CN103207993A - Face recognition method based on nuclear distinguishing random neighbor embedding analysis - Google Patents

Abstract

The invention discloses a face recognition method based on nuclear distinguishing random neighbor embedding analysis and relates to the field of pattern recognition. The method aims at extracting non-linear distinguishing information effectively and obtaining higher recognition rate. The face recognition method includes a training process and a testing process and includes the steps that (a) one sample of each object is selected randomly to conduct model training, a corresponding projection matrix B is obtained, and the rest data is used as a testing sample; (b) all training samples and testing samples are projected in a low-dimension manifold space; and (c) the recognition rate is detected by using a nearest neighbor classifier. On the basis of the prior art, the face recognition method effectively improves the recognition rate and well keeps an intra-class and inter-class sample structure. The face recognition method can be used in a domain of machine learning and pattern recognition and can be used in the fields of image recognition and target recognition and the like apart from face recognition.

Description

Based on the differentiation of nuclear at random the neighbour embed the face identification method of analysis

Technical field

The present invention is a kind of face identification method, specifically, relate to a kind of differentiation based on nuclear at random the neighbour embed the face identification method of analysis, can be used for recognition of face, image recognition, target identification etc.

Background technology

In current society, identity validation has very significant values.In recent years, the human biological characteristic identity that is applied to the individual is more and more widely authenticated, than traditional method safety, reliable, feature is unique, stability is high, be difficult for stolen with crack.Human intrinsic biological characteristic mainly contains: DNA, fingerprint, iris, voice, gait, palmmprint, people's face etc., based on people to the independently cognition of personal feature, computer technology and pattern recognition theory in conjunction with advanced grow up one after another such as DNA recognition technology, fingerprint identification technology, face recognition technology etc.With regard to present research level, DNA identifies and fingerprint recognition has high recognition, and reliability is the strongest but strong constraint condition its use has still limited the use of these two kinds of methods.Recognition of face has following powerful advantages than other living things feature recognition method: (1) need not the user and too much participates in, and contactless collection does not have the property of infringement; (2) to the user without any obvious stimulation, be convenient to hide; (3) equipment cost is cheap, mainly is to adopt camera to collect people's face.Thereby recognition of face has the applied environment of many uniquenesses as a kind of special biometrics identification technology, as criminal's arrest, automatically-controlled door access control system, customs pass by inspection, credit card affirmation etc.

Recognition of face becomes the research focus of pattern-recognition and image processing field already, and current main stream approach is based on the face recognition algorithms of subspace.For example edge Fisher analytic approach, local Fisher techniques of discriminant analysis, minimax distance analysis method and maximum spacing figure embedding inlay technique etc.In recent years, at the input data of nonlinear Distribution structure, propose the face identification method of many Nonlinear Dimension Reduction technology, wherein of greatest concernly be based on kernel method and based on two kinds of technology of geometry.For example equidistant reflection method, local linear embedding, laplacian eigenmaps and the arrangement of local tangent space etc.The method that the present invention proposes belongs to the recognition of face based on kernel method, and it can produce Nonlinear Mapping, represents the popular structure of sample data well, reaches more satisfactory dimensionality reduction effect.

Through the patent query statistic, have the patent of many recognitions of face aspect both at home and abroad: for example, keep embedding with the face identification method (200710114882.4) of support vector machine, based on the face identification method (200710300730.3) of general non-linear discriminating analysis, a kind of face identification method (200810030577.1) etc. based on the neighbour that supervision is arranged.

Summary of the invention

The present invention will solve the technical matters of the input data that the linear dimensionality reduction technology of existing technology can not fine processing nonlinear Distribution structure and can not improve discrimination effectively, kept in the class well and the shortcoming of the composition of sample between class, provide a kind of differentiation based on nuclear at random the neighbour embed the face identification method of analysis.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of differentiation based on nuclear neighbour at random embeds the face identification method of analysis, may further comprise the steps:

A) each object l sample of picked at random carries out model training, obtains corresponding projection matrix B, and remaining data are all as test sample book;

B) all training samples and test sample book are projected to low-dimensional stream shape space;

C) adopting nearest neighbor classifier to carry out discrimination detects.

