CN114677550B - Rapid image pixel screening method based on sparse discrimination K-means - Google Patents
Rapid image pixel screening method based on sparse discrimination K-means Download PDFInfo
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Abstract
The invention relates to a rapid image pixel screening method based on sparse discrimination K-means, belonging to the fields of image recognition, classification and pattern recognition. Obtaining an optimal low-dimensional projection matrix through mutual iteration of the binarization tag and the low-dimensional projection matrix, and sorting according to the low-dimensional projection matrix rows and descending order so as to screen out important pixels containing key classification information; and obtaining low-dimensional new data after compression scale according to the filtered pixels. The image data preprocessing method can quickly compress the image data scale and retain key classification information, so that the processing efficiency of the subsequent image data is improved, the information characterization capability of the whole data is improved, and the verification is generally required by methods such as classification, clustering and the like.
Description
Technical Field
The invention relates to a rapid image pixel screening method based on sparse discrimination K-means, and belongs to the fields of image recognition, classification and pattern recognition.
Background
The application of high-dimensional data in many scientific fields is more and more popular, but only a small amount of internal dimensions (key information features) in the high-dimensional data contain important information of clustering and classifying tasks, so that the dimension reduction becomes a key technology for exploring the internal information of the high-dimensional data. The feature selection method removes redundant dimensions by screening out the most important, representative and informative feature subsets. Compared with the feature extraction method, the feature selection method retains the original structure of the data features, so that the screened data is more interpretable, and the subsequent data processing is facilitated. It follows that the feature selection method occupies a critical position in the preprocessing step of the image classification and text recognition task.
Recently, unsupervised embedded feature selection methods have received extensive attention from students, who guide subsequent sparse projection matrix optimization by obtaining pseudo tag indication matrices. The main method for obtaining the pseudo tag matrix is to introduce spectral embedding constraint, however, the existing unsupervised embedded feature selection method generally separates a graph learning process and a sparse matrix optimization process into two isolated sub-processes, which can lead to that the information characterization performance of the selected feature subset is directly affected by the graph learning quality. For example, a fixed pattern containing noise typically severely affects the performance of the feature selection method.
Zhou Wanying et al (sparse regression and manifold learning unsupervised feature selection algorithm, computer applied research, 2020, (09): 80-85.) propose an unsupervised feature selection method combining self-expression similarity matrix and manifold learning that performs both graph learning and sparse matrix optimization in a joint combinatorial optimization framework to improve feature selection performance. Although the proposed model considers comprehensive factors such as sparsity, alternate optimization and the like, parameters in the model are too many, the model is redundant, and the relation between the parameters and the performance cannot be balanced, so that the model is difficult to apply in practice, and the practical effect is poorer than that of the model in the invention. For example, when processing a Coil20 object image dataset with only 50 features using the K-means method, zhou Wanying et al propose methods with clustering accuracy and normalized mutual information of only 41.74% and 52.34%, whereas the corresponding indices of the proposed methods in the present invention are 61.74% and 73.39%, respectively, with a significant improvement of 20 and 21.05% respectively. The clustering accuracy and the normalized mutual information are common indexes for evaluating the performance of the selected feature subset, and the larger the value of the clustering accuracy and the normalized mutual information is, the stronger the information characterization capability representing the selected feature is.
Currently, in the field of image recognition, a great number of image pixels cause great difficulty in image classification and retrieval processes, and further, the processing efficiency is drastically reduced. The feature selection method can mine the internal dimension of the data containing important classification information, and reject the noise dimension which is useless and even contains redundant information, so that the image processing speed is improved. Aiming at a text recognition and image classification system, a graph learning and sparse projection matrix joint optimization framework is one of the mainstream feature selection methods, and the most important features are screened through embedded low-dimensional sparse projection and are completely reserved. The precision of image classification and recognition tasks is effectively improved under the influence of graph learning optimization. However, these methods have too many tunable parameters and too many constraints, which results in a complex combined optimization model, and their too high computational complexity may also result in overall inefficiency. Therefore, how to simultaneously improve feature selection efficiency and subset screening performance remains a challenge for embedded feature selection methods.
Disclosure of Invention
Technical problem to be solved
The existing embedded feature selection method guides the learning of a low-dimensional sparse projection matrix by acquiring a pseudo tag matrix, however, the continuous pseudo tag matrix obtained based on the relaxation problem of spectrum embedding deviates from the actual situation to a certain extent. Aiming at the problem, the invention provides an efficient feature selection method for image pixel screening, namely a rapid image pixel screening method based on sparse discrimination K mean value, which aims to directly optimize a binarization label and achieve the aim of promoting the binarization label and a low-dimensional projection matrix to each other, so that the information representation capability of a screened pixel subset is effectively improved.
