CN103093248A - Semi-supervised image classification method based on multi-view study - Google Patents

Abstract

The invention discloses a semi-supervised image classification method based on multi-view study. The semi-supervised image classification method based on the multi-view study is used for solving the classification problem of multi-view image data with part labels. The image classification method of the semi-supervised image classification method based on the multi-view study can unite study image multi-view feature unify potential factor representation and a linear classifier with discrimination property under unify potential factor space according to image multi-view feature representation and classification of part images, wherein the image multi-view feature representation is input by users . Therefore, un-labeling images are classified efficiently.

Description

A kind of semi-supervision image classification method based on various visual angles study

Technical field

The present invention relates to various visual angles study, latent factor study and semi-supervised learning field, particularly a kind of semi-supervision image classification method based on various visual angles study.

Background technology

In the real world images classification problem, view data can be from such as color, texture, and the different visual angles such as shape are described.These different characteristics of image have disclosed the different attribute of the image of studying from different visual angles.Research to this type of various visual angles description object is referred to as various visual angles study in academia.Reasonably explore the complementary information and the relation that contain in the various visual angles data and can greatly promote results of learning.In general the research of various visual angles study has two main directions.First direction is based on the method that (co-training) practiced in mutual glossing, and its basic thought is training classifier in two visual angles respectively, gives the other side visual angle sorter the classification results of the tool confidence of each sorter as new training sample.There are two irrational places in this mode, and the one, different visual angles is not treated with a certain discrimination, the 2nd, each is taken turns iteration and all must again train, and computation burden is huge.Second direction is based on unified latent factor study, and most typical example is exactly canonical correlation analysis (Canonical Correlation Analysis, CCA).The present invention is based on the latter's thought.

The study of most latent factor is unsupervised learning, therefore the differentiation power of the latent factor that arrives of study a little less than.In actual conditions, fully the data of mark are very expensive, and obtain very difficult.And the data of part mark often can be got easily, and are especially more prevalent in internet, applications, in the situation that user tag increases rapidly.Incorporating the part labeled data carries out latent factor study and can greatly strengthen the differentiation power of latent factor undoubtedly.

Summary of the invention

The present invention proposes a kind of new semi-supervision image classification method based on various visual angles study, in order to solving under section's contingency table condition, the Images Classification problem of various visual angles character representation.

The semi-supervision image classification method based on various visual angles study that the present invention proposes, it comprises:

Step 1: obtain and comprise the sample data collection that marks classification and do not mark the image pattern data of classification, described sample data collection is made of the different visual angles sample data of various visual angles character representation;

Step 2: the combination learning of unifying latent factor and linear classifier by various visual angles obtains corresponding to the unified latent factor of described sample data collection with at the linear classifier of unifying under the latent factor space;

Step 3: obtain according to the unified latent factor that obtains and described linear classifier the mark classification that described sample data is concentrated the image pattern data that do not mark classification, and then the image pattern data that described sample data is concentrated are classified.

The invention allows for a kind of semi-supervision image classification device based on various visual angles, it comprises:

The sample acquisition device is used for obtaining comprising the sample data collection that marks classification and do not mark the image pattern data of classification that described sample data collection is made of the different visual angles sample data of various visual angles character representation;

The unified latent factor of various visual angles and linear classifier combination learning module, its combination learning acquisition of unifying latent factor and linear classifier by various visual angles is corresponding to the unified latent factor of described sample data collection with at the linear classifier of unifying under the latent factor space;

The Images Classification operational module, it obtains according to the unified latent factor that obtains and described linear classifier the mark classification that described sample data is concentrated the image pattern data that do not mark classification, and then the image pattern data that described sample data is concentrated are classified.

The present invention adopts the mode of semi-supervised learning.Semi-supervised learning is the method for using simultaneously unlabeled data and labeled data to learn, can greatly promote results of learning.In addition, Non-negative Matrix Factorization is a kind of effective latent factor learning method.The nonnegativity of Non-negative Matrix Factorization requires to cause a kind of expression based on the part.This Data Representation mode is the human brain process of cognition of coincideing, and therefore has good effect under a lot of practical application conditions.The present invention also adopts the Non-negative Matrix Factorization technology as basic latent factor learning method, and it has been expanded under the various visual angles condition.

Description of drawings

Fig. 1 is the system chart based on the semi-supervision image classification method of learning from various visual angles proposed by the invention.

