CN108573263A - A kind of dictionary learning method of co-ordinative construction rarefaction representation and low-dimensional insertion - Google Patents

Abstract

The invention discloses the dictionary learning methods of a kind of co-ordinative construction rarefaction representation and low-dimensional insertion, dictionary is constructed to carry out with dimensionality reduction projection matrix time-interleaved, pass through incoherence between forced class of the rarefaction representation coefficient matrix with block diagonalization structure to enhance dictionary in low dimension projective space, at the same time, correlation in class using the low-rank of the expression coefficient on class small pin for the case dictionary to keep dictionary, dictionary is constructed can promote mutually with projection study, fully to keep the sparsity structure of data, to encode out the code coefficient with more classification judgement index, the expression coefficient class discriminating power that the present invention solves higher-dimension characteristic in dictionary learning method existing in the prior art due to training sample data and lacks the dictionary of stringent block diagonalization structural constraint and go out coded by making is weak, the not strong problem of distinction.

Description

A kind of dictionary learning method of co-ordinative construction rarefaction representation and low-dimensional insertion

Technical field

The invention belongs to digital image processing techniques fields, and in particular to a kind of co-ordinative construction rarefaction representation and low-dimensional are embedding The dictionary learning method entered.

Background technology

The core concept of rarefaction representation is based primarily upon following objective fact：Many signals in nature can use a mistake Only a few dictionary item in saturation dictionary carrys out linear combination and indicates or encode.It is the most key in rarefaction representation research to ask Topic is the construction for having strong representation ability dictionary.Currently, rarefaction representation technology is widely used in many application fields, Such as image classification, recognition of face and human action identification.

Dictionary learning is dedicated to learning from training sample to optimal dictionary carrying out more given signal or feature It indicates or encodes well.For the Classification and Identification based on rarefaction representation, ideal sparse matrix of the training sample under dictionary Should be that block is diagonal, i.e., the coefficient on similar sub- dictionary of the sample where it is non-zero, and is on the sub- dictionary of foreign peoples Number is zero.Such structuring coefficient matrix will be with best class discrimination ability.In addition, the higher-dimension due to training data is special Property and the deficiency of training sample make dictionary learning method still suffer from great challenge.Therefore, people naturally enough exist Data Dimensionality Reduction processing is introduced during dictionary learning.But very unfortunately, these dictionary learning methods are often by Data Dimensionality Reduction It is individually studied as two independent processing steps with dictionary learning, i.e., dimension-reduction treatment is carried out to training data first, then Dictionary learning is carried out in low-dimensional feature space.This serial cascade system likely makes that the low-dimensional learnt in advance is thrown Shadow can not keep and be promoted well the potential sparsity structure of data, to be unfavorable for having the dictionary learning of strong identification.

Invention content

The object of the present invention is to provide the dictionary learning methods of a kind of co-ordinative construction rarefaction representation and low-dimensional insertion, solve Due to the higher-dimension characteristic of training sample data and lack stringent block diagonalization in dictionary learning method existing in the prior art The dictionary of structural constraint and make it is coded go out indicate coefficient class discriminating power is weak, distinction is not strong problem.

The technical solution adopted in the present invention is a kind of dictionary learning side of co-ordinative construction rarefaction representation and low-dimensional insertion Method is specifically implemented according to the following steps：

Step 1, the characteristic data set for reading in training sampleWherein C is classification number, and n is The dimension of feature,For the N of the i-th class_iThe character subset that a sample is constituted, i=1,2 ..., C,

Step 2, using alternating direction Lagrange multiplier method solving-optimizing problemsIt is encoded Dictionary D, dimensionality reduction projection matrix P and code coefficient matrix X；

Step 3 reads in test sample characteristicIt is by encoder dictionary D and dimensionality reduction projection matrix P and following by solving Optimization problem obtains test sampleRarefaction representation coefficient

Step 4, the rarefaction representation coefficient for calculating test sampleIn all kinds of small pin for the case dictionary D_iOn reconstructed error e_i：WhereinTo correspond in i-th of sub- dictionary D_iOn code coefficient D=[D₁,D₂,…,D_C], i=1, 2,…,C；