Technical proposal
A rapid image pixel screening method based on sparse discrimination K-means is characterized by comprising the following steps:
step 1: elongating a dataset comprising n a x b pixel-scale images into an image data matrixWhere n is the number of images and d=a×b is the total number of pixels of a single image;
step 2: matrix by subtracting corresponding row mean value from each elementPerforming a centering process with respect to the pixel dimension such that the row sum of the processed data matrices is 0, i.e., X1 n =0, where 1 n Is an n-dimensional full 1 vector; recording the image data matrix after the centralization treatment as +.>
Step 3: on the X basis after the centralization treatment, adopting a discrimination K-means model based on a regression model to construct an objective function of a feature selection method so as to directly optimize a binary label; first, the formulation of the discrimination K-means model objective function based on the regression model is expressed as follows:
wherein,representing a low-dimensional projection matrix, c being the true category number,/->For each class of linear projection deviations, +.>A binarized label, i.e., ind (Index), representing each sample, with γ > 0 being the regularization parameter of the second term from left to right; as can be seen from equation (1), the matrix G satisfies the relationship G T G＝I c Wherein I c For a c-dimensional unit matrix, the column vectors in the matrix are orthogonal in pairs and are called a weighted cluster indication matrix, and the matrix aims to avoid meaningless solutions generated when Y and W are optimized simultaneously, namely W=O;
to perform the feature selection task, the F-norm in equation (1) is replaced with a sparse regularization term, l 2,p The norm is used to satisfy the row sparsity of the low-dimensional projection matrix W, and the objective function to be solved is expressed as follows:
step 4: alternately iterating and optimizing the objective function (2) constructed in the step 3;
step 5: the low-dimensional projection matrix W after the convergence of the objective function (2) can be obtained through the alternate optimization of Y, W and b in the step 4, and the 2 norm values of each row vector of the low-dimensional projection matrix W are calculated j || 2 And sorted in descending order; as can be seen from the sparse regularization term mentioned in step 3, the higher the sparseness of a certain line, that is, the smaller the 2-norm value of the line, the lower the importance of the pixel represented by the line; therefore, selecting the 2 normals with the larger h before the image according to the descending order of the sorting values to screen the most important h pixels; through the screening operation, a more refined image data matrix is finally obtainedIt can be seen that the remaining d-h pixels of the image dataset are all culled.
The step 4 is specifically as follows:
(1) fixing the binarized label Y, and updating the linear low-dimensional projection matrix W and the deviation b:
when Y is fixed, problem (2) is equivalent to:
the conversion into trace representation is as follows:
wherein,a d-dimensional diagonal matrix; the j (j is not less than 1 and not more than d) element U of U jj Is represented as follows
Wherein U is according to d-dimensional unit array I d Initial settings are made and ε is intended to prevent the optimization procedure from being performed as w j || 2 When zero, singular operation occurs;
therefore, the lagrangian function corresponding to the problem (4) is constructed as follows:
in order to find the optimal W and b, the bias of the function L (W, b) to both W and b variables needs to be zero, then:
note that the original image data matrix in step 2Is subjected to a centring treatment, i.e. X1 n =0, therefore, the operations of the formulas (7) and (8) can be simplified and the following optimum W can be obtained * And b * ：
W * ＝(XX T +γU) -1 XG (9)
Since the matrix U is closely related to W, W is obtained * Then, U is updated by the following formula (5);
(2) fixing the linear low-dimensional projection matrix W and the deviation b, and updating the binarization label Y:
when W and b are fixed, problem (2) is equivalent to:
by further simplification, formula (11) is equivalent to the following problem:
wherein, the constant matrixSince equation (12) is a discrete problem, it is converted into the following vector representation:
wherein y is i And m i The ith column vector of the matrix Y and M, respectively; aiming at the problem (13), adopting a coordinate descent method based on incremental calculation to solve the problem; more specifically, for the binarized tag Y, optimization is performed with a policy that updates one row to fix other rows, assuming that the jth row is fixed, i.e., for the jth image, then all elements of that row correspond to an increment T ji The expression is as follows:
based on the delta expression (14), for each image, the binarized label Y updates the label according to the row maximum delta, namely:
wherein,for updated binarizationThe label is provided with a label which is arranged on the surface of the label,<·>a logical indicator, a logical true value is 1, otherwise a logical true value is 0.
