CN102156878A - Sparse embedding with manifold information-based human face identification method - Google Patents

Abstract

The invention discloses a sparse embedding with manifold information-based human face identification method, belonging to the field of human face identification. The method provides a novel sparse representing algorithm, namely the sparse embedding with manifold information (SEMI) algorithm. The method comprises the following steps: calculating a sparse reconstructing coefficient matrix among samples, and obtaining a new sample set after the sparse reconstruction; and preserving certain manifold information between the new sample set and original samples so that the manifold structure among the original samples can be preserved when the sparse relationship among the sample cannot preserved after projection. The method extracts the sparse information, and introduces the manifold structure characteristics of a human face sample into the sparse information, and obtains the projection sub-space of the sample by utilizing the common fused characteristic information of the sparse information and the human face sample, so that the identification effect is improved.

Description

A kind of based on the face identification method that has the sparse mapping of stream shape information

Technical field

The present invention relates to a kind of face identification method, relate in particular to a kind of face identification method, belong to the recognition of face field in the pattern-recognition based on sparse mapping (SEMI) algorithm that has stream shape information.

Background technology

Manifold learning is a kind of effective feature extraction and dimensionality reduction technology, has caused extensive studies interest now.This method can keep in low n-dimensional subspace n convection current shape structure.Traditional manifold learning arithmetic comprise equidistant mapping (Isometric featuremapping, ISOMAP), local linear mapping (Locally linear embedding, LLE) and laplacian eigenmaps (Laplacian eigenmaps) etc.Yet these methods only define at non-linear space training sample, and can not handle new test sample book.The proposition of linear manifold method is exactly in order to address the aforementioned drawbacks, such as the part keep projection (Locality preserving projection, LPP) and neighbour's reserved mapping (Neighborhood preserving embedding, NPE).Above-mentioned method is not all considered classification information in training process, in order to utilize classification advantage separatory, proposed to have the manifold learning method of supervision.(Local discriminant embedding is LDE) by being provided with the intrinsic neighbor relationships that similar weights keep sample in the class in local discriminating mapping; (Locally discriminating projection LDP) is a kind of LPP method of weighting, and it constructs a punishment similar matrix by the classification information of sample in local discriminating projection; Edge Fisher analyze (Marginal fisher analysis, MFA) assemble in the class by classification information structure sample with class in separate curve.

As the mode identification technology of other kinds, sparse maintenance method shows that a sample can be reconstructed by other sample and obtains.(Sparsity Preserving Projection SPP) minimizes the sparse reconstruct relation that keeps by sparse reconfiguring false rate to sparse retaining projection.In the real world applications of recognition of face, facial image often exists with the form of manifold structure, keeps manifold structure and can improve recognition effect.And existing sparse method only extracted sparse reconfiguration information between sample as SPP etc. and has been used for projection and obtains new subspace, and recognition effect is not ideal enough.

Summary of the invention

The present invention is directed to the deficiency that existing face recognition technology exists, and propose a kind of based on the face identification method that has the sparse mapping of stream shape information.

This method comprises following two parts content:

(1) the sparse reconstruct of sample set

A given sample set X=[x ₁, x ₂..., x _n], n is a total sample number, and each sample is by all the other n-1 sample linear reconstruction, and the sample set X '=XA after the reconstruct, A are sparse reconstruction coefficients matrix, A=[a ₁, a ₂..., a _n], a _i=[a _I1, a _I2..., a _In] be sample x _iReconstruction coefficients set, i=1,2 ..., n;

(2) have the sparse mapping algorithm that flows shape information, i.e. SEMI algorithm

Suppose sample set X=[x ₁, x ₂..., x _n] ∈ R ^{N * m}, R ^{N * m}Real number space for n * m dimension;

According to:

$H_{\mathrm{ij}}^b=\left\{\begin{array}{cc}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t),& \mathrm{if}{y}_i\≠y_j\\ 0,& \mathrm{otherwise}\end{array}\right.$

Wherein, i, j are sample number,

T is the parameter of all sample set variance, y _i, y _jBe respectively sample x _i, x _jClass label;

Sample weights matrix between compute classes And similar sample weights matrix

Total distance after calculating original sample and the reconstruct between foreign peoples's sample

V is the proper vector of corresponding matrix eigenvalue of maximum, and subscript T represents transposition, down together;