Step 5, according to minimal reconstruction error criterion to test sampleClassify, category labelFor：

The features of the present invention also characterized in that

In step 2

S.t.X=diag (X₁₁,X₂₂,…,X_CC),PP^T=I,

Wherein, parameter lambda₁,λ₂,λ₃＞ 0；For low dimension projective transformation matrix, m ＜ ＜ n；Training sample Y is in dictionaryUnder expression coefficient matrix be X：

For jth class training sample Y_jIn the sub- dictionary of the i-th classOn expression coefficient, i, j ∈ 1, 2,…,C}；

X is enabled to meet following block diagonalization structural constraint：

Step 2 is specifically implemented according to the following steps：

Step 2.1 introduces auxiliary variable collectionAnd enable Z_ii=X_ii, optimization problemConversion For：

S.t.X=diag (X₁₁,X₂₂,…,X_CC),PP^T=I,

Z_ii=X_ii, i=1,2 ..., C,

The Lagrange function expressions of its augmentation are：

s.t.PP^T=I,

Wherein, F_iiFor Lagrange multipliers, γ ＞ 0 are punishment parameter；

Step 2.2, alternating iteration update matrix P, D, X and Z_ii, until P, D, X and Z_iiConvergence.

Step 2.2 is specifically implemented according to the following steps：

Step 2.2.1, fixed other variables, update matrix X by following formula：

Wherein, sgn (x) is defined as：

Step 2.2.2, fixed other variables, update matrix Z by following formula_ii：

Wherein, U Λ V^TFor matrixSingular value decomposition,For soft-threshold operator,It is fixed Justice is as follows：

Step 2.2.3, fixed other variables, update matrix D by following formula：

After having been updated by column by above formula to dictionary D, that is, obtain the value after entire dictionary updating：

Step 2.2.4, fixed other variables, update matrix P by following formula：

First, to matrix (φ (P^(t-1))-λ₁S Eigenvalues Decomposition) is carried out：

[U, Λ, V]=EVD (φ (P^(t-1))-λ₁S),

Wherein, φ (P)=(Y-P^TΔ)(Y-P^TΔ)^T, Δ=DX, S=YY^T, Λ is matrix (φ (P^(t-1))-λ₁S spy) The diagonal matrix that value indicative is constituted is matrix (φ (P to the update of projection matrix P^(t-1))-λ₁S preceding m characteristic value institute) is right The feature vector U (1 answered:m,:), i.e.,：

P^(t)=U (1:m,:)；

Step 2.2.5, multiplier F is updated by following formula_iiAnd parameter γ：

γ^(t)=min { ρ γ^(t-1),γ^max}。

Wherein, ρ=1.1, γ^max=10⁶,

Encoder dictionary D and dimensionality reduction projection matrix P are obtained after updating above.

The invention has the advantages that the dictionary learning method of a kind of co-ordinative construction rarefaction representation and low-dimensional insertion, with Eliminate the correlation between class has the more preferable code coefficient for differentiating performance to obtain；Enhance sparse table in class by low-rank constraint Show the coherence between coefficient, with the birdsing of the same feather flock together property for indicating coefficient being further lifted on class small pin for the case dictionary；Meanwhile by projecting square The expression ability of battle array learnt to enhance dictionary and the robustness for improving sparse representation model in turn.

Specific implementation mode

The present invention is described in detail With reference to embodiment.