Fig. 2 is the structured flowchart that various visual angles of the present invention are unified latent factor and linear classifier combination learning.

Embodiment

The embodiment of the present invention provides a kind of image classification method.In the real world images classification task, image can be described by the feature of various visual angles, section's contingency table of image holds facile often, the present invention utilizes the various visual angles character representation combination learning of section's contingency table and image to unify latent factor and the linear classifier under unified latent factor space, unified latent factor can get through linear sorter operation the confidence value that sample belongs to a different category, judge sample class according to confidence value size, thereby reach the purpose of Images Classification.

For making the purpose, technical solutions and advantages of the present invention clearer, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.As shown in Figure 1, after acquisition unit contingency table and image various visual angles character representation, method disclosed by the invention comprises following two steps: 1) the unified latent factor of various visual angles and linear classifier combination learning, 2) the Images Classification operation.

The user will comprise the multi-view image data set { X of N sample ¹, X ²... X ^PAnd class mark matrix Y be input to described various visual angles and unify latent factor and linear classifier combination learning module.Wherein,

The data matrix that p visual angle characteristic of image set presents, M ^pIt is the dimension of p visual angle characteristic.The sample data that view data is concentrated belongs to C classification, and the class mark of a front R sample is known.The mark matrix

In order to characterizing this partial supervised information, when r sample data belongs to the c class, the element ycr in Y is 1, otherwise is 0.The unified latent factor of various visual angles and the output of linear classifier combination learning module do not mark the unified latent factor character representation V of image pattern _ul, and the linear classifier W under unified latent factor space.V _ulFurther be input to the Images Classification operational module with W, by not marking image pattern in different classes of confidence value, output does not at last mark the class mark L of image pattern _ul

The various visual angles that the embodiment of the present invention provides are unified regression model and the adaptive various visual angles weight allocation strategy that latent factor and linear classifier combination learning system have utilized collaborative Non-negative Matrix Factorization model from various visual angles, considered 2,1 model regular terms.

The collaborative Non-negative Matrix Factorization model of described various visual angles is as shown in Fig. 2 left-half.

It is the basis matrix of p visual angle sample data.

Be the latent factor matrix that share at all P visual angle, K is the dimension in unified latent factor space, and concrete value can be specified by user experience.

Indicate respectively front R the sample that is marked in V and the latent factor matrix that does not mark all the other samples.The collaborative Non-negative Matrix Factorization model of various visual angles is learnt basis matrix U simultaneously at the p visual angle ^pWith potential unified factor V, hope can be as far as possible reconstruct p visual angle sample data matrix X well ^pThe objective function of the collaborative Non-negative Matrix Factorization model of various visual angles is as follows:

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{{\mathrm{\π}}^p\left|\right|X^p-U^{p}V\left|\right|}_F^2$

|| || _FThe F norm,

The basis matrix set at P visual angle, π ^pIt is the weight at p visual angle.

The regression model of described 2,1 model regular terms is as shown in Fig. 2 right half part. Be a linear classifier under unified latent factor space.To described latent factor Classification of Matrix corresponding to classification that do not mark, can obtain the mark matrix Y of described sample data by described linear classifier.The objective function of the regression model of 2,1 model regular terms is as follows:

$\min {\left|\right|W^T{V}_l-Y\left|\right|}_F^2+\mathrm{\γ}{\left|\right|W\left|\right|}_{\mathrm{2,1}}$

s.t.V _l≥0

Wherein, γ is the weight parameter of 2,1 models, and 2,1 models are defined as follows:

${\left|\right|W\left|\right|}_{\mathrm{2,1}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\sqrt{\underset{c=1}{\overset{C}{\mathrm{\Σ}}}}{\mathrm{\ω}}_{\mathrm{kc}}^2$

Wherein, ω _kcBe the element in W, 2,1 models of W are first asked 2 models to every delegation, then row are asked 1 model, reach the sparse effect of row, thus realization character selection, match mark matrix Y better.

