CN111797911A - Image data multi-label classification method - Google Patents
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Abstract
The invention discloses a multi-label classification method for image data, which comprises the steps of firstly constructing a topological relation of pictures, and then solving the problem of semi-supervised multi-label learning (SSML) by using a multi-label propagation algorithm (CMLP) based on cooperation so as to obtain a confidence matrix of unmarked pictures
Description
Technical Field
The invention relates to the field of machine learning, in particular to a multi-label classification method for image data.
Background
Image classification is one of the most widely used machine learning problems. In real-world image classification applications, an image instance is often associated with multiple labels, and there is a correlation between the labels. Therefore, classifying images with multiple associated labels is an important research task. In the conventional picture label classification problem, a common assumption is that each picture in the training data set is accurately labeled. Unfortunately, in many real world problems, although a vast number of images are readily available, the labeling of the images requires an expensive and time-consuming manual labeling process to obtain.
For this reason, a semi-supervised learning method is proposed, in which a large number of unlabeled images are added to a limited number of labeled images and trained together, so as to improve the performance of the classifier. The label propagation method is a semi-supervised classification learning method based on a graph. However, when an image instance has multiple correlated labels, simple label propagation does not make good use of the correlation, resulting in a degradation of classification performance.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a multi-label classification method for image data.
The purpose of the invention is realized by the following technical scheme: a multi-label classification method for image data comprises the following steps:
(1) acquiring a picture set D ═ { pic) to be classifiediI is more than or equal to 1 and less than or equal to n, wherein n is the total number of the pictures in the picture set D; in the picture set D, each picture has q ordered tags to be marked, and totally l pictures are marked whether to have the q tags or not, wherein the marked pictures are pici,1≤i≤l;
(2) Calculating a weight matrix W and constructing a graph relation between pictures, wherein the step comprises the following substeps:
(2.1) inputting the pictures in the picture set into the trained convolutional neural network VGG Net, and acquiring the feature vector set of the pictures from the outputV={xiI is more than or equal to 1 and less than or equal to n, wherein xiIs a picture piciThe output obtained by inputting the convolutional neural network is a p-dimensional column vector;
(2.2) selecting a hyper-parameter k, and calculating a feature vector x according to the picture feature vector set ViK neighbor set kNN (x)i),kNN(xi) Is the picture feature vector set V and the feature vector xiA set of k picture feature vectors with the minimum Euclidean distance;
for non-negative weight matrix W ═ Wij]n×nIt is required to satisfy:
wii=0
wij≥0,j≠i,xj∈kNN(xi)
(2.3) feature vector x for each pictureiIs linearly reconstructed into sigma by other picture characteristic vectorsj≠iwijxjThe trade-off parameter θ is chosen, and the linear reconstruction error of the weight matrix W is defined as follows:
wherein | · | purple2A two-norm representing a matrix;
minimizing the linear reconstruction error (W) by using a constrained least square programming method, and establishing the following minimization model:
s.t.wii=0
wij≥0,j≠i,xj∈kNN(xi)
j=1,2,...,n
wherein, w·jIs the jth column vector of W, GjDenotes w·jCorresponding n rows and n columns of gray matrix, GjThe a-th row and the b-th column of the element (x)j-xa)′(xj-xb) V' denotes the transpose of a certain vector v;
solving the minimized model by an active set method of a convex quadratic programming problem to obtain a non-negative weight matrix W, thereby constructing a graph relation between pictures;
(3) solving semi-supervised multi-tag learning (SSML) problems with a collaboration-based multi-tag propagation algorithm (CMLP) to obtain a confidence matrix for unmarked picturesThe method comprises the following substeps:
(3.1) obtaining the propagation matrix P by normalizing the weight matrix W:
wherein D ═ diag { D ═ D1,d2,…,dnIs the diagonal matrix, the ith diagonal element of matrix D is Thus, the propagation matrix P is obtained by normalizing the weight matrix W, and the labels of the pictures with similar characteristics are also similar;
constructing an object matrix Y of the marked picture as Yij]l×qThe following were used:
yij1, picture piciHaving the jth label
yij1, picture piciWithout jth tag
Selecting a cooperation degree parameter alpha and a regularization parameter gamma, and calculating a correlation matrix R ═ Rij]q×q:
Wherein, y·j,r·jDenotes Y, the jth column of R, I denotes a q × q identity matrix,is thatTransposed matrix of (1), Ol×1Is a zero column vector of dimension l; a plurality of labels in the image often have certain correlation, for example, the labels "have the sun" and "are sunny days" have strong correlation; by calculating the correlation matrix, the invention extracts the correlation; when the classification task has a plurality of related labels, the related matrix provides a powerful tool for improving the accuracy of the prediction result;
(3.2) by iteratively updating F and Z alternately, the following loss function is minimized:
where F is the model output, F' is the transposed matrix of F, FlIs a matrix formed by the first row of the matrix F, represents the prediction result of the model on the marked image, Z is an intermediate variable of the model, P is a propagation matrix obtained in (2.1), the matrix Q is (1-alpha) I + alpha R, R is a correlation matrix obtained in (2.1), alpha is a cooperation degree parameter selected in (2.1), mu and lambda are balance parameters, tr is a trace function of the matrix, | | | | | I |, andFis the F-norm of the matrix;
initializing model output F by using the target matrix Y obtained in (2.1)0And intermediate variable Z0:
Z0=Y
Wherein, O(n-l)×qA zero matrix that is (n-l) xq;
selecting a hyper-parameter learning rate beta and an iteration number T, and outputting F to the initialized model0And intermediate variable Z0Updating to obtain FtAnd ZtThe iterative update formula is as follows:
wherein,is a matrix Ft+1The matrix formed by the first row, and Q' is a transposed matrix of the matrix Q;
by bringing the correlation matrix into the iteration process, the method makes full use of the correlation among the labels, considers the prediction of each label on other labels, and improves the accuracy of the prediction result;
when T iterations are finished, obtaining model output F ═ FT;
(3.3) converting the model output F to a final prediction:
E=FuQ=[eij](n-l)×q
wherein, FuIs the matrix formed by the l +1 th row to the n th row of the matrix F, Q is the matrix used in the iteration in (2.2), Ψ is the post-processing operator:
wherein sgn is a sign function;
obtaining a predicted result whenThen, the (q) th label is not on the (i + l) th picture; when in useThen, the (q) th label is arranged on the (i + l) th picture; when in useIn time, whether the q label is uncertain exists on the (i + l) th picture or not is determined.
The invention has the beneficial effects that: the invention solves the problem that the simple label propagation method can not utilize the correlation among a plurality of labels of the multi-label image data, introduces a correlation matrix in the iterative process of label propagation, only propagates the independent part of each label in the iterative process, considers the prediction of the label on the label when outputting the final label prediction result, also absorbs the prediction results of other labels on the label, fully utilizes the correlation among the labels and improves the accuracy of multi-label classification.
Detailed Description
Set of pictures to be classified D ═ { piciI is more than or equal to 1 and less than or equal to n, wherein n is the total number of the pictures in the picture set D. In the picture set D, each picture has q ordered tags to be marked, and totally l pictures are marked whether to have the q tags or not, wherein the marked pictures are pici,1≤i≤l。
(1) Calculating a weight matrix W and constructing a graph relation between pictures, wherein the step comprises the following substeps:
(1.1) Using the public data set ImageNet on the website http:// www.image-net.org/the convolutional neural network VGG Net proposed in the paper was trained according to the method provided by 3.1 in the paper VERY DEEP CONVOLUTIONAL NETWORKS FOR LARGE-SCALE IMAGE RECOGNITION, co-published in 2015 by KarenSimnyan and Andrew Zisserman. VGG Net is a visual geometry group and valley of Oxford universityResearchers of the song deep mind company research and develop together, and feature vectors of pictures required by classification can be well extracted. Inputting the pictures in the picture set into a trained convolutional neural network, and acquiring a feature vector set V ═ x of the pictures from the outputiI is more than or equal to 1 and less than or equal to n, wherein xiIs a picture piciThe output obtained by inputting the convolutional neural network is a p-dimensional column vector;
(1.2) firstly selecting a hyper-parameter k, and calculating a feature vector x according to the picture feature vector set ViK neighbor set kNN (x)i),kNN(xi) Is the picture feature vector set V and the feature vector xiA set of k picture feature vectors with the minimum Euclidean distance;
for the weight matrix W ═ Wij]n×nIt is required to satisfy:
wii=0
wij≥0,j≠i,xj∈kNN(xi)
under such constraints, the weight matrix W is sparse, which may speed up training.
