CN102270241A - Image retrieving method based on sparse nonnegative matrix factorization - Google Patents

Abstract

The invention discloses an image retrieving method based on sparse nonnegative matrix factorization. The method comprises the following steps of: 1) respectively querying and extracting an image and an adjoint text of the retrieve result under two different image data sources; 2) extracting a label from the adjoint text, and forming a word list according to the word frequency filtration result; 3) forming an incidence matrix of the label and the image by utilizing the incidence relation of the label and the image according to each image set; 4) analyzing the incidence matrix obtained in step 3) by utilizing sparse nonnegative matrix factorization so as to obtain a shared subspace of the data from different sources and a corresponding independent subspace; and 5) sending a retrieve request by the user to an image on a certain data source, forming a query vector and mapping the query vector to the subspace corresponding to the data source, calculating the similarity of all the images and sequencing the images, and then returning to the first N images which are most similar to one another. By the method, the incidence knowledge of the label and the image under a plurality of data sources are fully utilized for transfer learning by sparse nonnegative matrix factorization, so the accuracy of image retrieve on the target data source is improved.

Description

Image search method based on sparse nonnegative matrix decomposition

Technical field

The present invention relates to the searching field of image, relate in particular to a kind of image search method that decomposes based on sparse nonnegative matrix.

Background technology

As one of feature of web 2.0, current social label increased popularity.In websites such as Flickr, YouTube and Del.icio.us, but user's comparison film, video, webpage etc. mark, also can retrieve related resource by interest.But, user's problems such as having noise, ambiguousness and subjectivity that tags, the label search resource of directly utilizing the user to mark can't obtain satisfactory result.Therefore, how from existing label, improving the image retrieval effect is a hot issue of current research.In recent years, at this problem, a lot of methods are suggested.But these methods have a common limitation, and promptly it utilizes single data source information mostly, ignore the effect of other data sources.In fact, along with the fast development of network and multimedia technology, the data of separate sources are more easily obtained.Analyzing a certainly when coming source data, coming source data to make full use of other, will be better than the effect that only relies on the single source data obtained as supplementary.

As a sub spaces learning method, nonnegative matrix decomposes that (Nonnegative Matrix Factorization NMF) is widely used in the dimensionality reduction of high dimensional data.Nonnegative matrix is decomposed many times can obtain significant base vector in the raw data, conform to " whole by partly forming " this people's high-rise perception, so the nonnegative matrix decomposition has obtained comparatively widespread use.In reality, need remove redundancy to raw data, obtain its compact expression.Though the non-negativity constraint among the NMF also can produce the compactness of data and express (promptly bringing sparse property), this sparse property is not controlled.For addressing this problem, [1] (Bioinformatics/computer Applications in The Biosciences in " bioinformatics " magazine, 2007,23:1495-1502) propose a kind of sparse nonnegative matrix and decomposed (Sparse NMF) algorithm, the sparse degree of this algorithm may command basis matrix or matrix of coefficients.[2] (Proceedings of Knowledge Discovery and Data Mining is concentrated in Knowledge Discovery and data mining meeting in 2010,2010:1169-1178) utilize methods such as nonnegative matrix decomposition and shared Sub space learning, proposition is united shared nonnegative matrix and is decomposed (Multiple Shared Nonnegative Matrix Factorization, MS-NMF) algorithm, this algorithm utilizes in the multi-data source knowledge to come the assistant images retrieval, overcomes the deficiency of only utilizing single data source in the traditional algorithm.

Yet [1] though the middle method that proposes has been considered the control of sparse property in the matrix decomposition, this method only limits to the utilization of single data source (being single matrix); And [2] have ignored the control to sparse property though the middle method that proposes utilizes the knowledge in the multi-data source to come the assistant images retrieval.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art, a kind of image search method that decomposes based on sparse nonnegative matrix is provided.

The method of the image retrieval that decomposes based on sparse nonnegative matrix comprises the steps:

1) writes the reptile program, under two different image data source, inquire about and extract the image of result for retrieval respectively and follow text, constitute the first image data set D ₁With the second image data set D ₂

2) extract the label of following in the text, and filter the formation vocabulary according to word frequency;

3) to each image data set, utilize the incidence relation of label and image, form the incidence matrix of label and image;

4) utilize the incidence matrix of sparse nonnegative matrix decomposition analysis step 3) gained, obtain the subspace of separate sources data correspondence, corresponding subspace comprises the shared Sub space of separate sources data and the independent subspace of each data source correspondence;

5) to the image retrieval request on certain data source, the formation query vector also is mapped on the subspace of this data source correspondence, calculates similarity and ordering with all images, returns the most similar top n image.