Specifically, in face identification method of the present invention, specifically comprise training part and part of detecting two parts, wherein,

Described training process specifically comprises the steps:

A1 determines training sample matrix X=[x ₁, x ₂..., x _N] and class label, the definite kernel function is set variance parameter λ and maximum iteration time Mt;

A2 calculates between the input sample Euclidean distance in twos according to sample matrix X among the step a1, and the sample similarity in former space and class label calculate joint probability p _Ij:

$p_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{\exp (-(K_{\mathrm{ii}}+K_{\mathrm{jj}}-{2K}_{\mathrm{ij}})/2{\mathrm{\λ}}^2)}{{\mathrm{\Σ}}_{c_t=c_l}\exp (-(K_{\mathrm{tt}}+K_{\mathrm{ll}}-2K_{\mathrm{tl}})/2{\mathrm{\λ}}^2)}& \mathrm{if}{c}_i=c_j\\ \frac{\exp (-(K_{\mathrm{ii}}+K_{\mathrm{jj}}-{2K}_{\mathrm{ij}})/2{\mathrm{\λ}}^2)}{{\mathrm{\Σ}}_{c_t\≠c_m}\exp (-(K_{\mathrm{tt}}+K_{\mathrm{mm}}-2K_{\mathrm{tm}})/{2\mathrm{\λ}}^2)}& \mathrm{else}\end{array}\right.$

Joint probability p _IjIntroduced Gauss RBF kernel function κ (x, x ')=exp (σ || x-x ' || ₂ ²).The given n dimension sample x that class label is arranged ₁ ¹, x ₂ ¹..., x _N1 ¹, x ₁ ², x ₂ ²..., x _N2 ²..., x ₁ ^C, x ₂ ^C..., x _NC ^C, wherein

Represent i sample of c class, the total classification number of sample is C, N _iBe the sample number of i class, K _i=[κ (x ₁, x _i) ..., κ (x _N, x _i)] ^T, be a column vector;

A3 initialization transformation matrix B ⁰, make its element satisfy (0,1) Gaussian distribution;

A4 calculates joint probability q according to sample similarity and the class label of subspace _Ij, keep the similarity between similar sample as much as possible and reduce similarity between foreign peoples's sample by the KL divergence, utilize conjugate gradient method to upgrade transformation matrix B at last ^t:

A41 joint probability q _IjFor:

$q_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{{(1+{(K_i-K_j)}^T{B}^{T}B(K_i-K_j))}^{-1}}{{\mathrm{\Σ}}_{c_t=c_l}{(1+{(K_t-K_l)}^T{B}^{T}B(K_t-K_l))}^{-1}}& \mathrm{if}{c}_i=c_j\\ \frac{{(1+{(K_i-K_j)}^T{B}^{T}B(K_i-K_j))}^{-1}}{{\mathrm{\Σ}}_{c_t\≠c_m}{(1+{(K_t-K_m)}^T{B}^{T}B(K_t-K_m))}^{-1}}& \mathrm{else}\end{array}\right.$

The a42 objective cost function is:

$\min C\left(A\right)=\underset{c_i=c_j}{\mathrm{\Σ}}{p}_{\mathrm{ij}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}+\underset{c_i\≠c_k}{\mathrm{\Σ}}{p}_{\mathrm{ik}}\log \frac{p_{\mathrm{ik}}}{q_{\mathrm{ik}}}$

A43 upgrades transformation matrix B by the method for conjugate gradient of classics under this objective function ^tCarry out iterative, wherein come the parametrization cost functional by two kinds of methods:

A431. utilize projection matrix B parametrization cost functional:

$\frac{\mathrm{dC}\left(B\right)}{d\left(B\right)}=\underset{c_i=c_j}{\mathrm{\Σ}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}{\left(q_{\mathrm{ij}}\right)}^{\′}+\underset{c_i\≠c_t}{\mathrm{\Σ}}\frac{p_{\mathrm{it}}}{q_{\mathrm{it}}}{\left(q_{\mathrm{it}}\right)}^{\′}$

$=2B[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}(K_i-K_j){(K_i-K_j)}^T+\underset{c_i\≠c_t}{\mathrm{\Σ}}{u}_{\mathrm{it}}(K_i-K_t){(K_i-K_t)}^T]$

Express conveniently for making, define following auxiliary variable:

w _ij=[1+(K _i-K _j) ^ΤB ^ΤB(K _i-K _j)] ^-1

u _ij=(p _ij-q _ij)w _ij

$u_{\mathrm{ij}}^{\mathrm{in}}=\left\{\begin{array}{c}\\ \end{array}\right.\begin{array}{cc}{u}_{\mathrm{ij}}& \mathrm{if}{c}_i=c_j\\ 0& \mathrm{else}\end{array}$

