CN103886066A - Image retrieval method based on robust non-negative matrix factorization - Google Patents

Abstract

The invention discloses an image retrieval method based on robust non-negative matrix factorization. In order to overcome the defects of a non-negative matrix factorization algorithm model on expression of the relation between images and noise resistance, the method comprises the steps of firstly, constructing an image L1 constraint for representing the data distribution relation according to a visual feature set X of image data, and adding a sparse noise item so as to construct a robust non-negative matrix factorization algorithm model; then, in the model training phase, adopting the iterative optimization solving method to obtain an image feature basic matrix U and a feature expression V of all images in a subspace expanded by the U from the X; finally, during image retrieval, converting an image x with retrieval reference into the subspace of the U to obtain a new feature expression v; according to the distance between the v and the images in an image data set, sorting the images, returning front K images with the smallest distance to a user, and achieving the image retrieval function. The method has the stronger anti-noise capacity, the processing and calculating time for new images is linear time, and image retrieval can be rapidly and accurately carried out.

Description

A kind of image search method based on robust Non-negative Matrix Factorization

Technical field

The present invention relates to CBIR and Non-negative Matrix Factorization method, relate in particular to a kind of image search method based on robust Non-negative Matrix Factorization.

Background technology

In recent years, universal along with internet and smart mobile phone, digital camera, a large amount of image resources is generated continuously.For these image resources are carried out to effective organization and administration and retrieval, various image retrieval technologies are also suggested thereupon.At present, image retrieval has become computer vision, especially a study hotspot in multimedia retrieval field.

Except the image retrieval technologies based on key word the earliest, the image retrieval technologies of the overwhelming majority is all CBIR technology at present.CBIR technology is by extract the visual signature that characterizes various Image Visual Feature from image, then the similarity in the image to be retrieved of submitting to based on specific algorithm calculating user and image data base between each picture, it is distance, thereby according to the size of characteristic distance, image is sorted, return to the image that user distance value is less, realize the retrieval to image in image data base.

In CBIR algorithm, Data Dimensionality Reduction Algorithm is a kind of technology extensively being used.The core concept of this technology is to think that original image feature space exists certain deficiency, cannot effectively dissimilar image area be separated, therefore wish to search out a suitable proper subspace, image dissimilar on this subspace is separated from each other, and image of the same type is gathered each other.These class methods comprise: principal component analysis (PCA) (Principal Component Analysis, PCA), linear discriminant analysis (Linear Discriminant Analysis, LDA), Non-negative Matrix Factorization (Nonnegative Matrix Factorization, and various manifold learning arithmetic NMF), as multidimensional scaling analysis (Multidimensional Scaling, MDS), locally linear embedding (Local Linear Embedded, LLE), locality preserving projections (Local Preserving Projection, LPP) etc.

In these subspace methods, the data of NMF after to dimensionality reduction have been added non-negativity constraint, and its objective function is to solve two nonnegative matrix U and V, makes X ≈ UV.Due to the introducing of non-negativity constraint, make NMF can learn to obtain having the basis matrix U of local feature, also obtain the data representation method based on local a kind of and that in people's cognition, local formation entirety is consistent.Therefore the interpretation of the method is more intense, is widely applied to image retrieval, recognition of face, numeral identification, the application such as text classification.

Liang etc. expand to the initialization procedure of NMF the initialization of supervision, then use NMF in Latent Semantic Indexing, are used for finding from bottom visual signature to the relation high-level semantics features.The people such as BeAbdallah adopt the implicit expression of NMF design of graphics picture, are used for improving the mark accuracy of image.The people such as Caicedo generate multi-modality images based on NMF and express, and consider image, semantic information in building NMF objective function.

But, more weak to the relationship expression between view data and anti-noise acoustic energy method at traditional NMF.For this two aspects problem, this method is the automatic selectivity characteristic at visual signature by L1 figure, builds vision L1 constraint diagram, introduces sparse noise item constraint simultaneously, then these two kinds of constraint conditions are joined in traditional NMF algorithm frame, obtain robust Algorithms of Non-Negative Matrix Factorization model.Based on proposed model, to processing computing time of new images be linear session, can carry out rapidly and accurately image retrieval.

Summary of the invention

The object of the invention is to overcome existing based on Non-negative Matrix Factorization the deficiency on aspect relationship expression between image and antinoise two, a kind of image search method based on robust Non-negative Matrix Factorization is proposed.