Described step 2) be:

1) from the first image data set D ₁Follow in the text and to extract label and constitute the first tag set T ₁, from the second image data set D ₂Follow in the text and to extract label and constitute the second tag set T ₂

2) the statistics first tag set T ₁With the second tag set T ₂In label at the first image data set D ₁With the second image data set D ₂Follow occurrence number in the text, only keep occurrence number greater than 10 times label, constitute the first tag set S after filtering ₁With the second tag set S after the filtration ₂, the first tag set S after the filtration ₁Radix be m ₁, the second tag set S after the filtration ₁Radix be m ₂

3) get the first tag set S after the filtration ₁With the second tag set S after the filtration ₂Common factor and the union common factor S that obtains two tag sets successively _jUnion S with two tag sets _u, the common factor S of two tag sets _jRadix be m _j, the union S of two tag sets _uRadix be m _u, the union S of two tag sets _uBe vocabulary.

Described step 3) is: according to the union S of two tag sets _u, at the first image data set D ₁Last structure first incidence matrix

At the second image data set D ₂Last structure second incidence matrix

M=m wherein _u, n ₁Be the first image data set D ₁The number of middle image, n ₂Be the second image data set D ₂The number of middle image, the corresponding label of each row of matrix, the corresponding document of each row of matrix, the first incidence matrix X ₁Element Or the second incidence matrix X ₂Element Press following assignment: as the first image data set D ₁Or the second image data set D ₂During j document of i label for labelling, assignment is 1; Otherwise assignment is 0.

Described step 4) is: utilize sparse nonnegative matrix to decompose the first incidence matrix X of Conjoint Analysis step 3) gained ₁With the second incidence matrix X ₂, the shared Sub space that obtains two incidence matrix is designated as w ₁₂, the first incidence matrix X ₁Independent subspace be designated as w ₁, the second incidence matrix X ₂Independent subspace w ₂, in matrix decomposition, above-mentioned three sub spaces are expressed as follows:

Represent the decomposition of data source level with capital W, H, represent the decomposition of subspace level, in view of the above, add the constraint of sparse property, can get the objective function that above-mentioned nonnegative matrix decomposes and be with lowercase w, h

$\underset{W_1,W_2,H_1,H_2\≥0}{\min }\frac{1}{2}\left\{\underset{i\∈\left\{\mathrm{1,2}\right\}}{\mathrm{\Σ}}{\mathrm{\λ}}_i\right\{{\left|\right|X_i-W_i{H}_i\left|\right|}_F^2+{\mathrm{\η}}_i{\left|\right|W_i\left|\right|}_F^2+{\mathrm{\β}}_i\underset{j=1}{\overset{n_i}{\mathrm{\Σ}}}{\left|\right|H_i(:,j)\left|\right|}_1^2\left\}\right\}---\left(2\right)$

Also can write

$\underset{h_{\mathrm{2,12}},h_{\mathrm{2,2}}\≥0}{\underset{h_{\mathrm{1,12}},h_{\mathrm{1,1}},}{\underset{w_{12},w_1,w_2,}{\min }}}\frac{1}{2}\left\{\underset{i\∈\left\{\mathrm{1,2}\right\}}{\mathrm{\Σ}}{\mathrm{\λ}}_i\right\{{\left|\right|X_i-\underset{v\∈S(2,i)}{\mathrm{\Σ}}{w}_v{h}_{i,v}\left|\right|}_F^2+{\mathrm{\η}}_i{\left|\right|w_{12}\left|w_i\right||}_F^2+{\mathrm{\β}}_i\underset{v\∈S(2,i)}{\mathrm{\Σ}}\underset{j=1}{\overset{n_i}{\mathrm{\Σ}}}{\left|\right|h_{i,v}(:,j)\left|\right|}_1^2\left\}\right\}---\left(3\right)$

H wherein _i(:, j) be H _iJ column vector, η _i＞0 in order to compression

Parameter, β _iThe＞0th, regularization parameter is in order to the degree of rarefication of equilibrium approximation accuracy and H matrix, wherein S (2,1) expression set 1,12}, S (2,2) expression set 2, and 12}, the objective function that adopts the following multi-source that decomposes based on sparse nonnegative matrix to utilize algorithm solution formula (2) and (3) defined nonnegative matrix to decompose:

Input: the matrix X that makes up on two image data sets ₁, X ₂, parameters R ₁, R ₂, k, η ₁, β ₁, η ₂, β ₂And threshold epsilon;