Described adaptive various visual angles weight allocation strategy effectively distributes the weight of various visual angles take the reconstructed error at visual angle as foundation.The different visual angles data suffer noise pollution and information loss in various degree, thus different visual angles to contain information quality uneven.Higher weight allocation should be enjoyed in high-quality data visual angle.The objective function of adaptive various visual angles weight allocation strategy is as follows:

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{c}^p{\mathrm{\π}}^p+\mathrm{\λ}{\left|\right|\mathrm{\Π}\left|\right|}^2$

$s.t.\mathrm{\Π}\≥0,\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p=1$

Wherein

It is the reconstructed error of p visual angle sample data matrix., ∏=(π ¹, π ²... π ^P) be the weight set at P visual angle.Parameter lambda is controlled the flatness of parameter ∏, and larger λ causes the visual angle weight more level and smooth, and namely each visual angle characteristic plays a role more fifty-fifty.

Consider above three parts, it is as follows that the various visual angles that the embodiment of the present invention provides are unified the combined optimization function of latent factor and linear classifier combination learning module:

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p{\left|\right|X^p-U^{p}V\left|\right|}_F^2+\mathrm{\λ}{\left|\right|\mathrm{\Π}\left|\right|}^2+\mathrm{\β}({\left|\right|W^T{V}_l-Y\left|\right|}_F^2+\mathrm{\γ}{\left|\right|W\left|\right|}_{\mathrm{2,1}})$

Weight between the parameter beta balance module.

Introduce for convenience optimized algorithm of the present invention, the objective definition function is as follows:

Optimization problem of the present invention can be optimized subproblems by following 4 of iterative: 1) fixing V minimizes

Fixedly V, minimize Fixing

And ∏, minimize With 4) fixing And V, minimize

Namely take turns iteration one and find the solution successively above-mentioned 4 in upgrading and optimize subproblems, last round of iteration is upgraded the worthwhile known number of doing that upgraded of iteration of the value that obtains or epicycle, find the solution each optimization subproblem.

The update scheme of described optimization subproblem 1 is as follows:

Consider that W is not had the nonnegativity requirement, we are right

Differentiate,

The E here is a diagonal matrix, and diagonal element

w _kK row element for W.Order

Obtain

The more new formula of W is as follows:

$W={(V_l{V}_l^T+\mathrm{\γE})}^{-1}{V}_l{Y}^T$

Order W=A ^-1V _lY ^T, the value that before the equation right side is, iteration was upgraded is the value of this iteration renewal on the left of equation.

The update scheme of described optimization subproblem 2 is as follows:

The basis matrix set

In basis matrix be full symmetric, for the purpose of general, below the basis matrix renewal at p visual angle done be described in detail.U ^pHas non-negative restriction, order

Be Lagrange multiplier, in order to retrain U ^pIn element

Wherein, m is less than or equal to M ^pPositive integer.Lagrangian function

As follows:

Tr (.) is the operation of Matrix Calculating mark, i.e. matrix diagonal element sum.

Right

Differentiate gets:

By the Kuhn-Tucker condition

Obtain following relational expression:

$-{\left(X^p{V}^T\right)}_{\mathrm{mk}}{u}_{\mathrm{mk}}^p+{\left(U^{p}V{V}^T\right)}_{\mathrm{mk}}{u}_{\mathrm{mk}}^p=0$

And then can get U ^pUpdate rule:

${\left(u_{\mathrm{mk}}^p\right)}^{,}\←u_{\mathrm{mk}}^p\frac{{\left(X^p{V}^T\right)}_{\mathrm{mk}}}{{\left(U^{p}V{V}^T\right)}_{\mathrm{mk}}}$

Wherein, ← expression assign operation, the value that before ← right side is, iteration was upgraded,

Upgrade the value that obtains for the epicycle iteration.

The update scheme of described optimization subproblem 3 is as follows:

V comprises V _ul, V _lTwo parts are for convenience of introducing, X ^pAlso be divided into accordingly With

Order

Be Lagrange multiplier, in order to retrain the element u in V _kn〉=0, and Φ=[Φ _l, Φ _ul]=[φ _kn].Lagrangian function

As follows

With W=β A ¹V _lY ^TThe substitution formula, and notice that A is a symmetrical matrix,

F is a constant.