Total distance after calculating original sample and the reconstruct between this class sample

According to overall reconstructed error

With S _wBe fused to following formula with two expression formulas of E:

$S=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left|\right|v^T{x}_j-v^T{\mathrm{Xa}}_i\left|\right|}^2{H}_{\mathrm{ij}}$

Wherein,

To SEMI algorithm objective function The abbreviation of deriving obtains SEMI algorithm objective function transform:

$\stackrel{\‾}{v}=\underset{v}{\arg \max }\frac{v^{T}X(D_b+{\mathrm{AD}}_b{A}^T-H_b{A}^T-{\mathrm{AH}}_b)X^{T}v}{v^{T}X(D+{\mathrm{ADA}}^T-{\mathrm{HA}}^T-\mathrm{AH})X^{T}v}$

Wherein, Represent optimum projection vector, D=diag{D _n} _{N * n}And Be two n dimension diagonal matrixs, H is the matrix of coefficients in the S expression formula;

Define two matrixes:

L _b＝D _b+AD _bA ^T-H _bA ^T-AH _b

L＝D+ADA ^T-HA ^T-AH

Utilize the Laplace operator method, SEMI algorithm objective function transform be equivalent to a problem that solves generalized eigenvalue:

[XL _bX ^T] [XLX ^T] ^-1V=λ v, λ are Lagrange multiplier;

Calculated characteristics matrix V=[v ₁, v ₂..., v _l], v ₁～v _lBe matrix [XL _bX ^T] [XLX ^T] ^-1L the maximum pairing proper vector of eigenwert;

Sample set Y=V after the calculating projection ^TX projects to the subspace of asking with this sample set, finishes algorithm.

The present invention proposes a kind of new rarefaction representation algorithm, promptly have sparse mapping (SEMI) algorithm of stream shape information.This method is in face recognition application, not only extracted the sparse information of people's face sample, the manifold structure feature that also people's face sample itself is had incorporates wherein simultaneously, utilizes both common characteristic informations that merge to obtain the projection subspace of sample, has improved the recognition of face effect.

Embodiment

Below the present invention is described in further detail.

The inventive method comprises following two parts content:

(1) the sparse reconstruct of sample set

A given sample set X=[x ₁, x ₂..., x _n], n is a total sample number, and each sample is by all the other n-1 sample linear reconstruction, and the computing method of reconstruct are:

x _i＝a _i1x ₁+a _i2x ₂+…+a _ij·x _j+…+a _inx _n

Wherein, a _IjJ pairing reconstruction coefficients of sample during for i sample of reconstruct;

Sample set X '=XA after the reconstruct, A are sparse reconstruction coefficients matrix, A=[a ₁, a ₂..., a _n], a _i=[a _I1, a _I2..., a _In] be sample x _iReconstruction coefficients set, i=1,2 ..., n;

Reconstruction coefficients set a _iCan calculate by following formula:

$\underset{a}{\min }{\left|\right|a\left|\right|}_0$

s.t.x′＝Xa

Wherein, || || ₀The zero norm size of expression compute vector, s.t. represents constraint, and x ' is the sample after the reconstruct, and a is sparse coefficient.This formula is the number of the nonzero element in the compute vector, and it is separated is a NP difficult problem, list of references [1] if in explanation this separate enough sparsely, can come equivalence by solving 1 a relevant norm problem so, as follows:

$\underset{a}{\min }{\left|\right|a\left|\right|}_1$

s.t.x′＝Xa

Wherein || || ₁1 norm size of expression compute vector;

In list of references [2], following formula can solve by a linear programming problem.

[1]D.Donoho，“Compressed?sensing，”IEEE?Trans.Inform.Theory，vol.52，pp.1289-1306，Apr.2006.

[2]S.Chen，D.Donoho?and?M.Saunders，“Atomic?decomposition?by?basis?pursuit，”SIAMReview，vol.43，pp.129-159，2001.

(2) have the sparse mapping algorithm that flows shape information, i.e. SEMI algorithm

Sparse retaining projection (SPP) method has only kept the sparse reconstruct relation between sample, but it does not consider the manifold structure that people's face sample exists in sample space, therefore, the present invention proposes a kind of new SEMI algorithm, in the sparse reconstruct relation that keeps between original sample, the manifold structure of retain sample collection in sample space as much as possible also.