Output: share basic subspace w ₁₂, independently basic subspace w ₁, w ₂, and matrix of coefficients H ₁, H ₂

Step 1. is got

Wherein i ∈ 1,2};

Step 2. random initializtion w ₁₂, w ₁, w ₂, H ₁, H ₂

Step 3. is W fixedly _i(i.e. [w ₁₂| w _i]) utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{H_i}{\min }{\left|\right|\left(\begin{array}{c}{W}_i\\ \sqrt{{\mathrm{\β}}_i}{e}_{1\×R_i}\end{array}\right)H_i-\left(\begin{array}{c}{X}_i\\ 0_{1\×n_i}\end{array}\right)\left|\right|}_F^2,$ S.t.H _i〉=0 upgrades H _i, wherein i ∈ 1,2}, R _iIt is matrix W _iThe row dimension, Element be 1,

Be null vector;

Step 4. is H fixedly ₁(promptly $\left[\begin{array}{c}{h}_{\mathrm{1,12}}\\ h_{\mathrm{1,1}}\end{array}\right]$ ), H ₂(promptly $\left[\begin{array}{c}{h}_{\mathrm{2,12}}\\ h_{\mathrm{2,2}}\end{array}\right]$ ), w ₁And w ₂Utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{w_{12}}{\min }{\left|\right|\left(\begin{array}{c}\sqrt{{\mathrm{\λ}}_1}{h}_{\mathrm{1,12}}^T\\ \sqrt{{\mathrm{\λ}}_1{\mathrm{\η}}_1}{I}_k\\ \sqrt{{\mathrm{\λ}}_2}{h}_{\mathrm{2,12}}^T\\ \sqrt{{\mathrm{\λ}}_2{\mathrm{\η}}_2}{I}_k\end{array}\right)w_{12}^T-\left(\begin{array}{c}\sqrt{{\mathrm{\λ}}_1}{(X_1-w_1{h}_{\mathrm{1,1}})}^T\\ 0_{k\×m}\\ \sqrt{{\mathrm{\λ}}_2}{(X_2-w_2{h}_{\mathrm{2,2}})}^T\\ 0_{k\×m}\end{array}\right)\left|\right|}_F^2,$ S.t.w ₁₂〉=0 upgrades w ₁₂, I wherein _kBe a k rank unit matrix, 0 _{K * m}Be the null matrix of a k * m, k is the dimension in shared Sub space;

Step 5. is H fixedly ₁(promptly $\left[\begin{array}{c}{h}_{\mathrm{1,12}}\\ h_{\mathrm{1,1}}\end{array}\right]$ ), H ₂(promptly $\left[\begin{array}{c}{h}_{\mathrm{2,12}}\\ h_{\mathrm{2,2}}\end{array}\right]$ ) and w ₁₂, utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{w_i}{\min }{\left|\right|\left(\begin{array}{c}{h}_{i,i}^T\\ \sqrt{{\mathrm{\η}}_i}{I}_{R_i-k}\end{array}\right)w_i^T-\left(\begin{array}{c}(X_i-w_{12}{h}_{i,12})\\ 0_{(R_i-k)\×m}\end{array}\right)\left|\right|}_F^2,$ S.t.w _i〉=0 upgrades w _i, wherein

Be (R _i-k) rank unit matrix,

Be (R _i-k) * the m null matrix, i ∈ 1,2};

Step 6. iterative step 3 arrives step 5 until convergence.

Described step 5) is: adopt the following image retrieval algorithm that decomposes based on sparse nonnegative matrix to carry out image retrieval:

Input: on target data set and auxiliary data collection, make up matrix X respectively ₁And X ₂, query vector q, the picture that needs retrieval to return is counted N;

Output: retrieval obtains maximally related top n picture, returns by the similarity descending;

Step 1. utilizes the multi-source that decomposes based on sparse nonnegative matrix to utilize algorithm, to matrix X ₁And X ₂Decompose and obtain X ₁=W ₁H ₁, X ₂=W ₂H ₂

Step 2. utilizes the least square method of nonnegativity restrictions to find the solution problem S.t.h 〉=0 obtains q at basis matrix W ₁On mapping h;

Step 3. is for each pictures of target data set, such as r opens, and it is at basis matrix W ₁On mapping h _r(be matrix H ₁R column vector), can be by formula sim (h, h _r)=h ^Th _r/ || h|| ₂|| h _r|| ₂Calculate the similarity of this picture and query vector;

Step 4. is by all pictures of sequencing of similarity;

Step 5. descending returns maximally related preceding N pictures.