$u_{\mathrm{ij}}^{\mathrm{ou}}=\left\{\begin{array}{cc}{u}_{\mathrm{ij}}& \mathrm{if}{c}_i\≠c_j\\ 0& \mathrm{else}\end{array}\right.$

By above-mentioned auxiliary variable, above-mentioned gradient formula can be reduced to:

$\frac{\mathrm{dC}\left(B\right)}{d\left(B\right)}=2B[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}(K_i-K_j){(K_i-K_j)}^T+\underset{c_i\≠c_j}{\mathrm{\Σ}}{u}_{\mathrm{it}}(K_i-K_t){(K_i-K_t)}^T]$

$=4B\left[K(D^{\mathrm{in}}-U^{\mathrm{in}}+D^{\mathrm{ou}}-U^{\mathrm{ou}})K^T\right]$

Diagonal matrix D wherein ^In, D ^OuIn element by corresponding U ^InAnd U ^OuEvery row and composition (or every row and, because U ^InAnd U ^OuBe symmetric matrix), namely

And

A432. utilize the cost functional in projection matrix A parameter characteristic space, the linear projection transformation matrix A among the feature space F can be according to the Nonlinear Mapping function

Be expressed as (following usefulness

Substitute

):

A=B Φ wherein, B=[b ⁽¹⁾..., b ^(r)] ^TAnd

$\frac{{\mathrm{dC}}^F\left(A\right)}{d\left(A\right)}=\underset{c_i=c_j}{\mathrm{\Σ}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}{\left(q_{\mathrm{ij}}\right)}^{\′}+\underset{c_i\≠c_t}{\mathrm{\Σ}}\frac{p_{\mathrm{it}}}{q_{\mathrm{it}}}{\left(q_{\mathrm{it}}\right)}^{\′}$

$=2[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}{\mathrm{BQ}}_{\mathrm{ij}}^{(K_i-K_j)}+\underset{c_i\≠c_t}{\mathrm{\Σ}}{u}_{\mathrm{it}}{\mathrm{BQ}}_{\mathrm{it}}^{(K_i-K_t)}]\mathrm{\Φ}$

Wherein

Be N * N matrix, the i of matrix is listed as by vectorial K _i-K _jForm, j is listed as by vectorial K _j-K _iForm, all the other row are made up of null vector;

A5 exports final projection matrix B ^t

Described training process specifically comprises the steps:

A51. determine training sample matrix X=[x ₁, x ₂..., x _N] and class label;

A52. utilize projection matrix B ^tTraining sample is projected to low-dimensional stream shape space;

A53. utilize projection matrix B ^tTraining sample is projected to low-dimensional stream shape space.

Technical conceive of the present invention: to a kind of new Dimension Reduction Analysis method that is proposed by Zheng Jianwei etc. recently, be called and differentiate at random that the neighbour embeds that (discriminative stochastic neighbor embedding DSNE) carries out improvement based on nuclear.DSNE is the embedding of neighbour at random (the stochastic neighbor embedding in propositions such as Hinton, SNE) and the improved t distribution SNE(t-distributed stochastic neighbor embedding that proposes such as Laurens, introduce linear projective transformation thought and class label information on basis t-SNE).SNE is converted into the probability expression-form with the Euclidean distance between high dimensional data, its cost functional makes up criterion and requires the subspace to have identical form of probability with the former input space, and t-SNE adopts the conditional probability form that has among the alternative SNE of symmetric joint probability expression, and introducing t distribution shows the similarity between sample in twos in the subspace.Because SNE and t-SNE belong to non-linear unsupervised dimension reduction method, so have " sample exterior problem " and be not suitable for the defective of pattern discrimination task.2011, (the manifold-oriented stochastic neighbor projection of the projection of neighbour at random towards popular study by propositions such as Wu, MSNP) solved " sample exterior problem " well, but be linear unsupervised dimension reduction method based on MSNP, it still is not suitable for pattern recognition task.And the linear DSNE that supervision arranged has solved the problem of this two aspect dexterously, extracts problem but linear characteristics make it can't solve non-linear characteristics effectively, and DSNE is for different classes of sample, and its probability density still remains to be improved.The present invention utilize the thought of kernel method propose a kind of differentiation based on nuclear at random the neighbour embed the face identification method of analysis (kernel DSNE KDSNE), overcome the defective of DSNE well.