Respectively to V _ul, V L differentiate (for simplicity, supposing that herein A is constant matrices)

By Kuhn-Tucker condition φ _Knukn=0, obtain following relational expression

$\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p({\left(U^p\right)}^T{(U^p{V}_l-X_l^p)}_{\mathrm{kn}}{\left(u_l\right)}_{\mathrm{kn}}-\mathrm{\β}{\left(A^{-1}{V}_l{Y}^{T}Y\right)}_{\mathrm{kn}}{\left(u_l\right)}_{\mathrm{kn}}$

$\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p({\left(U^p\right)}^T{(U^p{V}_{\mathrm{ul}}-X_{\mathrm{ul}}^p)}_{\mathrm{kn}}{\left(u_{\mathrm{ul}}\right)}_{\mathrm{kn}}=0$

And then can get V _ul, V _lUpdate rule

${\left(u_l\right)}_{\mathrm{kn}}^{,}\←{\left(u_l\right)}_{\mathrm{kn}}\sqrt{\frac{{({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{X}_l^p+{\mathrm{\βB}}^{+})}_{\mathrm{kn}}}{{({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{U}^p{V}_l+{\mathrm{\βB}}^{-})}_{\mathrm{kn}}}}$

${\left(u_{\mathrm{ul}}\right)}_{\mathrm{kn}}^{,}\←{\left(u_{\mathrm{ul}}\right)}_{\mathrm{kn}}\sqrt{\frac{{\left({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{X}_{\mathrm{ul}}^p\right)}_{\mathrm{kn}}}{{\left({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{U}^p{V}_{\mathrm{ul}}\right)}_{\mathrm{kn}}}}$

Here B=A ^-1V _lY ^TY, and B ⁺=(| B|+B)/2, B ^-=(| B|-B)/2.(u _l) _kn(u _ul) _knBe V _lAnd V _ulIn element, the value upgraded of iteration before ← right side is,

With Upgrade the value that obtains for the epicycle iteration.

The update scheme of described optimization subproblem 4 is as follows:

When

Fix with V,

Deteriorate to optimization problem as protruding in the next one,

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{c}^p{\mathrm{\π}}^p+\mathrm{\λ}{\left|\right|\mathrm{\Π}\left|\right|}^2$

$s.t.\mathrm{\Π}\≥0,\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p=1$

Here

It is the reconstructed error of p perspective data matrix.So protruding optimization problem can solve by the kit of maturation, for example CVX kit (http://cvxr.com/cvx/).

The present invention passes through above 4 the extremely convergences of optimization subproblems of loop iteration successively, thereby obtains the final optimization pass result.Every iteration of taking turns is take last round of iteration result as initial value, and the initial value of first round iteration is chosen at random.V _ulBe the unified latent factor character representation of final unmarked sample, the linear classifier of W for have differentiation power under unified latent factor space.

The Images Classification operational module that the embodiment of the present invention provides receives the unified latent factor feature V of the unmarked image pattern of the unified latent factor of various visual angles and the output of linear classifier combination learning module _ulWith the linear classifier W under unified latent factor space, can obtain not marking the inhomogeneity mark of the image pattern data of classification according to following formula:

Y _ul＝W ^TV _ul

After in the expression sample data, (NR) individual image pattern that do not mark is at the confidence value matrix of C classification.Seek Y _ulEvery row maximal value place line number is the classification of this row representative sample, thereby obtains not mark the classification results L of image pattern _ul

Above-described specific embodiment; purpose of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the above is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (10)

1. semi-supervision image classification method based on various visual angles study, it comprises:

Step 1: obtain and comprise the sample data collection that marks classification and do not mark the image pattern data of classification, described sample data collection is made of the different visual angles sample data of various visual angles character representation;

Step 2: the combination learning of unifying latent factor and linear classifier by various visual angles obtains corresponding to the unified latent factor of described sample data collection with at the linear classifier of unifying under the latent factor space;

Step 3: obtain according to the unified latent factor that obtains and described linear classifier the mark classification that described sample data is concentrated the image pattern data that do not mark classification, and then the image pattern data that described sample data is concentrated are classified.

2. the method for claim 1, it is characterized in that, the combination learning of the unified latent factor of various visual angles described in step 2 and linear classifier is completed based on regression model and the adaptive various visual angles weight allocation strategy of the collaborative Non-negative Matrix Factorization model of various visual angles, consideration 2,1 model regular terms; The collaborative Non-negative Matrix Factorization model of wherein said various visual angles is shared the hypothesis of latent factor based on the different visual angles sample data, described different visual angles sample data is carried out non-heavy burden structure, the final reconstructed error that obtains minimum; Described consideration 2, the regression model of 1 model regular terms is used for by described sample data being concentrated the image pattern data that marked classification minimize the restriction of predicated error under described unified latent factor space, build sorter, and according to described sorter under unified latent factor space to not marking the sample prediction of classifying; Described adaptive various visual angles weight allocation strategy take the reconstructed error of different visual angles sample data as foundation, is that the various visual angles sample data is distributed different weights.