Image search method based on robust Non-negative Matrix Factorization comprises the steps:

1) from common image data set Corel5K, select 50 classes totally 5000 images, extract PHOG visual signature [1] collection X=[x ₁..., x _n], wherein n=5000, x _ibe that i opens the corresponding PHOG visual feature vector of image; Summit using PHOG visual signature collection X as the L1 figure that will build, the limit weight matrix W=[w of L1 figure ₁..., w _n],, wherein w _ibe calculated as follows:

$\begin{array}{c}\min {\left|\right|w_i\left|\right|}_1\\ s.t.\left|\right|x_i-X{w}_i\left|\right|\≤\mathrm{\ϵ},w_{\mathrm{ii}}=0\∀i\end{array}---1$

Wherein, x _ibe the visual signature of i width image, w _ifor the i row of matrix W, ε is error coefficient, w _iifor vectorial w _ii component;

The L1 constraint diagram that builds token image data distribution architecture relation is as follows:

$\begin{array}{c}\min R_g={\mathrm{\&Sigma;}}_{i=1}^n{\left|\right|v_i-V{w}_i\left|\right|}^2={\left|\right|V-\mathrm{VW}\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2\\ =\mathrm{tr}\left(V(I-W){(I-W)}^T{V}^T\right)=\mathrm{tr}\left({\mathrm{VGV}}^T\right)\end{array}---2$

Wherein, G=(I-W) (I-W) ^t, V=[v ₁..., v _n] be the feature representation of image set on subspace, I is unit matrix;

2) L1 constraint diagram and sparse noise constraints item E are joined in traditional Algorithms of Non-Negative Matrix Factorization framework, build robust nonnegative matrix matrix decomposition algorithm model:

$\underset{U,V\&GreaterEqual;0,E}{\min }{\left|\right|X-\mathrm{UV}-E\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2+{\mathrm{\&lambda;}}_1\&CenterDot;\left|\right|E\left|\right|+{\mathrm{\&lambda;}}_2\&CenterDot;{\left|\right|U\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2+{\mathrm{\&lambda;}}_3\&CenterDot;\mathrm{tr}\left({\mathrm{VGV}}^T\right)---3$

Wherein, λ ₁, λ ₂and λ ₃for regularization parameter, in experiment, be set to respectively 0.01,0.001 and 0.1, U ∈ R ^{d × r}for keeping the image basis matrix of vision and Semantic Similarity, V ∈ R ^{r × n}feature representation in the subspace of launching for image basis matrix U, E ∈ R ^{d × n}sparse noise constraints item, the dimension that d is characteristics of image, the dimension that r is low dimensional feature space;

3) utilize view data set pair formula 3 algorithm models to train, employing iteration optimization solves, calculate the feature representation V keeping in the image basis matrix U of vision and Semantic Similarity and subspace that all images launch at image basis matrix U, calculation procedure is as follows:

I) random initializtion U, V and E matrix, make intermediate variable X _e=X-E;

Ii) fixing E, iterative computation U and V, computing formula is as follows:

$U_{\mathrm{ij}}\&LeftArrow;U_{\mathrm{ij}}\frac{{\left({\tilde{X}}_e{\tilde{V}}^T\right)}_{\mathrm{ij}}}{{\left(U\tilde{V}{\tilde{V}}^T\right)}_{\mathrm{ij}}}---4$

$V_{\mathrm{ij}}\&LeftArrow;V_{\mathrm{ij}}\sqrt{\frac{{(U^T{X}_e+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{-})}_{\mathrm{ij}}}{{(U^T\mathrm{UV}+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{+})}_{\mathrm{ij}}}}---5$

Wherein ${\tilde{X}}_e=(X_e,0_{d\&times;r}),\tilde{V}=(V,\sqrt{{\mathrm{\&lambda;}}_2}{I}_r),$ $G^{+}=\frac{1}{2}(G+|G\left|\right),$ $G^{-}=\frac{1}{2}(G-|G\left|\right),$ | G| gets the matrix that corresponding absolute value forms for all elements in matrix G;

Iii) fixing U and V, calculate best E, and computing formula is as follows:

$E=f_{\frac{{\mathrm{\&lambda;}}_1}{2}}(X-\mathrm{UV})---6$

Wherein function f is defined as:

4) in the time carrying out image retrieval, using being transformed into as the image x of retrieving reference in the subspace that image basis matrix U launches, obtain new feature representation v, be calculated as follows:

v＝(U ^TU) ^-1U ^Tx＝Mx， 8

Wherein, M=(U ^tu) ^-1u ^t, U ^tfor matrix U transposition, (U ^tu) ^-1for U ^tthe inverse matrix of U;

5) v obtaining according to step 4), calculates v and view data and concentrates arbitrary image x _isubspace feature representation v _ibetween distance s _i, computing formula is as follows:

s _i＝exp(-||v-v _i|| ²) 9

Finally according to apart from s _iconcentrate all images to sort to view data, front K image of layback value minimum be to user, thereby realize image retrieval.