Advantage of the present invention is: input data that can fine processing nonlinear Distribution structure, improved discrimination effectively, kept in the class well and the composition of sample between class.

Description of drawings

Fig. 1 is the groups of people's face image pattern in the ORL face database;

Fig. 2 is the groups of people's face image pattern in the Yale face database;

Fig. 3 is that the discrimination under the different subspace dimension changes in the ORL face database;

Fig. 4 is that the discrimination under the different subspace dimension changes in the Yale face database;

Fig. 5 is process flow diagram of the present invention.

Embodiment

Below the present invention is further described.With reference to accompanying drawing 1-4:

A kind of differentiation based on nuclear neighbour at random embeds the face identification method of analysis, may further comprise the steps:

A) each object l sample of picked at random carries out model training, obtains corresponding projection matrix B, and remaining data are all as test sample book;

B) all training samples and test sample book are projected to low-dimensional stream shape space;

C) adopting nearest neighbor classifier to carry out discrimination detects.

Specifically, in face identification method of the present invention, specifically comprise training part and part of detecting two parts, wherein,

Described training process specifically comprises the steps:

A1 determines training sample matrix X=[x ₁, x ₂..., x _N] and class label, the definite kernel function is set variance parameter λ and maximum iteration time Mt;

A2 calculates between the input sample Euclidean distance in twos according to sample matrix X among the step a1, and the sample similarity in former space and class label calculate joint probability p _Ij:

$p_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{\exp (-(K_{\mathrm{ii}}+K_{\mathrm{jj}}-{2K}_{\mathrm{ij}})/2{\mathrm{\λ}}^2)}{{\mathrm{\Σ}}_{c_t=c_l}\exp (-(K_{\mathrm{tt}}+K_{\mathrm{ll}}-2K_{\mathrm{tl}})/2{\mathrm{\λ}}^2)}& \mathrm{if}{c}_i=c_j\\ \frac{\exp (-(K_{\mathrm{ii}}+K_{\mathrm{jj}}-{2K}_{\mathrm{ij}})/2{\mathrm{\λ}}^2)}{{\mathrm{\Σ}}_{c_t\≠c_m}\exp (-(K_{\mathrm{tt}}+K_{\mathrm{mm}}-2K_{\mathrm{tm}})/{2\mathrm{\λ}}^2)}& \mathrm{else}\end{array}\right.$

Joint probability p _IjIntroduced Gauss RBF kernel function The given n dimension sample x that class label is arranged ₁ ¹, x ₂ ¹..., x _N1 ¹, x ₁ ², x ₂ ²..., x _N2 ²..., x ₁ ^C, x ₂ ^C..., x _NC ^C, wherein

Represent i sample of c class, the total classification number of sample is C, N _iBe the sample number of i class, K _i=[κ (x ₁, x _i) ..., κ (x _N, x _i)] ^T, be a column vector;

A3 initialization transformation matrix B ⁰, make its element satisfy (0,1) Gaussian distribution;

A4 calculates joint probability q according to sample similarity and the class label of subspace _Ij, keep the similarity between similar sample as much as possible and reduce similarity between foreign peoples's sample by the KL divergence, utilize conjugate gradient method to upgrade transformation matrix B at last ^t:

A41 joint probability q _IjFor:

$q_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{{(1+{(K_i-K_j)}^T{B}^{T}B(K_i-K_j))}^{-1}}{{\mathrm{\Σ}}_{c_t=c_l}{(1+{(K_t-K_l)}^T{B}^{T}B(K_t-K_l))}^{-1}}& \mathrm{if}{c}_i=c_j\\ \frac{{(1+{(K_i-K_j)}^T{B}^{T}B(K_i-K_j))}^{-1}}{{\mathrm{\Σ}}_{c_t\≠c_m}{(1+{(K_t-K_m)}^T{B}^{T}B(K_t-K_m))}^{-1}}& \mathrm{else}\end{array}\right.$

The a42 objective cost function is:

$\min C\left(A\right)=\underset{c_i=c_j}{\mathrm{\Σ}}{p}_{\mathrm{ij}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}+\underset{c_i\≠c_k}{\mathrm{\Σ}}{p}_{\mathrm{ik}}\log \frac{p_{\mathrm{ik}}}{q_{\mathrm{ik}}}$