3. method as claimed in claim 2, is characterized in that, described various visual angles are worked in coordination with the following expression of Non-negative Matrix Factorization model:

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p{\left|\right|X^p-U^{p}V\left|\right|}_F^2$

Wherein, || || _FBe the F norm, described sample data collection is { X ¹, X ²... X ^P, wherein P visual angle sample data matrix,

Be that described sample data is concentrated basis matrix set corresponding to different visual angles sample data matrix, π p is the weight of p visual angle sample data matrix;

Be the unified latent factor matrix that described sample data concentrates different visual angles sample data matrix to be shared, P is the number of different visual angles, and N is the sample data number, M ^pBe the dimension of p visual angle characteristic, R represents to mark the number of classification sample, and K is the dimension in described latent factor space.

4. method as claimed in claim 2, is characterized in that, the following expression of regression model of described consideration 2,1 model regular terms:

$\begin{array}{c}\min {\left|\right|W^T{V}_l-Y\left|\right|}_F^2+\mathrm{\γ}{\left|\right|W\left|\right|}_{\mathrm{2,1}}\\ s.t.V_l\≥0\end{array}$

${\left|\right|W\left|\right|}_{\mathrm{2,1}}=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\sqrt{\underset{c=1}{\overset{C}{\mathrm{\Σ}}}{\mathrm{\ω}}_{\mathrm{kc}}^2}$

Wherein, γ is weight parameter,

Be the linear classifier under unified latent factor space, ω _kcBe the element in W;

Be the mark classification matrix of sample data,

Expression has marked the latent factor matrix corresponding to sample data of classification, and K is the dimension in described latent factor space, and C is the sample class number.

5. method as claimed in claim 2, is characterized in that, the following function representation of described adaptive various visual angles weight allocation strategy:

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{c}^p{\mathrm{\π}}^p+\mathrm{\λ}{\left|\right|\mathrm{\Π}\left|\right|}^2$

$s.t.\mathrm{\Π}\≥0,\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p=1$

Wherein, The reconstructed error of p visual angle sample data matrix of its expression; Described sample data collection is { X ¹, X ²... X ^P, wherein

Be p visual angle sample data matrix, P is the number of different visual angles,

That described sample data is concentrated basis matrix set corresponding to different visual angles sample data matrix, ∏=(π ¹, π ²... π ^P) be the weight set of different visual angles sample data matrix; λ is for the parameter of controlling the ∏ flatness.

6. method as claimed in claim 2, it is characterized in that, the described described various visual angles that realize based on the collaborative Non-negative Matrix Factorization model of various visual angles, the regression model of considering 2,1 model regular terms and adaptive various visual angles weight allocation strategy are unified the following function representation of combination learning of latent factor and linear classifier:

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p{\left|\right|X^p-U^{p}V\left|\right|}_F^2+\mathrm{\λ}{\left|\right|\mathrm{\Π}\left|\right|}^2+\mathrm{\β}({\left|\right|W^T{V}_l-Y\left|\right|}_F^2+\mathrm{\γ}{\left|\right|W\left|\right|}_{\mathrm{2,1}})$

Wherein, β is predetermined balance parameters; || || _FIt is the F norm; Described sample data collection is { X ¹, X ²... X ^P, wherein

Be p visual angle sample data matrix, P is the number of different visual angles;

That described sample data is concentrated basis matrix set corresponding to different visual angles sample data matrix; ∏=(π ¹, π ²... π ^P) be the weight set of different visual angles sample data matrix, π ^pIt is the weight of p visual angle sample data matrix;

Be the unified latent factor matrix that described sample data concentrates different visual angles sample data matrix to be shared, its front R row consist of

Expression has marked the latent factor matrix corresponding to sample data of classification, and rear N-R row consist of

Expression does not mark the latent factor matrix corresponding to sample data of classification;

Be the linear classifier under unified latent factor space, ω _kcBe the element in W;

Mark classification matrix for sample data; N is the sample data number, M ^pBe the dimension of p visual angle characteristic, R represents to mark the number of classification sample, and K is the dimension in described latent factor space, and C is the sample class number, and λ is that γ is weight parameter for the parameter of controlling the ∏ flatness.