The present invention makes full use of the view data of separate sources, utilize sparse nonnegative matrix to decompose the shared structure and the corresponding absolute construction of Conjoint Analysis separate sources data, realize the transfer learning of knowledge between multi-data source, therefore can be lifted at the image retrieval performance on a certain data source.

Description of drawings

Fig. 1 is based on the method flow diagram of the image retrieval of sparse nonnegative matrix decomposition.

Fig. 2 is the comparing result of image retrieval of the present invention and additive method, wherein NMF represents general nonnegative matrix decomposition method, SNMF represents the sparse nonnegative matrix decomposition method in [1], MS-NMF represents uniting in [2] to share the nonnegative matrix decomposition method, MtBSNMF represents to utilize Multi-source Boosting by Sparse Nonnegative Matrix Factorization algorithm based on the multi-source that sparse nonnegative matrix is decomposed, and is image search method of the present invention.

Embodiment

The method of the image retrieval that decomposes based on sparse nonnegative matrix comprises the steps:

1) writes the reptile program, under two different image data source, inquire about and extract the image of result for retrieval respectively and follow text, constitute the first image data set D ₁With the second image data set D ₂

2) extract the label of following in the text, and filter the formation vocabulary according to word frequency;

3) to each image data set, utilize the incidence relation of label and image, form the incidence matrix of label and image;

4) utilize the incidence matrix of sparse nonnegative matrix decomposition analysis step 3) gained, obtain the subspace of separate sources data correspondence, corresponding subspace comprises the shared Sub space of separate sources data and the independent subspace of each data source correspondence;

5) to the image retrieval request on certain data source, the formation query vector also is mapped on the subspace of this data source correspondence, calculates similarity and ordering with all images, returns the most similar top n image.

Described step 2) be:

1) from the first image data set D ₁Follow in the text and to extract label and constitute the first tag set T ₁, from the second image data set D ₂Follow in the text and to extract label and constitute the second tag set T ₂

2) the statistics first tag set T ₁With the second tag set T ₂In label at the first image data set D ₁With the second image data set D ₂Follow occurrence number in the text, only keep occurrence number greater than 10 times label, constitute the first tag set S after filtering ₁With the second tag set S after the filtration ₂, the first tag set S after the filtration ₁Radix be m ₁, the second tag set S after the filtration ₁Radix be m ₂

3) get the first tag set S after the filtration ₁With the second tag set S after the filtration ₂Common factor and the union common factor S that obtains two tag sets successively _jUnion S with two tag sets _u, the common factor S of two tag sets _jRadix be m _j, the union S of two tag sets _uRadix be m _u, the union S of two tag sets _uBe vocabulary.

Described step 3) is: according to the union S of two tag sets _u, at the first image data set D ₁Last structure first incidence matrix

At the second image data set D ₂Last structure second incidence matrix

M=m wherein _u, n ₁Be the first image data set D ₁The number of middle image, n ₂Be the second image data set D ₂The number of middle image, the corresponding label of each row of matrix, the corresponding document of each row of matrix, the first incidence matrix X ₁Element

Or the second incidence matrix X ₂Element

Press following assignment: as the first image data set D ₁Or the second image data set D ₂During j document of i label for labelling, assignment is 1; Otherwise assignment is 0.

Described step 4) is: utilize sparse nonnegative matrix to decompose the first incidence matrix X of Conjoint Analysis step 3) gained ₁With the second incidence matrix X ₂, the shared Sub space that obtains two incidence matrix is designated as w ₁₂, the first incidence matrix X ₁Independent subspace be designated as w ₁, the second incidence matrix X ₂Independent subspace w ₂, in matrix decomposition, above-mentioned three sub spaces are expressed as follows:

Represent the decomposition of data source level with capital W, H, represent the decomposition of subspace level, in view of the above, add the constraint of sparse property, can get the objective function that above-mentioned nonnegative matrix decomposes and be with lowercase w, h

$\underset{W_1,W_2,H_1,H_2\≥0}{\min }\frac{1}{2}\left\{\underset{i\∈\left\{\mathrm{1,2}\right\}}{\mathrm{\Σ}}{\mathrm{\λ}}_i\right\{{\left|\right|X_i-W_i{H}_i\left|\right|}_F^2+{\mathrm{\η}}_i{\left|\right|W_i\left|\right|}_F^2+{\mathrm{\β}}_i\underset{j=1}{\overset{n_i}{\mathrm{\Σ}}}{\left|\right|H_i(:,j)\left|\right|}_1^2\left\}\right\}---\left(2\right)$