A43 upgrades transformation matrix B by the method for conjugate gradient of classics under this objective function ^tCarry out iterative, wherein come the parametrization cost functional by two kinds of methods:

A431. utilize projection matrix B parametrization cost functional:

$\frac{\mathrm{dC}\left(B\right)}{d\left(B\right)}=\underset{c_i=c_j}{\mathrm{\Σ}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}{\left(q_{\mathrm{ij}}\right)}^{\′}+\underset{c_i\≠c_t}{\mathrm{\Σ}}\frac{p_{\mathrm{it}}}{q_{\mathrm{it}}}{\left(q_{\mathrm{it}}\right)}^{\′}$

$=2B[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}(K_i-K_j){(K_i-K_j)}^T+\underset{c_i\≠c_t}{\mathrm{\Σ}}{u}_{\mathrm{it}}(K_i-K_t){(K_i-K_t)}^T]$

Express conveniently for making, define following auxiliary variable:

w _ij=[1+(K _i-K _j) ^ΤB ^ΤB(K _i-K _j)] ^-1

u _ij=(p _ij-q _ij)w _ij

$u_{\mathrm{ij}}^{\mathrm{in}}=\left\{\begin{array}{c}\\ \end{array}\right.\begin{array}{cc}{u}_{\mathrm{ij}}& \mathrm{if}{c}_i=c_j\\ 0& \mathrm{else}\end{array}$

$u_{\mathrm{ij}}^{\mathrm{ou}}=\left\{\begin{array}{cc}{u}_{\mathrm{ij}}& \mathrm{if}{c}_i\≠c_j\\ 0& \mathrm{else}\end{array}\right.$

By above-mentioned auxiliary variable, above-mentioned gradient formula can be reduced to:

$\frac{\mathrm{dC}\left(B\right)}{d\left(B\right)}=2B[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}(K_i-K_j){(K_i-K_j)}^T+\underset{c_i\≠c_t}{\mathrm{\Σ}}{u}_{\mathrm{it}}(K_i-K_t){(K_i-K_t)}^T]$

$=4B\left[K(D^{\mathrm{in}}-U^{\mathrm{in}}+D^{\mathrm{ou}}-U^{\mathrm{ou}})K^T\right]$

Diagonal matrix D wherein ^In, D ^OuIn element by corresponding U ^InAnd U ^OuEvery row and composition (or every row and, because U ^InAnd U ^OuBe symmetric matrix), namely

And A432. utilize the cost functional in projection matrix A parameter characteristic space, the linear projection transformation matrix A among the feature space F can be according to the Nonlinear Mapping function Be expressed as (following usefulness

Substitute ):

A=B Φ wherein, B=[b ⁽¹⁾..., b ^(r)] ^TAnd

$\frac{{\mathrm{dC}}^F\left(A\right)}{d\left(A\right)}=\underset{c_i=c_j}{\mathrm{\Σ}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}{\left(q_{\mathrm{ij}}\right)}^{\′}+\underset{c_i\≠c_t}{\mathrm{\Σ}}\frac{p_{\mathrm{it}}}{q_{\mathrm{it}}}{\left(q_{\mathrm{it}}\right)}^{\′}$

$=2[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}{\mathrm{BQ}}_{\mathrm{ij}}^{(K_i-K_j)}+\underset{c_i\≠c_t}{\mathrm{\Σ}}{u}_{\mathrm{it}}{\mathrm{BQ}}_{\mathrm{it}}^{(K_i-K_t)}]\mathrm{\Φ}$

Wherein

Be N * N matrix, the i of matrix is listed as by vectorial K _i-K _jForm, j is listed as by vectorial K _j-K _iForm, all the other row are made up of null vector;

A5 exports final projection matrix B ^t

Described training process specifically comprises the steps:

A1 determines training sample matrix X=[x ₁, x ₂..., x _N] and class label;

A2 utilizes projection matrix B ^tTraining sample is projected to low-dimensional stream shape space;

A3 utilizes projection matrix B ^tTraining sample is projected to low-dimensional stream shape space.