The dictionary learning method of a kind of co-ordinative construction rarefaction representation of the present invention and low-dimensional insertion, dictionary construction are thrown with dimensionality reduction Shadow matrix parallel alternately, passes through the forced rarefaction representation coefficient matrix with block diagonalization structure in low dimension projective space At the same time incoherence between class to enhance dictionary keeps word using the low-rank of the expression coefficient on class small pin for the case dictionary Correlation in the class of allusion quotation.Dictionary is constructed can promote mutually with projection study, fully to keep the sparsity structure of data, to compile Code goes out the code coefficient with more classification judgement index, is specifically implemented according to the following steps：

Step 1, the characteristic data set for reading in training sampleWherein C is classification number, and n is The dimension of feature,For the N of the i-th class_iThe character subset that a sample is constituted, i=1,2 ..., C,

Step 2, using alternating direction Lagrange multiplier method solving-optimizing problemsIt is encoded Dictionary D, dimensionality reduction projection matrix P and code coefficient matrix X, wherein

S.t.X=diag (X₁₁,X₂₂,…,X_CC),PP^T=I,

Wherein, parameter lambda₁,λ₂,λ₃＞ 0；For low dimension projective transformation matrix, m ＜ ＜ n；Training sample Y is in dictionaryUnder expression coefficient matrix be X：

For jth class training sample Y_jIn the sub- dictionary of the i-th classOn expression coefficient, i, j ∈ 1, 2,…,C}；

X is enabled to meet following block diagonalization structural constraint：

Step 2 is specifically implemented according to the following steps：

Step 2.1 introduces auxiliary variable collectionAnd enable Z_ii=X_ii, optimization problemConversion For：

S.t.X=diag (X₁₁,X₂₂,…,X_CC),PP^T=I,

Z_ii=X_ii, i=1,2 ..., C,

The Lagrange function expressions of its augmentation are：

s.t.PP^T=I,

Wherein, F_iiFor Lagrange multipliers, γ ＞ 0 are punishment parameter；

Step 2.2, alternating iteration update matrix P, D, X and Z_ii, until P, D, X and Z_iiConvergence, specifically according to the following steps Implement：

Step 2.2.1, fixed other variables, update matrix X by following formula：

Wherein, sgn (x) is defined as：

Step 2.2.2, fixed other variables, update matrix Z by following formula_ii：

Wherein, U Λ V^TFor matrixSingular value decomposition,For soft-threshold operator,It is fixed Justice is as follows：

Step 2.2.3, fixed other variables, update matrix D by following formula：

After having been updated by column by above formula to dictionary D, that is, obtain the value after entire dictionary updating：

Step 2.2.4, fixed other variables, update matrix P by following formula：

First, to matrix (φ (P^(t-1))-λ₁S Eigenvalues Decomposition) is carried out：

[U, Λ, V]=EVD (φ (P^(t-1))-λ₁S),

Wherein, φ (P)=(Y-P^TΔ)(Y-P^TΔ)^T, Δ=DX, S=YY^T, Λ is matrix (φ (P^(t-1))-λ₁S spy) The diagonal matrix that value indicative is constituted is matrix (φ (P to the update of projection matrix P^(t-1))-λ₁S preceding m characteristic value institute) is right The feature vector U (1 answered:m,:), i.e.,：

P^(t)=U (1:m,:)；

Step 2.2.5, multiplier F is updated by following formula_iiAnd parameter γ：

γ^(t)=min { ρ γ^(t-1),γ^max}。

Wherein, ρ=1.1, γ^max=10⁶,

Encoder dictionary D and dimensionality reduction projection matrix P are obtained after updating above；

Step 3 reads in test sample characteristicIt is by encoder dictionary D and dimensionality reduction projection matrix P and following by solving Optimization problem obtains test sampleRarefaction representation coefficient

Step 4, the rarefaction representation coefficient for calculating test sampleIn all kinds of small pin for the case dictionary D_iOn reconstructed error e_i：WhereinTo correspond in i-th of sub- dictionary D_iOn code coefficient D=[D₁,D₂,…,D_C], i=1, 2,…,C；

Step 5, according to minimal reconstruction error criterion to test sampleClassify, category labelFor：

The dictionary learning method of a kind of co-ordinative construction rarefaction representation of the present invention and low-dimensional insertion, in dictionary building process In take full advantage of category prior information in lower dimensional space come the sparse coding for learning sample carrying out that there is block structure, with So that the coefficient after coding has stronger expression ability and class discrimination ability, the accuracy rate of classification problem is significantly improved.