Also can write

$\underset{h_{\mathrm{2,12}},h_{\mathrm{2,2}}\≥0}{\underset{h_{\mathrm{1,12}},h_{\mathrm{1,1}},}{\underset{w_{12},w_1,w_2,}{\min }}}\frac{1}{2}\left\{\underset{i\∈\left\{\mathrm{1,2}\right\}}{\mathrm{\Σ}}{\mathrm{\λ}}_i\right\{{\left|\right|X_i-\underset{v\∈S(2,i)}{\mathrm{\Σ}}{w}_v{h}_{i,v}\left|\right|}_F^2+{\mathrm{\η}}_i{\left|\right|w_{12}\left|w_i\right||}_F^2+{\mathrm{\β}}_i\underset{v\∈S(2,i)}{\mathrm{\Σ}}\underset{j=1}{\overset{n_i}{\mathrm{\Σ}}}{\left|\right|h_{i,v}(:,j)\left|\right|}_1^2\left\}\right\}---\left(3\right)$

H wherein _i(:, j) be H _iJ column vector, η _i＞0 in order to compression

Parameter, β _iThe＞0th, regularization parameter is in order to the degree of rarefication of equilibrium approximation accuracy and H matrix, wherein

S (2,1) expression set 1,12}, S (2,2) expression set 2, and 12}, the objective function that adopts the following multi-source that decomposes based on sparse nonnegative matrix to utilize algorithm solution formula (2) and (3) defined nonnegative matrix to decompose:

Input: the matrix X that makes up on two image data sets ₁, X ₂, parameters R ₁, R ₂, k, η ₁, β ₁, η ₂, β ₂And threshold epsilon;

Output: share basic subspace w ₁₂, independently basic subspace w ₁, w ₂, and matrix of coefficients H ₁, H ₂

Step 1. is got

Wherein i ∈ 1,2};

Step 2. random initializtion w ₁₂, w ₁, w ₂, H ₁, H ₂

Step 3. is W fixedly _i(i.e. [w ₁₂| w _i]) utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{H_i}{\min }{\left|\right|\left(\begin{array}{c}{W}_i\\ \sqrt{{\mathrm{\β}}_i}{e}_{1\×R_i}\end{array}\right)H_i-\left(\begin{array}{c}{X}_i\\ 0_{1\×n_i}\end{array}\right)\left|\right|}_F^2,$ S.t.H _i〉=0 upgrades H _i, wherein i ∈ 1,2}, R _iIt is matrix W _iThe row dimension,

Element be 1,

Be null vector;

Step 4. is H fixedly ₁(promptly $\left[\begin{array}{c}{h}_{\mathrm{1,12}}\\ h_{\mathrm{1,1}}\end{array}\right]$ ), H ₂(promptly $\left[\begin{array}{c}{h}_{\mathrm{2,12}}\\ h_{\mathrm{2,2}}\end{array}\right]$ ), w ₁And w ₂Utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{w_{12}}{\min }{\left|\right|\left(\begin{array}{c}\sqrt{{\mathrm{\λ}}_1}{h}_{\mathrm{1,12}}^T\\ \sqrt{{\mathrm{\λ}}_1{\mathrm{\η}}_1}{I}_k\\ \sqrt{{\mathrm{\λ}}_2}{h}_{\mathrm{2,12}}^T\\ \sqrt{{\mathrm{\λ}}_2{\mathrm{\η}}_2}{I}_k\end{array}\right)w_{12}^T-\left(\begin{array}{c}\sqrt{{\mathrm{\λ}}_1}{(X_1-w_1{h}_{\mathrm{1,1}})}^T\\ 0_{k\×m}\\ \sqrt{{\mathrm{\λ}}_2}{(X_2-w_2{h}_{\mathrm{2,2}})}^T\\ 0_{k\×m}\end{array}\right)\left|\right|}_F^2,$ S.t.w ₁₂〉=0 upgrades w ₁₂, I wherein _kBe a k rank unit matrix, 0 _{K * m}Be the null matrix of a k * m, k is the dimension in shared Sub space;