Adopt the face database of ORL and two classics of Yale to carry out the discrimination detection.Unification is adjusted to 32 * 32 pixels with above-mentioned face database in the experiment, and the gray-scale value of every pixel is within the 0-255 scope.In the ORL face database, select 3 of every classes and 5 samples to carry out discrimination at random and detect, in the Yale face database, then select 4 of every classes and 6 samples at random.The present invention adopts DSNE and two kinds of linear dimensionality reduction algorithms of MSNP to compare test, wherein proposition such as Wu in the projection of the neighbour at random paper of popular study empirical tests the MSNP algorithm be better than general dimensionality reduction algorithm such as SNE, t-SNE, LLTSA, LPP in recognition capability.The concrete configuration parameter of various algorithms is as follows: variance parameter λ=0.1 and maximum iteration time are 300 among KDSNE1, KDSNE2 and the DSNE; Cauchy distributes among the MSNP sample degree of freedom γ=4 and maximum iteration time are 1000.

Table 1 is best identified rate and the respective subspace dimensions (bracket inner digital) of all algorithms in two face databases, and wherein thickened portion is the highest discrimination under the identical training sample.As seen from Table 1, KDSNE1 has optimum discrimination in the ORL face database, and KDSNE2 has optimum discrimination in the Yale face database, this shows, the height of KDSNE1 and KDSNE2 discrimination is different and different with database also.As for KDSNE1 and the KDSNE2 comparison than other algorithms, from figure and table, can learn, KDSNE2 has promoted than the DSNE of discrimination suboptimum in Yale〉3%, though and the KDSNE2 discrimination promotes average less than 2% in ORL, and DSNE is in close proximity to KDSNE2 in the l=5 experiment, yet DSNE has but used higher subspace dimension just to reach the discrimination that approaches, and is inferior to KDSNE1 and KDSNE2 from recognition of face in essence.

Best identified rate and respective dimensions that the various algorithms of table 1 are obtained in ORL and Yale database

Claims (6)

1. One kind based on the differentiation of nuclear at random the neighbour embed the face identification method of analysis, comprise training process and test process, it is characterized in that, may further comprise the steps:

   A) each object l sample of picked at random carries out model training, obtains corresponding projection matrix B ∈ R ^{R * N}, wherein N is training sample quantity, and r is sample dimension after the projection, and remaining data are all as test sample book;

   B) all training samples and test sample book are projected to low-dimensional stream shape space;

   C) adopting nearest neighbor classifier to carry out discrimination detects.
2. 2. face identification method according to claim 1 is characterized in that, in described step a), each object l sample of picked at random carries out model training and comprises following five steps:

   A1 determines sample matrix X=[x ₁, x ₂..., x _N] and class label, the definite kernel function is set variance parameter λ and maximum iteration time Mt, wherein x _i∈ R ^{D * N}, be i input sample, λ is the variance parameter of corresponding Gaussian function, Mt is maximum iteration time;

   A2 calculates between the input sample Euclidean distance in twos according to sample matrix X among the step a1, and the sample similarity in former space and class label calculate joint probability p _Ij

   A3 initialization transformation matrix B ⁰, make its element satisfy (0,1) Gaussian distribution;

   A4 calculates joint probability q according to sample similarity and the class label of subspace _Ij, keep the similarity between similar sample as much as possible and reduce similarity between foreign peoples's sample by the KL divergence, utilize conjugate gradient method to upgrade transformation matrix B at last ^t

   A5 exports final projection matrix B ^t
3. 3. face identification method according to claim 2 is characterized in that, calculates joint probability p in described step a2 _IjThe time introduced Gauss RBF kernel function

   

   The given n dimension sample x that class label is arranged ₁ ¹, x ₂ ¹..., x _N1 ¹, x ₁ ², x ₂ ²..., x _N2 ²..., x ₁ ^C, x ₂ ^C..., x _NC ^C, wherein

   

   Represent i sample of c class, the total classification number of sample is C, N _iIt is the sample number of i class.After introducing kernel function, the joint probability of the sample in former space is:

   $p_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{\exp (-(K_{\mathrm{ii}}+K_{\mathrm{jj}}-{2K}_{\mathrm{ij}})/2{\mathrm{\λ}}^2)}{{\mathrm{\Σ}}_{c_t=c_l}\exp (-(K_{\mathrm{tt}}+K_{\mathrm{ll}}-2K_{\mathrm{tl}})/2{\mathrm{\λ}}^2)}& \mathrm{if}{c}_i=c_j\\ \frac{\exp (-(K_{\mathrm{ii}}+K_{\mathrm{jj}}-{2K}_{\mathrm{ij}})/2{\mathrm{\λ}}^2)}{{\mathrm{\Σ}}_{c_t\≠c_m}\exp (-(K_{\mathrm{tt}}+K_{\mathrm{mm}}-2K_{\mathrm{tm}})/{2\mathrm{\λ}}^2)}& \mathrm{else}\end{array}\right.$