The space structure relation of this method between can token image, there is stronger noise resisting ability, obtaining after image basis matrix U, be linear session the computing time of the low n-dimensional subspace n feature representation to new images, can carry out more rapidly and accurately compared with the conventional method image retrieval.

Accompanying drawing explanation

Fig. 1 is the part sample image on Corel5K image data set;

When Fig. 2 (a) is antelope image as retrieval example, algorithm retrieval sample figure;

When Fig. 2 (b) is antelope image as retrieval example, front 10 the result for retrieval figure of algorithm;

When Fig. 3 (a) is hot air balloon image as retrieval example, algorithm retrieval sample figure;

When Fig. 3 (b) is hot air balloon image as retrieval example, front 10 the result for retrieval figure of algorithm;

When Fig. 4 (a) is cupboard image as retrieval example, algorithm retrieval sample figure;

When Fig. 4 (b) is cupboard image as retrieval example, front 10 the result for retrieval figure of algorithm;

When Fig. 5 (a) is bus image as retrieval example, algorithm retrieval sample figure;

When Fig. 5 (b) is bus image as retrieval example, front 10 the result for retrieval figure of algorithm.

Embodiment

Image search method based on robust Non-negative Matrix Factorization comprises the steps:

1) from common image data set Corel5K, select 50 classes totally 5000 images, extract PHOG visual signature [1] collection X=[x ₁..., x _n], wherein n=5000, x _ibe that i opens the corresponding PHOG visual feature vector of image; Summit using PHOG visual signature collection X as the L1 figure that will build, the limit weight matrix W=[w of L1 figure ₁..., w _n],, wherein w _ibe calculated as follows:

$\begin{array}{c}\min {\left|\right|w_i\left|\right|}_1\\ s.t.\left|\right|x_i-X{w}_i\left|\right|\&le;\mathrm{\&epsiv;},w_{\mathrm{ii}}=0\&ForAll;i\end{array}---1$

Wherein, x _ibe the visual signature of i width image, w _ifor the i row of matrix W, ε is error coefficient, w _iifor vectorial w _ii component;

The L1 constraint diagram that builds token image data distribution architecture relation is as follows:

$\begin{array}{c}\min R_g={\mathrm{\&Sigma;}}_{i=1}^n{\left|\right|v_i-V{w}_i\left|\right|}^2={\left|\right|V-\mathrm{VW}\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2\\ =\mathrm{tr}\left(V(I-W){(I-W)}^T{V}^T\right)=\mathrm{tr}\left({\mathrm{VGV}}^T\right)\end{array}---2$

Wherein, G=(I-W) (I-W) ^t, V=[v ₁..., v _n] be the feature representation of image set on subspace, I is unit matrix;

2) L1 constraint diagram and sparse noise constraints item E are joined in traditional Algorithms of Non-Negative Matrix Factorization framework, build robust nonnegative matrix matrix decomposition algorithm model:

$\underset{U,V\&GreaterEqual;0,E}{\min }{\left|\right|X-\mathrm{UV}-E\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2+{\mathrm{\&lambda;}}_1\&CenterDot;\left|\right|E\left|\right|+{\mathrm{\&lambda;}}_2\&CenterDot;{\left|\right|U\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2+{\mathrm{\&lambda;}}_3\&CenterDot;\mathrm{tr}\left({\mathrm{VGV}}^T\right)---3$

Wherein, λ ₁, λ ₂and λ ₃for regularization parameter, in experiment, be set to respectively 0.01,0.001 and 0.1, U ∈ R ^{d × r}for keeping the image basis matrix of vision and Semantic Similarity, V ∈ R ^{r × n}feature representation in the subspace of launching for image basis matrix U, E ∈ R ^{d × n}sparse noise constraints item, the dimension that d is characteristics of image, the dimension that r is low dimensional feature space;