Step 5. is H fixedly ₁(promptly $\left[\begin{array}{c}{h}_{\mathrm{1,12}}\\ h_{\mathrm{1,1}}\end{array}\right]$ ), H ₂(promptly $\left[\begin{array}{c}{h}_{\mathrm{2,12}}\\ h_{\mathrm{2,2}}\end{array}\right]$ ) and w ₁₂, utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{w_i}{\min }{\left|\right|\left(\begin{array}{c}{h}_{i,i}^T\\ \sqrt{{\mathrm{\η}}_i}{I}_{R_i-k}\end{array}\right)w_i^T-\left(\begin{array}{c}(X_i-w_{12}{h}_{i,12})\\ 0_{(R_i-k)\×m}\end{array}\right)\left|\right|}_F^2,$ S.t.w _i〉=0 upgrades w _i, wherein Be (R _i-k) rank unit matrix,

Be (R _i-k) * the m null matrix, i ∈ 1,2};

Step 6. iterative step 3 arrives step 5 until convergence.

Described step 5) is: adopt the following image retrieval algorithm that decomposes based on sparse nonnegative matrix to carry out image retrieval:

Input: on target data set and auxiliary data collection, make up matrix X respectively ₁And X ₂, query vector q, the picture that needs retrieval to return is counted N;

Output: retrieval obtains maximally related top n picture, returns by the similarity descending;

Step 1. utilizes the multi-source that decomposes based on sparse nonnegative matrix to utilize algorithm, to matrix X ₁And X ₂Decompose and obtain X ₁=W ₁H ₁, X ₂=W ₂H ₂

Step 2. utilizes the least square method of nonnegativity restrictions to find the solution problem

S.t.h 〉=0 obtains q at basis matrix W ₁On mapping h;

Step 3. is for each pictures of target data set, such as r opens, and it is at basis matrix W ₁On mapping h _r(be matrix H ₁R column vector), can be by formula sim (h, h _r)=h ^Th _r/ || h|| ₂|| h _r|| ₂Calculate the similarity of this picture and query vector;

Step 4. is by all pictures of sequencing of similarity;

Step 5. descending returns maximally related preceding N pictures.

Embodiment

Fig. 2 has provided the comparing result of image retrieval of the present invention and additive method.

1) is combined under two different image data sources according to two different keyword set and inquires about and extract the image of result for retrieval respectively and follow text, form the first image data set D ₁With the second image data set D ₂

2) extract the label of following in the text, and filter the formation vocabulary according to word frequency;

3) to each image data set, utilize the incidence relation of label and image, form the incidence matrix X of label and image ₁, X ₂

4) utilize the incidence matrix of sparse nonnegative matrix decomposition analysis step 3) gained, obtain the shared Sub space w of separate sources data ₁₂And corresponding independent subspace w ₁, w ₂

5) image on certain data source is carried out a series of inquiry, each inquiry at first forms query vector q and is mapped on the corresponding subspace of this data source again, calculates similarity and ordering with all images, returns the most similar top n image;

6) to 5) in return results utilize PN (precision-scope estimates relevance ranking at different cut offs) to estimate, at last evaluation result is averaged as net result.

Can see from the experiment of contrast, compare with other control methods, the present invention makes full use of the view data of separate sources, utilize sparse nonnegative matrix to decompose the shared structure and the corresponding absolute construction of Conjoint Analysis separate sources data, realize the transfer learning of knowledge between multi-data source, therefore can be lifted at the image retrieval performance on a certain data source.

Claims (5)

1. the method based on the image retrieval of sparse nonnegative matrix decomposition is characterized in that comprising the steps:

1) writes the reptile program, under two different image data source, inquire about and extract the image of result for retrieval respectively and follow text, constitute the first image data set D ₁With the second image data set D ₂

2) extract the label of following in the text, and filter the formation vocabulary according to word frequency;

3) to each image data set, utilize the incidence relation of label and image, form the incidence matrix of label and image;

4) utilize the incidence matrix of sparse nonnegative matrix decomposition analysis step 3) gained, obtain the subspace of separate sources data correspondence, corresponding subspace comprises the shared Sub space of separate sources data and the independent subspace of each data source correspondence;

5) to the image retrieval request on certain data source, the formation query vector also is mapped on the subspace of this data source correspondence, calculates similarity and ordering with all images, returns the most similar top n image.