Claims (4)

1. the dictionary learning method of a kind of co-ordinative construction rarefaction representation and low-dimensional insertion, which is characterized in that specifically according to following Step is implemented：

Step 1, the characteristic data set for reading in training sampleWherein C is classification number, and n is characterized Dimension,For the N of the i-th class_iThe character subset that a sample is constituted, i=1,2 ..., C,

Step 2, using alternating direction Lagrange multiplier method solving-optimizing problemsObtain encoder dictionary D, dimensionality reduction projection matrix P and code coefficient matrix X；

Step 3 reads in test sample characteristicBy encoder dictionary D and dimensionality reduction projection matrix P and by solving following optimization Problem obtains test sampleRarefaction representation coefficient

Step 4, the rarefaction representation coefficient for calculating test sampleIn all kinds of small pin for the case dictionary D_iOn reconstructed error e_i：WhereinTo correspond in i-th of sub- dictionary D_iOn code coefficient D=[D₁,D₂,…,D_C], i=1, 2,…,C；

Step 5, according to minimal reconstruction error criterion to test sampleClassify, category labelFor：

2. the dictionary learning method of a kind of co-ordinative construction rarefaction representation according to claim 1 and low-dimensional insertion, special Sign is, in the step 2

S.t.X=diag (X₁₁,X₂₂,…,X_CC),PP^T=I,

Wherein, parameter lambda₁,λ₂,λ₃＞ 0；For low dimension projective transformation matrix, m ＜ ＜ n；Training sample

This Y is in dictionaryUnder expression coefficient matrix be X：

For jth class training sample Y_jIn the sub- dictionary of the i-th classOn expression coefficient, i, j ∈ 1,2 ..., C}；

X is enabled to meet following block diagonalization structural constraint：

3. the dictionary learning method of a kind of co-ordinative construction rarefaction representation according to claim 2 and low-dimensional insertion, special Sign is that the step 2 is specifically implemented according to the following steps：

Step 2.1 introduces auxiliary variable collectionAnd enable Z_ii=X_ii, optimization problemIt is converted into：

S.t.X=diag (X₁₁,X₂₂,…,X_CC),PP^T=I,

Z_ii=X_ii, the Lagrange function expressions of i=1,2 ..., C, augmentation are：

s.t.PP^T=I,

Wherein, F_iiFor Lagrange multipliers, γ ＞ 0 are punishment parameter；

Step 2.2, alternating iteration update matrix P, D, X and Z_ii, until P, D, X and Z_iiConvergence.

4. the dictionary learning method of a kind of co-ordinative construction rarefaction representation according to claim 3 and low-dimensional insertion, special Sign is that the step 2.2 is specifically implemented according to the following steps：

Step 2.2.1, fixed other variables, update matrix X by following formula：

Wherein, sgn (x) is defined as：

Step 2.2.2, fixed other variables, update matrix Z by following formula_ii：

Wherein, U Λ V^TFor matrixSingular value decomposition,For soft-threshold operator,Definition is such as Under：

Step 2.2.3, fixed other variables, update matrix D by following formula：

After having been updated by column by above formula to dictionary D, that is, obtain the value after entire dictionary updating：

Step 2.2.4, fixed other variables, update matrix P by following formula：

First, to matrix (φ (P^(t-1))-λ₁S Eigenvalues Decomposition) is carried out：

[U, Λ, V]=EVD (φ (P^(t-1))-λ₁S),

Wherein, φ (P)=(Y-P^TΔ)(Y-P^TΔ)^T, Δ=DX, S=YY^T, Λ is matrix (φ (P^(t-1))-λ₁S characteristic value) The diagonal matrix constituted is matrix (φ (P to the update of projection matrix P^(t-1))-λ₁S corresponding to preceding m characteristic value) Feature vector U (1:m,:), i.e.,：

P^(t)=U (1:m,:)；

Step 2.2.5, multiplier F is updated by following formula_iiAnd parameter γ：

γ^(t)=min { ρ γ^(t-1),γ^max}。

Wherein, ρ=1.1, γ^max=10⁶,

Encoder dictionary D and dimensionality reduction projection matrix P are obtained after updating above.