 5 on three face databases compares

Algorithm	Yale	ORL	CMU PIE
				Interior point method	158.7 seconds	263.4 seconds	2134.9 seconds
Decomposition method	103.5 seconds	147.2 seconds	1158.4 seconds
				Cutting plane algorithm	49.8 seconds	71.6 seconds	570.1 seconds
Stochastic gradient descent method	12.6 seconds	19.3 seconds	38.5 seconds

Presently preferred embodiments of the present invention is the foregoing is only, is merely illustrative for invention, and it is nonrestrictive. Those skilled in the art understanding, can carry out many changes in the spirit and scope that invention claim is limited to it, change, It is even equivalent, but fall within protection scope of the present invention.

Claims (5)

1. a kind of face identification method based on manifold self-adaptive kernel, it is characterised in that detailed process is：

Step a, vector form, i.e. X=[x are expressed as using the method for expressing based on profile by facial image₁, x₂..., x_n], its Middle x_iRepresent the i-th width facial image；

Step b, calculates figure Laplace operator L；

Step c, calculates nonparametric kernel matrix K；

Step d, substitutes into following formula, you can obtain and face by the above-mentioned figure Laplace operator L for calculating and nonparametric kernel matrix K The manifold self-adaptive kernel function that data are closely related：

$\tilde{K}={(I+KL)}^{-1}K$

In formula, I represents unit matrix, and K represents nonparametric kernel matrix；

Step e, builds the optimization object function of core NMF according to following formula first：

The constraints of above formula is：W >=0, V >=0；In formula, W is side right weight, and V is the embeded matrix of X, input data matrix X= [x₁..., x_n] be a m- dimension datas vector set, then in nonlinear mapping functionIn the presence of, in feature space F Image data accordingly becomes

The Lagrangian that foundation is shown below：

Wherein, α and β are the Lagrange coefficient more than or equal to zero；

The partial derivative of above formula is made to be respectively zero, the multiplying property that can be shown below updates rule, and kernel function therein is manifold Self-adaptive kernel function；

$W_{ij}\←W_{ij}\frac{{\left(KV\right)}_{ij}}{{\left({\mathrm{KWV}}^{T}V\right)}_{ij}}$

$V_{ij}\←V_{ij}\frac{{\left(KW\right)}_{ij}}{{\left({\mathrm{VW}}^{T}KW\right)}_{ij}};$

Step f, with fusionThe low-rank approximation technique of method realizes the nuclear matrix calculating process in core NMF；

Step g, calculates the W and V of optimization, then test facial image z new for a width_test, it is by after core NMF dimensionality reductions Low-dimensional character representation is：

Wherein,Represent V^TPseudo inverse matrix；

Step h, the optimization object function of SVM is set up according to following formula；

In formula, λ represents the characteristic value of vectorial w,It is a mapping function without explicitly knowing concrete form, its calculating side Method can be by kernel functionTo realize；<W, x>Represent the inner product between vector w and x, l (；) represent loss function and then carry out rapid solving come the optimization object function to SVM using stochastic gradient descent method；

Optimization solution α is calculated, then SVM is that facial image is classified and adjudicated using following formula；

$f\left(x\right)=\mathrm{sgn}\left(\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&alpha;}}_i{y}_{i}k\right(x_i,x\left)\right)$

Wherein, k (x_i, x) represent the manifold self-adaptive kernel function for above calculating.

2. the face identification method based on manifold self-adaptive kernel according to claim 1, it is characterised in that in above-mentioned steps In b, if G represents a non-directed graph with n summit, wherein i vertex representation facial image x_i, for each data point x_i, find its p nearest-neighbors point set N (x_i)；If x_iIt is x_jP- nearest-neighbors or x_jIt is x_iP- nearest-neighbors, then exist A line is built between them, side right weight determines according to following formula：

$W_{ij}=\left\{\begin{array}{cc}1,& \begin{array}{cc}if& x_i\&Element;N\left(x_j\right)or{x}_j\&Element;N\left(x_i\right)\end{array}\\ 0,& otherwise\end{array}\right.$

Then figure Laplace operator L=D-W, wherein D are a diagonal matrix, and its value is D_ii=∑_jW_ij, D_iiDescribe data point x_iThe local density of surrounding.

3. the face identification method based on manifold self-adaptive kernel according to claim 1 and 2, it is characterised in that above-mentioned In step c, similarity matrix E is built using following formula；

Then, similar paired constraint set S and dissimilar paired constraint set D is given, one similarity matrix E of construction comes The paired constraint between data is represented, i.e.,：

$E_{i,j}=\left\{\begin{array}{cc}+1,& (x_i,x_j)\&Element;S\\ -1,& (x_i,x_j)\&Element;D\\ 0,& otherwise\end{array}\right.$

One core K_{I, j}Should as much as possible with side information E_{I, j}Alignment is kept, i.e.,：The alignment E of each core_{I, j}K_{I, j}Should be most Bigization.

4. the face identification method based on manifold self-adaptive kernel according to claim 3, it is characterised in that in above-mentioned steps In c, the optimization problem in following formula is solved using global optimization approach obtain the nonparametric kernel matrix K of optimization,

Wherein, C is the positive parameter traded off between a control side information and regularization term, l (E_{I, j}K_{I, j}) it is an empirical loss Function；It is normalized figure Laplace operator, it is defined as follows：

$\tilde{L}=I-D^{-1/2}{\mathrm{WD}}^{-1/2}$

One nonparametric kernel matrix K can be expressed as K=V relative to n data^TV ＞ 0, wherein, V=[v₁..., v_n]^TIt is data Point X=[x₁..., x_n]^TEmbeded matrix；Thus, being defined as follows can describe to be embedded in v_iAnd v_jBetween local correlations nuclear moment Battle array regularization term：

$\begin{array}{c}\underset{i,j=1}{\overset{n}{\&Sigma;}}{W}_{ij}\left|\right|\frac{v_i}{\sqrt{D_{ii}}}-\frac{v_j}{\sqrt{D_{jj}}}|{|}^2\\ =Tr\left(V^T\tilde{L}V\right)=Tr\left(\tilde{L}K\right)\end{array}$

It is above-mentioned to merge, obtain nonparametric kernel matrix K.

5. the face identification method based on manifold self-adaptive kernel according to claim 1, it is characterised in that in above-mentioned steps In f,

Make the multiplying property in above-mentioned formula update rule nuclear matrix K to be replaced with following formula, utilizeThe approximate skill of low-rank of method Art realizes the nuclear matrix calculating process in core NMF；

K is positive definite nuclear matrix, E_ij=k (x_i, z_j), k (x_i, z_j) represent kernel function, z_jIt is j-th new facial image,Λ_kPoint The characteristic vector and characteristic value and W of W are not contained_ij=k (z_i, z_j)。