2. the method for a kind of image retrieval that decomposes based on sparse nonnegative matrix according to claim 1 is characterized in that described step 2) be:

1) from the first image data set D ₁Follow in the text and to extract label and constitute the first tag set T ₁, from the second image data set D ₂Follow in the text and to extract label and constitute the second tag set T ₂

2) the statistics first tag set T ₁With the second tag set T ₂In label at the first image data set D ₁With the second image data set D ₂Follow occurrence number in the text, only keep occurrence number greater than 10 times label, constitute the first tag set S after filtering ₁With the second tag set S after the filtration ₂, the first tag set S after the filtration ₁Radix be m ₁, the second tag set S after the filtration ₁Radix be m ₂

3) get the first tag set S after the filtration ₁With the second tag set S after the filtration ₂Common factor and the union common factor S that obtains two tag sets successively _jUnion S with two tag sets _u, the common factor S of two tag sets _jRadix be m _j, the union S of two tag sets _uRadix be m _u, the union S of two tag sets _uBe vocabulary.

3. the method for a kind of image retrieval that decomposes based on sparse nonnegative matrix according to claim 1 is characterized in that described step 3) is: according to the union S of two tag sets _u, at the first image data set D ₁Last structure first incidence matrix

At the second image data set D ₂Last structure second incidence matrix

M=m wherein _u, n ₁Be the first image data set D ₁The number of middle image, n ₂Be the second image data set D ₂The number of middle image, the corresponding label of each row of matrix, the corresponding document of each row of matrix, the first incidence matrix X ₁Element

Or the second incidence matrix X ₂Element

Press following assignment: as the first image data set D ₁Or the second image data set D ₂During j document of i label for labelling, assignment is 1; Otherwise assignment is 0.

4. the method for a kind of image retrieval that decomposes based on sparse nonnegative matrix according to claim 1 is characterized in that described step 4) is: utilize sparse nonnegative matrix to decompose the first incidence matrix X of Conjoint Analysis step 3) gained ₁With the second incidence matrix X ₂, the shared Sub space that obtains two incidence matrix is designated as w ₁₂, the first incidence matrix X ₁Independent subspace be designated as w ₁, the second incidence matrix X ₂Independent subspace w ₂, in matrix decomposition, above-mentioned three sub spaces are expressed as follows:

Represent the decomposition of data source level with capital W, H, represent the decomposition of subspace level, in view of the above, add the constraint of sparse property, can get the objective function that above-mentioned nonnegative matrix decomposes and be with lowercase w, h

$\underset{W_1,W_2,H_1,H_2\≥0}{\min }\frac{1}{2}\left\{\underset{i\∈\left\{\mathrm{1,2}\right\}}{\mathrm{\Σ}}{\mathrm{\λ}}_i\right\{{\left|\right|X_i-W_i{H}_i\left|\right|}_F^2+{\mathrm{\η}}_i{\left|\right|W_i\left|\right|}_F^2+{\mathrm{\β}}_i\underset{j=1}{\overset{n_i}{\mathrm{\Σ}}}{\left|\right|H_i(:,j)\left|\right|}_1^2\left\}\right\}---\left(2\right)$

Also can write

$\underset{h_{\mathrm{2,12}},h_{\mathrm{2,2}}\≥0}{\underset{h_{\mathrm{1,12}},h_{\mathrm{1,1}},}{\underset{w_{12},w_1,w_2,}{\min }}}\frac{1}{2}\left\{\underset{i\∈\left\{\mathrm{1,2}\right\}}{\mathrm{\Σ}}{\mathrm{\λ}}_i\right\{{\left|\right|X_i-\underset{v\∈S(2,i)}{\mathrm{\Σ}}{w}_v{h}_{i,v}\left|\right|}_F^2+{\mathrm{\η}}_i{\left|\right|w_{12}\left|w_i\right||}_F^2+{\mathrm{\β}}_i\underset{v\∈S(2,i)}{\mathrm{\Σ}}\underset{j=1}{\overset{n_i}{\mathrm{\Σ}}}{\left|\right|h_{i,v}(:,j)\left|\right|}_1^2\left\}\right\}---\left(3\right)$

H wherein _i(:, j) be H _iJ column vector, η _i＞0 in order to compression

Parameter, β _iThe＞0th, regularization parameter is in order to the degree of rarefication of equilibrium approximation accuracy and H matrix, wherein S (2,1) expression set 1,12}, S (2,2) expression set 2, and 12}, the objective function that adopts the following multi-source that decomposes based on sparse nonnegative matrix to utilize algorithm solution formula (2) and (3) defined nonnegative matrix to decompose:

Input: the matrix X that makes up on two image data sets ₁, X ₂, parameters R ₁, R ₂, k, η ₁, β ₁, η ₂, β ₂And threshold epsilon;

Output: share basic subspace w ₁₂, independently basic subspace w ₁, w ₂, and matrix of coefficients H ₁, H ₂

Step 1. is got

Wherein i ∈ 1,2};