3) utilize view data set pair formula 3 algorithm models to train, employing iteration optimization solves, calculate the feature representation V keeping in the image basis matrix U of vision and Semantic Similarity and subspace that all images launch at image basis matrix U, calculation procedure is as follows:

I) random initializtion U, V and E matrix, make intermediate variable X _e=X-E;

Ii) fixing E, iterative computation U and V, computing formula is as follows:

$U_{\mathrm{ij}}\&LeftArrow;U_{\mathrm{ij}}\frac{{\left({\tilde{X}}_e{\tilde{V}}^T\right)}_{\mathrm{ij}}}{{\left(U\tilde{V}{\tilde{V}}^T\right)}_{\mathrm{ij}}}---4$

$V_{\mathrm{ij}}\&LeftArrow;V_{\mathrm{ij}}\sqrt{\frac{{(U^T{X}_e+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{-})}_{\mathrm{ij}}}{{(U^T\mathrm{UV}+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{+})}_{\mathrm{ij}}}}---5$

Wherein ${\tilde{X}}_e=(X_e,0_{d\&times;r}),\tilde{V}=(V,\sqrt{{\mathrm{\&lambda;}}_2}{I}_r),$ $G^{+}=\frac{1}{2}(G+|G\left|\right),$ $G^{-}=\frac{1}{2}(G-|G\left|\right),$ | G| gets the matrix that corresponding absolute value forms for all elements in matrix G;

Iii) fixing U and V, calculate best E, and computing formula is as follows:

$E=f_{\frac{{\mathrm{\&lambda;}}_1}{2}}(X-\mathrm{UV})---6$

Wherein function f is defined as:

4) in the time carrying out image retrieval, using being transformed into as the image x of retrieving reference in the subspace that image basis matrix U launches, obtain new feature representation v, be calculated as follows:

v＝(U ^TU) ^-1U ^Tx＝Mx， 8

Wherein, M=(U ^tu) ^-1u ^t, U ^tfor matrix U transposition, (U ^tu) ^-1for U ^tthe inverse matrix of U;

5) v obtaining according to step 4), calculates v and view data and concentrates arbitrary image x _isubspace feature representation v _ibetween distance s _i, computing formula is as follows:

s _i＝exp(-||v-v _i|| ²) 9

Finally according to apart from s _iconcentrate all images to sort to view data, front K image of layback value minimum be to user, thereby realize image retrieval.

List of references

[1] PHOG feature code is realized: http:// www.robots.ox.ac.uk/～vgg/research/caltech/phog.html.

Embodiment 1

Adopt Corel5K image data set (as shown in Figure 1) to test, Fig. 2, Fig. 3, Fig. 4, Fig. 5 shows respectively four result for retrieval.Below in conjunction with foregoing method step, illustrate this embodiment as follows:

1) to the image in Corel5K extract respectively image 680 dimension PHOG original image visual signatures, set it as image feature representation, obtain Image Visual Feature matrix X=[x ₁..., x _n], n=5000.

2) according to Image Visual Feature matrix X, to visual similarity modeling, with the original visual signature X=[x of image set ₁..., x _n] as the summit of L1 figure, the limit weight matrix W=[w of figure ₁..., w _n] middle w _ibe calculated as follows:

$\begin{array}{c}\min {\left|\right|w_i\left|\right|}_1\\ s.t.\left|\right|x_i-X{w}_i\left|\right|\&le;\mathrm{\&epsiv;},w_{\mathrm{ii}}=0\&ForAll;i\end{array}---1$

ε=0.001 is set, adopts L1_LS to solve kit objective function 1 is above optimized and is solved, calculate W matrix, thereby obtain as next vision L1 constraint diagram:

$\begin{array}{c}\min R_g={\mathrm{\&Sigma;}}_{i=1}^n{\left|\right|v_i-V{w}_i\left|\right|}^2={\left|\right|V-\mathrm{VW}\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2\\ =\mathrm{tr}\left(V(I-W){(I-W)}^T{V}^T\right)=\mathrm{tr}\left({\mathrm{VGV}}^T\right)\end{array}---2$

Wherein, G=(I-W) (I-W) ^t, V=[v ₁..., v _n] be the feature representation of image set on subspace, I is unit matrix.