By final described unified latent factor V and the linear classifier W under unified latent factor space of obtaining of the above-mentioned combination learning function of iterative.

7. method as claimed in claim 6, is characterized in that, described iterative combination learning function is divided into four optimizes subproblems: 1) fixing V minimizes W, 2) fixing V, minimize

3) fixing

And ∏, minimize V and 4) fixing

And V, minimize ∏;

Upgrade above-mentioned four by iteration successively and optimize subproblems, finally obtain described unified latent factor V and the linear classifier W under unified latent factor space.

8. method as claimed in claim 6, is characterized in that,

The 1st) the following expression of individual optimization subproblem:

W＝A ^-1V _lY ^T

Wherein,

E is diagonal matrix, and diagonal element

w _kBe the k row element of W, be before the value upgraded of iteration;

The 2nd) the following expression of individual optimization subproblem:

${\left(u_{\mathrm{mk}}^p\right)}^{,}\←u_{\mathrm{mk}}^p\frac{{\left(X^p{V}^T\right)}_{\mathrm{mk}}}{{\left(U^{p}V{V}^T\right)}_{\mathrm{mk}}}$

Wherein,

Be basis matrix U ^pIn element, be before the value upgraded of iteration, and

Upgrade the value that obtains for the epicycle iteration;

The 3rd) the following expression of individual optimization subproblem:

${\left(u_l\right)}_{\mathrm{kn}}^{,}\←{\left(u_l\right)}_{\mathrm{kn}}\sqrt{\frac{{({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{X}_l^p+{\mathrm{\βB}}^{+})}_{\mathrm{kn}}}{{({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{U}^p{V}_l+{\mathrm{\βB}}^{-})}_{\mathrm{kn}}}}$

${\left(u_{\mathrm{ul}}\right)}_{\mathrm{kn}}^{,}\←{\left(u_{\mathrm{ul}}\right)}_{\mathrm{kn}}\sqrt{\frac{{\left({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{X}_{\mathrm{ul}}^p\right)}_{\mathrm{kn}}}{{\left({\mathrm{\Σ}}_{p=1}^P{\mathrm{\π}}^p{\left(U^p\right)}^T{U}^p{V}_{\mathrm{ul}}\right)}_{\mathrm{kn}}}}$

Wherein, B=A ^-1V _lY ^TY, and B ⁺=(| B|+B)/2, B ^-=(| B|-B)/2; (u _l) _kn(u _ul) _knBe respectively V _lAnd V _ulIn element, be before the value upgraded of iteration, and With Upgrade the value that obtains for the epicycle iteration;

The 4th) the following expression of individual optimization subproblem:

$\min \underset{p=1}{\overset{P}{\mathrm{\Σ}}}{c}^p{\mathrm{\π}}^p+\mathrm{\λ}{\left|\right|\mathrm{\Π}\left|\right|}^2$

$s.t.\mathrm{\Π}\≥0,\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\π}}^p=1$

Wherein,

The reconstructed error of its expression p visual angle sample data matrix, following formula is found the solution by protruding optimization method.

9. the method for claim 1, is characterized in that, acquisition does not mark the classification mark matrix of the sample data of classification according to following formula:

Y _ul＝W ^TV _ul

Wherein,

Expression does not mark sample data classification mark matrix, and C is total classification number, and N is the sample data number, and R represents to mark the sample data number of classification, V _ulFor not marking unified latent factor corresponding to classification sample data, W is the linear classifier under unified latent factor space.

One kind based on various visual angles the semi-supervision image classification device, it comprises:

The sample acquisition device is used for obtaining comprising the sample data collection that marks classification and do not mark the image pattern data of classification that described sample data collection is made of the different visual angles sample data of various visual angles character representation;

The unified latent factor of various visual angles and linear classifier combination learning module, its combination learning acquisition of unifying latent factor and linear classifier by various visual angles is corresponding to the unified latent factor of described sample data collection with at the linear classifier of unifying under the latent factor space;

The Images Classification operational module, it obtains according to the unified latent factor that obtains and described linear classifier the mark classification that described sample data is concentrated the image pattern data that do not mark classification, and then the image pattern data that described sample data is concentrated are classified.

Images