(1.3) feature vector x for each pictureiIs linearly reconstructed into sigma by other picture characteristic vectorsj≠iwijxjThe trade-off parameter θ is chosen, and the linear reconstruction error of the weight matrix W is defined as follows:
wherein | · | purple2A two-norm representing a matrix;
minimizing the linear reconstruction error (W) by using a constrained least square programming method, and establishing the following minimization model:
s.t.wii=0
wij≥0,j≠i,xj∈kNN(xi)
j=1,2,...,n
wherein, w·jIs the jth column vector of W, W'·jIs w·jTransposed vector of (1), GjDenotes w·jCorresponding n rows and n columns of gray matrix, GjThe a-th row and the b-th column of the element (x)j-xa)′(xj-xb);
The non-negative weight matrix W can be obtained by solving the above minimization model by the active set method of the convex quadratic programming problem with reference to the Numerical Optimization (Second Edition) book 16.5, thereby constructing the graph relationship between the pictures.
(2) Solving semi-supervised multi-tag learning (SSML) problems with a collaboration-based multi-tag propagation algorithm (CMLP) to obtain a confidence matrix for unmarked picturesThe method comprises the following substeps:
(2.1) obtaining the propagation matrix P by normalizing the weight matrix W:
wherein D ═ diag { D ═ D1,d2,…,dnIs the diagonal matrix, the ith diagonal element of matrix D is Thus, the propagation matrix P is obtained by normalizing the weight matrix W, and the labels of the pictures with similar characteristics are also similar;
constructing tagged picturesIs given as the target matrix Y ═ Yij]l×qThe following were used:
yij1, picture piciHaving the jth label
yij1, picture piciWithout jth tag
Selecting a cooperation degree parameter alpha and a regularization parameter gamma, and calculating a correlation matrix R ═ Rij]q×q:
Wherein, y·j,r·jDenotes Y, the jth column of R, I denotes a q × q identity matrix,is thatTransposed matrix of (1), Ol×1Is a zero column vector of dimension l. The labels in the image often have a certain correlation, for example, the labels "have the sun" and "are sunny" have a strong correlation. The invention extracts this correlation by computing a correlation matrix. When the classification task has a plurality of related labels, the related matrix provides a powerful tool for improving the accuracy of the prediction result.
(2.2) by iteratively updating F and z alternately, the following loss function is minimized:
where F is the model output, F' is the transposed matrix of F, FlIs a matrix formed by the first row of the matrix F, represents the prediction result of the model on the marked image, Z is an intermediate variable of the model, P is a propagation matrix obtained in (2.1), the matrix Q is (1-alpha) I + alpha R, and R is in (2.1)The obtained correlation matrix, alpha is the cooperation degree parameter selected in (2.1), mu and lambda are balance parameters, tr (-) is the trace function of the matrix, | | |FIs the F-norm of the matrix.
Initializing model output F by using the target matrix Y obtained in (2.1)0And intermediate variable Z0:
Z0=Y
Wherein, O(n-l)×qIs a zero matrix of (n-l) × q.
Selecting a hyper-parameter learning rate beta and an iteration number T, and outputting F to the initialized model0And intermediate variable Z0Updating to obtain FtAnd ZtThe iterative update formula is as follows:
By incorporating the correlation matrix into the iterative process, the method makes full use of the correlation among the labels, considers the prediction of each label on other labels, and improves the accuracy of the prediction result.
When T iterations are finished, obtaining model output F ═ FT;
(2.3) converting the model output F to a final prediction:
E=FuQ=[eij](n-l)×q
wherein, FuIs a matrix formed by the l +1 th to n th rows of the matrix F, Q is the matrix used in (2.2), Ψ is the post-processing operator:
where sgn is a sign function.