The flow process of described SEMI algorithm is as follows:

Suppose sample set X=[x ₁, x ₂..., x _n] ∈ R ^{N * m}, R ^{N * m}For the real number space of n * m dimension, establish A=[a ₁, a ₂... a _n] be the sparse reconstruction coefficients matrix of having tried to achieve;

According to:

$H_{\mathrm{ij}}^b=\left\{\begin{array}{cc}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t),& \mathrm{if}{y}_i\≠y_j\\ 0,& \mathrm{otherwise}\end{array}\right.$

Wherein, i, j are sample number, and i ≠ j, t are the parameter of all sample set variance, y _i, y _jBe respectively sample x _i, x _jClass label;

Sample weights matrix between compute classes

And similar sample weights matrix

Total distance after calculating original sample and the reconstruct between foreign peoples's sample

V is the proper vector of corresponding matrix eigenvalue of maximum, and subscript T represents transposition, down together;

Total distance after calculating original sample and the reconstruct between this class sample

According to the overall reconstructed error of mentioning in the SPP algorithm With S _wBe fused to following formula with two expression formulas of E:

$S=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left|\right|v^T{x}_j-v^T{\mathrm{Xa}}_i\left|\right|}^2{H}_{\mathrm{ij}}$

Wherein,

Based on S _bWith the expression formula of S, we seek the objective function of a kind of optimization criterion as the SEMI algorithm, make at maximization S _bThe time minimize S, this objective function is:

$\mathrm{Max}\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left|\right|v^T{x}_j-v^T{\mathrm{Xa}}_i\left|\right|}^2{H}_{\mathrm{ij}}^b}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left|\right|v^T{x}_j-v^T{\mathrm{Xa}}_i\left|\right|}^2{H}_{\mathrm{ij}}}$

To molecule, the denominator of the SEMI algorithm objective function abbreviation of deriving, obtain this objective function transform:

$\stackrel{\‾}{v}=\underset{v}{\arg \max }\frac{v^{T}X(D_b+{\mathrm{AD}}_b{A}^T-H_b{A}^T-{\mathrm{AH}}_b)X^{T}v}{v^{T}X(D+{\mathrm{ADA}}^T-{\mathrm{HA}}^T-\mathrm{AH})X^{T}v}$

Wherein,

Represent optimum projection vector, D=diag{D _n} _{N * n}And

Be two n dimension diagonal matrixs,

H is the matrix of coefficients in the S expression formula;

For making formula for simplicity, define two matrixes here:

L _b＝D _b+AD _bA ^T-H _bA ^T-AH _b

L＝D+ADA ^T-HA ^T-AH

Utilize the Laplace operator method, SEMI algorithm objective function transform be equivalent to a problem that solves generalized eigenvalue:

[XL _bX ^T] [XLX ^T] ^-1V=λ .v, λ are Lagrange multiplier;

Calculated characteristics matrix V=[v ₁, v ₂..., v _l], v ₁～v _lBe matrix [XL _bX ^T] [XLX ^T] ^-1L the maximum pairing proper vector of eigenwert;

Sample set Y=V after the calculating projection ^TX projects to the subspace of asking with this sample set, finishes algorithm.

An example laboratory and data result are provided below:

The experiment operation platform is Matlab, and the ORL face database is selected in experiment for use.ORL face database [3] has comprised 40 people, everyone 10 pictures, and wherein, everyone picture includes different postures, illumination condition and human face expression.In our experiment, every pictures is cut to the 46*56 size, and its gray scale is demarcated again in the scope of [0,1].

[3]F.Samaria?and?A.Harter，“Parameterisation?of?a?Stochastic?Model?for?Human?FaceIdentification，”Proceedings?of?2nd?IEEE?Workshop?on?Applications?of?Computer?Vision，1994.

For the validity of SEMI algorithm relatively, we have compared the discrimination of it and other correlation techniques (as LPP, LDE, SPP etc.).According to final experimental result, arest neighbors number k chooses the value that can produce the best identified rate.In all comparative approach, we at first carry out the PCA algorithm and reduce data dimension, thereby have avoided the unusual problem of inverse matrix.Table 1 has been listed the average recognition rate of distinct methods on ORL, and by table 1 as can be seen, the average recognition rate of SEMI algorithm has improved 6.26% at least than additive method on ORL, and the lifting of recognition effect still is more satisfactory.