   K wherein _i=[κ (x ₁, x _i) ..., κ (x _N, x _i)] ^T, be a column vector of being formed by the kernel function value.
4. 4. face identification method according to claim 3 is characterized in that, at the fall into a trap joint probability q in operator space of described step a4 _IjThe time also introduced Gauss RBF kernel function κ (x, x ')=exp (λ | x-x ' || ₂ ²), that is:

   $q_{\mathrm{ij}}=\left\{\begin{array}{cc}\frac{{(1+{(K_i-K_j)}^T{B}^{T}B(K_i-K_j))}^{-1}}{{\mathrm{\Σ}}_{c_t=c_l}{(1+{(K_t-K_l)}^T{B}^{T}B(K_t-K_l))}^{-1}}& \mathrm{if}{c}_i=c_j\\ \frac{{(1+{(K_i-K_j)}^T{B}^{T}B(K_i-K_j))}^{-1}}{{\mathrm{\Σ}}_{c_t\≠c_m}{(1+{(K_t-K_m)}^T{B}^{T}B(K_t-K_m))}^{-1}}& \mathrm{else}\end{array}\right.$
5. 5. face identification method according to claim 4 is characterized in that, in described step a4 by minimize in the similar sample and between foreign peoples's sample separately KL divergence obtain objective cost function:

   $\min C\left(B\right)=\underset{c_i=c_j}{\mathrm{\Σ}}{p}_{\mathrm{ij}}\log \frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}+\underset{c_i\≠c_t}{\mathrm{\Σ}}{p}_{\mathrm{it}}\log \frac{p_{\mathrm{it}}}{q_{\mathrm{it}}}$
6. 6. face identification method according to claim 5 is characterized in that, under described objective function, comes the parametrization cost functional by two kinds of methods:

   A41. utilize projection matrix B parametrization cost functional:

   $\frac{\mathrm{dC}\left(B\right)}{d\left(B\right)}=\underset{c_i=c_j}{\mathrm{\Σ}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}{\left(q_{\mathrm{ij}}\right)}^{\′}+\underset{c_i\≠c_t}{\mathrm{\Σ}}\frac{p_{\mathrm{it}}}{q_{\mathrm{it}}}{\left(q_{\mathrm{it}}\right)}^{\′}$

   $=2B[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}(K_i-K_j){(K_i-K_j)}^T+\underset{c_i\≠c_t}{\mathrm{\Σ}}{u}_{\mathrm{it}}(K_i-K_t){(K_i-K_t)}^T]$

   A42. utilize projection matrix A ∈ R ^{R * d}The cost functional in parameter characteristic space, the line in the feature space

   Property projective transformation matrix A can be according to the Nonlinear Mapping function

   

   Be expressed as (following usefulness

   

   Substitute

   

   ):

   A=B Φ wherein, B=[b ⁽¹⁾..., b ^(r)] ^TAnd

   

   $\frac{{\mathrm{dC}}^F\left(A\right)}{d\left(A\right)}=\underset{c_i=c_j}{\mathrm{\Σ}}\frac{p_{\mathrm{ij}}}{q_{\mathrm{ij}}}{\left(q_{\mathrm{ij}}\right)}^{\′}+\underset{c_i\≠c_t}{\mathrm{\Σ}}\frac{p_{\mathrm{it}}}{q_{\mathrm{it}}}{\left(q_{\mathrm{it}}\right)}^{\′}$

   $=2[\underset{c_i=c_j}{\mathrm{\Σ}}{u}_{\mathrm{ij}}{\mathrm{BQ}}_{\mathrm{ij}}^{(K_i-K_j)}+\underset{c_i\≠c_t}{\mathrm{\Σ}}{u}_{\mathrm{it}}{\mathrm{BQ}}_{\mathrm{it}}^{(K_i-K_t)}]\mathrm{\Φ}$

   Wherein

   

   Be N * N matrix, the i of matrix is listed as by vectorial K _i-K _jForm, j is listed as by vectorial K _j-K _iForm, all the other row are made up of null vector.

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