3) L1 constraint diagram and sparse noise constraints item E are joined in traditional Algorithms of Non-Negative Matrix Factorization framework, build robust nonnegative matrix matrix decomposition algorithm model:

$\underset{U,V\&GreaterEqual;0,E}{\min }{\left|\right|X-\mathrm{UV}-E\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2+{\mathrm{\&lambda;}}_1\&CenterDot;\left|\right|E\left|\right|+{\mathrm{\&lambda;}}_2\&CenterDot;{\left|\right|U\left|\right|}_{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="140320154219.png"\; state="\{\{state\}\}">F</figure-callout>}}^2+{\mathrm{\&lambda;}}_3\&CenterDot;\mathrm{tr}\left({\mathrm{VGV}}^T\right)---3$

Wherein, λ ₁, λ ₂and λ ₃for regularization parameter, be set to respectively 1.6,0.1 and 0.01, U ∈ R ^{d × r}for keeping the image basis matrix of vision and Semantic Similarity, V ∈ R ^{r × n}feature representation in the subspace of launching for image basis matrix U, E ∈ R ^{d × n}sparse noise constraints item, the dimension that d is characteristics of image, i.e. 680 dimensions, the dimension that r is low dimensional feature space, is set to 150 dimensions;

4) utilize view data set pair formula 3 algorithm models to train, employing iteration optimization solves, calculate the feature representation V keeping in the image basis matrix U of vision and Semantic Similarity and subspace that all images launch at image basis matrix U, calculation procedure is as follows:

I) random initializtion U, V and E matrix, make intermediate variable X _e=X-E;

Ii) fixing E, iterative computation U and V, computing formula is as follows:

$U_{\mathrm{ij}}\&LeftArrow;U_{\mathrm{ij}}\frac{{\left({\tilde{X}}_e{\tilde{V}}^T\right)}_{\mathrm{ij}}}{{\left(U\tilde{V}{\tilde{V}}^T\right)}_{\mathrm{ij}}}---4$

$V_{\mathrm{ij}}\&LeftArrow;V_{\mathrm{ij}}\sqrt{\frac{{(U^T{X}_e+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{-})}_{\mathrm{ij}}}{{(U^T\mathrm{UV}+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{+})}_{\mathrm{ij}}}}---5$

Wherein ${\tilde{X}}_e=(X_e,0_{d\&times;r}),\tilde{V}=(V,\sqrt{{\mathrm{\&lambda;}}_2}{I}_r),$ $G^{+}=\frac{1}{2}(G+|G\left|\right),$ $G^{-}=\frac{1}{2}(G-|G\left|\right),$ | G| gets the matrix that corresponding absolute value forms for all elements in matrix G;

Iii) fixing U and V, calculate best E, and computing formula is as follows:

$E=f_{\frac{{\mathrm{\&lambda;}}_1}{2}}(X-\mathrm{UV})---6$

Wherein function f is defined as:

5) in the time carrying out image retrieval, using being transformed into as the image x of retrieving reference in the subspace that image basis matrix U launches, obtain new feature representation v, be calculated as follows:

v＝(U ^TU) ^-1U ^Tx＝Mx， 8

Wherein, M=(U ^tu) ^-1u ^t, U ^tfor matrix U transposition, (U ^tu) ^-1for U ^tthe inverse matrix of U;

6) v obtaining according to step 5), calculates v and view data and concentrates arbitrary image x _isubspace feature representation v _ibetween distance s _i, computing formula is as follows:

s _i＝exp(-||v-v _i|| ²) 9

Finally according to apart from s _iconcentrate all images to sort to Corel5K view data, front 10 images of layback value minimum are to user, thereby realize image retrieval.

Claims (1)

1. the image search method based on robust Non-negative Matrix Factorization, is characterized in that comprising the steps:

1) from common image data set Corel5K, select 50 classes totally 5000 images, extract PHOG visual signature collection X=[x ₁..., x _n], wherein n=5000, x _ibe that i opens the corresponding PHOG visual feature vector of image; Summit using PHOG visual signature collection X as the L1 figure that will build, the limit weight matrix W=[w of L1 figure ₁..., w _n],, wherein w _ibe calculated as follows:

$\begin{array}{c}\min {\left|\right|w_i\left|\right|}_1\\ s.t.\left|\right|x_i-X{w}_i\left|\right|\&le;\mathrm{\&epsiv;},w_{\mathrm{ii}}=0\&ForAll;i\end{array}---1$