Step 2. random initializtion w ₁₂, w ₁, w ₂, H ₁, H ₂

Step 3. is W fixedly _i(i.e. [w ₁₂| w _i]) utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{H_i}{\min }{\left|\right|\left(\begin{array}{c}{W}_i\\ \sqrt{{\mathrm{\β}}_i}{e}_{1\×R_i}\end{array}\right)H_i-\left(\begin{array}{c}{X}_i\\ 0_{1\×n_i}\end{array}\right)\left|\right|}_F^2,$ S.t.H _i〉=0 upgrades H _i, wherein i ∈ 1,2}, R _iIt is matrix W _iThe row dimension,

Element be 1,

Be null vector;

Step 4. is H fixedly ₁(promptly $\left[\begin{array}{c}{h}_{\mathrm{1,12}}\\ h_{\mathrm{1,1}}\end{array}\right]$ ), H ₂(promptly $\left[\begin{array}{c}{h}_{\mathrm{2,12}}\\ h_{\mathrm{2,2}}\end{array}\right]$ ), w ₁And w ₂Utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{w_{12}}{\min }{\left|\right|\left(\begin{array}{c}\sqrt{{\mathrm{\λ}}_1}{h}_{\mathrm{1,12}}^T\\ \sqrt{{\mathrm{\λ}}_1{\mathrm{\η}}_1}{I}_k\\ \sqrt{{\mathrm{\λ}}_2}{h}_{\mathrm{2,12}}^T\\ \sqrt{{\mathrm{\λ}}_2{\mathrm{\η}}_2}{I}_k\end{array}\right)w_{12}^T-\left(\begin{array}{c}\sqrt{{\mathrm{\λ}}_1}{(X_1-w_1{h}_{\mathrm{1,1}})}^T\\ 0_{k\×m}\\ \sqrt{{\mathrm{\λ}}_2}{(X_2-w_2{h}_{\mathrm{2,2}})}^T\\ 0_{k\×m}\end{array}\right)\left|\right|}_F^2,$ S.t.w ₁₂〉=0 upgrades w ₁₂, I wherein _kBe a k rank unit matrix, 0 _{K * m}Be the null matrix of a k * m, k is the dimension in shared Sub space;

Step 5. is H fixedly ₁(promptly $\left[\begin{array}{c}{h}_{\mathrm{1,12}}\\ h_{\mathrm{1,1}}\end{array}\right]$ ), H ₂(promptly $\left[\begin{array}{c}{h}_{\mathrm{2,12}}\\ h_{\mathrm{2,2}}\end{array}\right]$ ) and w ₁₂, utilize the least square method of nonnegativity restrictions to find the solution problem $\underset{w_i}{\min }{\left|\right|\left(\begin{array}{c}{h}_{i,i}^T\\ \sqrt{{\mathrm{\η}}_i}{I}_{R_i-k}\end{array}\right)w_i^T-\left(\begin{array}{c}(X_i-w_{12}{h}_{i,12})\\ 0_{(R_i-k)\×m}\end{array}\right)\left|\right|}_F^2,$ S.t.w _i〉=0 upgrades w _i, wherein

Be (R _i-k) rank unit matrix,

Be (R _i-k) * the m null matrix, i ∈ 1,2};

Step 6. iterative step 3 arrives step 5 until convergence.

5. the method for a kind of image retrieval that decomposes based on sparse nonnegative matrix according to claim 1 is characterized in that described step 5) is: adopts the following image retrieval algorithm based on sparse nonnegative matrix decomposition to carry out image retrieval:

Input: on target data set and auxiliary data collection, make up matrix X respectively ₁And X ₂, query vector q, the picture that needs retrieval to return is counted N;

Output: retrieval obtains maximally related top n picture, returns by the similarity descending;

Step 1. utilizes the multi-source that decomposes based on sparse nonnegative matrix to utilize algorithm, to matrix X ₁And X ₂Decompose and obtain X ₁=W ₁H ₁, X ₂=W ₂H ₂

Step 2. utilizes the least square method of nonnegativity restrictions to find the solution problem

S.t.h 〉=0 obtains q at basis matrix W ₁On mapping h;

Step 3. is for each pictures of target data set, such as r opens, and it is at basis matrix W ₁On mapping h _r(be matrix H ₁R column vector), can be by formula sim (h, h _r)=h ^Th _r/ || h|| ₂|| h _r|| ₂Calculate the similarity of this picture and query vector;

Step 4. is by all pictures of sequencing of similarity;

Step 5. descending returns maximally related preceding N pictures.

Images