The average recognition rate (%) of each method of table 1 on ORL

Method name	PCA	LPP	NPE	LDE	MFA	SPP	SEMI
								Average recognition rate	80.36	80.50	80.79	82.43	82.86	80.37	89.12

Claims (3)

1. one kind based on the face identification method that has stream shape information sparse mapping, it is characterized in that:

This method comprises following two parts content:

(1) the sparse reconstruct of sample set

A given sample set X=[x ₁, x ₂..., x _n], n is a total sample number, and each sample is by all the other n-1 sample linear reconstruction, and the sample set X '=XA after the reconstruct, A are sparse reconstruction coefficients matrix, A=[a ₁, a ₂..., a _n], a _I1=[a _I1, a _I2, a _In] be sample x _iReconstruction coefficients set, i=1,2 ..., n;

(2) have the sparse mapping algorithm that flows shape information, i.e. SEMI algorithm

Suppose sample set X=[x ₁, x ₂..., x _n] ∈ R ^{N * m}, R ^{N * m}Real number space for n * m dimension;

According to:

$H_{\mathrm{ij}}^b=\left\{\begin{array}{cc}\exp (-{\left|\right|x_i-x_j\left|\right|}^2/t),& \mathrm{if}{y}_i\≠y_j\\ 0,& \mathrm{otherwise}\end{array}\right.$

Wherein, i, j are sample number, and i ≠ j, t are the parameter of all sample set variance, y _i, y _jBe respectively sample x _i, x _jClass label;

Sample weights matrix between compute classes

And similar sample weights matrix

Total distance after calculating original sample and the reconstruct between foreign peoples's sample

V is the proper vector of corresponding matrix eigenvalue of maximum, and subscript T represents transposition, down together;

Total distance after calculating original sample and the reconstruct between this class sample According to overall reconstructed error

With S _wBe fused to following formula with two expression formulas of E:

$S=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left|\right|v^T{x}_j-v^T{\mathrm{Xa}}_i\left|\right|}^2{H}_{\mathrm{ij}}$

Wherein,

To SEMI algorithm objective function

The abbreviation of deriving obtains SEMI algorithm objective function transform:

$\stackrel{\‾}{v}=\underset{v}{\arg \max }\frac{v^{T}X(D_b+{\mathrm{AD}}_b{A}^T-H_b{A}^T-{\mathrm{AH}}_b)X^{T}v}{v^{T}X(D+{\mathrm{ADA}}^T-{\mathrm{HA}}^T-\mathrm{AH})X^{T}v}$

Wherein,

Represent optimum projection vector, D=diag{D _n} _{N * n}And

Be two n dimension diagonal matrixs,

H is the matrix of coefficients in the S expression formula;

Define two matrixes:

L _b＝D _b+AD _bA ^T-H _bA ^T-AH _b

L＝D+ADA ^T-HA ^T-AH

Utilize the Laplace operator method, SEMI algorithm objective function transform be equivalent to a problem that solves generalized eigenvalue:

[XL _bX ^T] [XLX ^T] ^-1V=λ v, λ are Lagrange multiplier;

Calculated characteristics matrix V=[v ₁, v ₂..., v _l], v ₁～v _lBe matrix [XL _bX ^T] [XLX ^T] ^-1L the maximum pairing proper vector of eigenwert;

Sample set Y=V after the calculating projection ^TX projects to the subspace of asking with this sample set.

2. according to claim 1 based on the face identification method that has the sparse mapping of stream shape information, it is characterized in that: in the described part (), each sample by the computing method of all the other n-1 sample linear reconstruction is:

x _i＝a _i1x ₁+a _i2x ₂+…+a _ij·x _j+…+a _inx _n

Wherein, a _IjJ pairing reconstruction coefficients of sample during for i sample of reconstruct.

3. according to claim 1 based on the face identification method that has the sparse mapping of stream shape information, it is characterized in that: in the described part (), sample x _iReconstruction coefficients set a _iComputing method be:

$\underset{a}{\min }{\left|\right|a\left|\right|}_1$

s.t.x′＝Xa

Wherein, || || ₁1 norm size of expression compute vector, s.t. represents constraint, and x ' is the sample after the reconstruct, and a is sparse coefficient.