Wherein, x _ibe the visual signature of i width image, w _ifor the i row of matrix W, ε is error coefficient, w _iifor vectorial w _ii component;

The L1 constraint diagram that builds token image data distribution architecture relation is as follows:

$\begin{array}{c}\min R_g={\mathrm{\&Sigma;}}_{i=1}^n{\left|\right|v_i-V{w}_i\left|\right|}^2={\left|\right|V-\mathrm{VW}\left|\right|}_F^2\\ =\mathrm{tr}\left(V(I-W){(I-W)}^T{V}^T\right)=\mathrm{tr}\left({\mathrm{VGV}}^T\right)\end{array}---2$

Wherein, G=(I-W) (I-W) ^t, V=[v ₁..., v _n] be the feature representation of image set on subspace, I is unit matrix;

2) L1 constraint diagram and sparse noise constraints item E are joined in traditional Algorithms of Non-Negative Matrix Factorization framework, build robust nonnegative matrix matrix decomposition algorithm model:

$\underset{U,V\&GreaterEqual;0,E}{\min }{\left|\right|X-\mathrm{UV}-E\left|\right|}_F^2+{\mathrm{\&lambda;}}_1\&CenterDot;\left|\right|E\left|\right|+{\mathrm{\&lambda;}}_2\&CenterDot;{\left|\right|U\left|\right|}_F^2+{\mathrm{\&lambda;}}_3\&CenterDot;\mathrm{tr}\left({\mathrm{VGV}}^T\right)---3$

Wherein, λ ₁, λ ₂and λ ₃for regularization parameter, in experiment, be set to respectively 0.01,0.001 and 0.1, U ∈ R ^{d × r}for keeping the image basis matrix of vision and Semantic Similarity, V ∈ R ^{r × n}feature representation in the subspace of launching for image basis matrix U, E ∈ R ^{d × n}sparse noise constraints item, the dimension that d is characteristics of image, the dimension that r is low dimensional feature space;

3) utilize view data set pair formula 3 algorithm models to train, employing iteration optimization solves, calculate the feature representation V keeping in the image basis matrix U of vision and Semantic Similarity and subspace that all images launch at image basis matrix U, calculation procedure is as follows:

I) random initializtion U, V and E matrix, make intermediate variable X _e=X-E;

Ii) fixing E, iterative computation U and V, computing formula is as follows:

$U_{\mathrm{ij}}\&LeftArrow;U_{\mathrm{ij}}\frac{{\left({\tilde{X}}_e{\tilde{V}}^T\right)}_{\mathrm{ij}}}{{\left(U\tilde{V}{\tilde{V}}^T\right)}_{\mathrm{ij}}}---4$

$V_{\mathrm{ij}}\&LeftArrow;V_{\mathrm{ij}}\sqrt{\frac{{(U^T{X}_e+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{-})}_{\mathrm{ij}}}{{(U^T\mathrm{UV}+{\mathrm{\&lambda;}}_3{\mathrm{VG}}^{+})}_{\mathrm{ij}}}}---5$

Wherein ${\tilde{X}}_e=(X_e,0_{d\&times;r}),\tilde{V}=(V,\sqrt{{\mathrm{\&lambda;}}_2}{I}_r),$ $G^{+}=\frac{1}{2}(G+|G\left|\right),$ $G^{-}=\frac{1}{2}(G-|G\left|\right),$ | G| gets the matrix that corresponding absolute value forms for all elements in matrix G;

Iii) fixing U and V, calculate best E, and computing formula is as follows:

$E=f_{\frac{{\mathrm{\&lambda;}}_1}{2}}(X-\mathrm{UV})---6$

Wherein function f is defined as:

4) in the time carrying out image retrieval, using being transformed into as the image x of retrieving reference in the subspace that image basis matrix U launches, obtain new feature representation v, be calculated as follows:

v＝(U ^TU) ^-1U ^Tx＝Mx， 8

Wherein, M=(U ^tu) ^-1u ^t, U ^tfor matrix U transposition, (U ^tu) ^-1for U ^tthe inverse matrix of U;

5) v obtaining according to step 4), calculates v and view data and concentrates arbitrary image x _isubspace feature representation v _ibetween distance s _i, computing formula is as follows:

s _i＝exp(-||v-v _i|| ²) 9

Finally according to apart from s _iconcentrate all images to sort to view data, front K image of layback value minimum be to user, thereby realize image retrieval.

Images