Claims (1)
1. A multi-label classification method for image data is characterized by comprising the following steps: the method comprises the following steps:
(1) acquiring a picture set D ═ { pic) to be classifiediI is more than or equal to 1 and less than or equal to n, wherein n is the total number of the pictures in the picture set D. In the picture set D, each picture has q ordered tags to be marked, and totally l pictures are marked whether to have the q tags or not, wherein the marked pictures are pici,1≤i≤l。
(2) Calculating a weight matrix W and constructing a graph relation between pictures, wherein the step comprises the following substeps:
(2.1) inputting the pictures in the picture set into the trained convolutional neural network VGG Net, and acquiring the feature vector set V of the pictures from the output, wherein the feature vector set V is { x }iI is more than or equal to 1 and less than or equal to n, wherein xiIs a picture piciThe output obtained by inputting the convolutional neural network is a p-dimensional column vector;
(2.2) selecting a hyper-parameter k, and according to the picture feature vector set VComputing a feature vector xiK neighbor set kNN (x)i),kNN(xi) Is the picture feature vector set V and the feature vector xiA set of k picture feature vectors with the minimum Euclidean distance;
for non-negative weight matrix W ═ Wij]n×nIt is required to satisfy:
wii=0
wij≥0,j≠i,xj∈kNN(xi)
(2.3) feature vector x for each pictureiIs linearly reconstructed into sigma by other picture characteristic vectorsj≠iwijxjThe trade-off parameter θ is chosen, and the linear reconstruction error of the weight matrix W is defined as follows:
wherein | · | purple2A two-norm representing a matrix;
minimizing the linear reconstruction error (W) by using a constrained least square programming method, and establishing the following minimization model:
s.t.wii=0
wij≥0,j≠i,xj∈kNN(xi)
j=1,2,...,n
wherein, w·jIs the jth column vector of W, GjDenotes w·jCorresponding n rows and n columns of grayMatrix, GjThe a-th row and the b-th column of the element (x)j-xa)′(xj-xb) V' denotes the transpose of a certain vector v;
solving the minimized model by an active set method of a convex quadratic programming problem to obtain a non-negative weight matrix W, thereby constructing a graph relation between pictures.
(3) Solving semi-supervised multi-tag learning (SSML) problems with a collaboration-based multi-tag propagation algorithm (CMLP) to obtain a confidence matrix for unmarked picturesThe method comprises the following substeps:
(3.1) obtaining the propagation matrix P by normalizing the weight matrix W:
wherein D ═ diag { D ═ D1,d2,…,dnIs the diagonal matrix, the ith diagonal element of matrix D is Thus, the propagation matrix P is obtained by normalizing the weight matrix W, and the labels of the pictures with similar characteristics are also similar;
constructing an object matrix Y of the marked picture as Yij]l×qThe following were used:
yij1, picture piciHaving the jth label
yij1, picture piciWithout jth tag
Selecting a cooperation degree parameter alpha and a regularization parameter gamma, and calculating a correlation matrix R ═ Rij]q×q:
Wherein, y·j,r·jDenotes Y, the jth column of R, I denotes a q × q identity matrix,is thatTransposed matrix of (1), Ol×1Is a zero column vector of dimension l. The labels in the image often have a certain correlation, for example, the labels "have the sun" and "are sunny" have a strong correlation. The invention extracts this correlation by computing a correlation matrix. When the classification task has a plurality of related labels, the related matrix provides a powerful tool for improving the accuracy of the prediction result.
(3.2) by iteratively updating F and Z alternately, the following loss function is minimized:
where F is the model output, F' is the transposed matrix of F, FlIs a matrix formed by the first row of the matrix F, represents the prediction result of the model on the marked image, Z is an intermediate variable of the model, P is a propagation matrix obtained in (2.1), the matrix Q is (1-alpha) I + alpha R, R is a correlation matrix obtained in (2.1), alpha is a cooperation degree parameter selected in (2.1), mu and lambda are balance parameters, tr is a trace function of the matrix, | | | | | I |, andFis the F-norm of the matrix.
Initializing model output F by using the target matrix Y obtained in (2.1)0And intermediate variable Z0:
Z0=Y
Wherein, O(n-l)×qIs a zero matrix of (n-l) × q.
Selecting a hyper-parameter learning rate beta and an iteration number T, and outputting F to the initialized model0And intermediate variable Z0Updating to obtain FtAnd ZtThe iterative update formula is as follows:
By incorporating the correlation matrix into the iterative process, the method makes full use of the correlation among the labels, considers the prediction of each label on other labels, and improves the accuracy of the prediction result.
When T iterations are finished, obtaining model output F ═ FT;
(3.3) converting the model output F to a final prediction:
E=FuQ=[eij](n-l)×q
wherein, FuIs the matrix formed by the l +1 th row to the n th row of the matrix F, Q is the matrix used in the iteration in (2.2), Ψ is the post-processing operator:
where sgn is a sign function.
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