The epsilon is set to 2X 10 -16 。
Advantageous effects
The invention provides a rapid image pixel screening method based on sparse discrimination K-means, which has the beneficial effects that:
(1) The calculation complexity of the invention is linearly related to the number n of images, and the preprocessing efficiency of the image data is obviously improved. Therefore, the invention has stronger practicability in practical engineering application.
(2) According to the invention step 4(2), the invention is directly optimized for the binarized label Y in the alternate iteration algorithm, so that Y is closer to the real label, which can more effectively guide the learning of the low-dimensional projection matrix W in the alternate iteration process.
(3) The method provided by the invention has fewer model parameters, namely the sparse regularization parameter gamma and the norm parameter p, so that the model is simpler, and the parameters are easier to adjust. And l is introduced for W in inventive step 3 2,p Norms regularization term, generalized traditional l 2,1 And norms enable the generalization capability of the model in sparse screening to be stronger.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
FIG. 1 is a flow chart of a method for filtering pixels of an image;
fig. 2 is a flowchart of an implementation on a Coil20 object dataset.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention provides a rapid image pixel screening method based on sparse discrimination K-means, which comprises the following specific steps:
step 1: elongating a dataset comprising n a x b pixel-scale images into an image data matrixWhere n is the number of images and d=a×b is the total number of pixels for a single image. Obviously, the method aims at selecting h key pixels containing important classification information and simultaneously eliminating useless pixels, wherein h is the pixel screening quantity.
Step 2: for the image data matrix obtained in the last stepMatrix is +.>Performing a centering process with respect to the pixel dimension such that the row sum of the processed data matrices is 0, i.e., X1 n =0, where 1 n Is an n-dimensional all 1 vector. Recording the image data matrix after the centralization treatment as +.>This centralized approach helps to simplify subsequent computations.
Step 3: on the X basis after the centralization treatment, adopting a discrimination K-means model based on a regression model to construct an objective function of a feature selection method so as to directly optimize the binary label. First, the formulation of the discrimination K-means model objective function based on the regression model is expressed as follows:
wherein,representing a low-dimensional projection matrix, c being the true category number,/->For each class of linear projection deviations, +.>Representing the binarized label, i.e., ind (Index), for each sample, γ > 0 is the regularization parameter for the second term from left to right. As can be seen from equation (1), the matrix G satisfies the relationship G T G＝I c Wherein I c For a c-dimensional unit matrix, the column vectors within the matrix are orthogonal two by two and are therefore referred to as a weighted cluster indication matrix, which is intended to avoid meaningless solutions, i.e., w=o, that occur when Y and W are simultaneously optimized.
To perform the feature selection task, the F-norm in equation (1) is replaced with a sparse regularization term, l 2,p The norm is such that the line sparsity of the low-dimensional projection matrix W is satisfied, and therefore the objective function to be solved by the present invention is expressed as follows:
step 4: and (5) alternately iterating and optimizing the objective function (2) constructed in the step 3.
(1) Fixing the binarized label Y, and updating the linear low-dimensional projection matrix W and the deviation b:
when Y is fixed, problem (2) is equivalent to:
the conversion into trace representation is as follows:
wherein,is a d-dimensional diagonal matrix. The j (j is not less than 1 and not more than d) element U of U jj Is represented as follows
Wherein U is according to d-dimensional unit array I d Initial settings are made and ε is intended to prevent the optimization procedure from being performed as w j || 2 Singular operations occur when zero.
Therefore, the lagrangian function corresponding to the problem (4) is constructed as follows:
in order to find the optimal W and b, the bias of the function L (W, b) to both W and b variables needs to be zero, then:
note that the original image data matrix in step 2Is subjected to a centring treatment, i.e. X1 n =0, therefore, the operations of the formulas (7) and (8) can be simplified and the following optimum W can be obtained * And b * ：
W * ＝(XX T +γU) -1 XG (24)
Since the matrix U is closely related to WAfter obtaining W * After that, U also needs to be updated by the formula (5).
(2) Fixing the linear low-dimensional projection matrix W and the deviation b, and updating the binarization label Y:
when W and b are fixed, problem (2) is equivalent to:
by further simplification, formula (11) is equivalent to the following problem:
wherein, the constant matrixSince equation (12) is a discrete problem, it is converted into the following vector representation:
wherein y is i And m i The ith column vector of matrices Y and M, respectively. The problem (13) is solved by adopting a coordinate descent method based on incremental calculation. More specifically, for the binarized tag Y, optimization is performed with a policy that updates one row to fix other rows, assuming that the jth row (for the jth image) is fixed, then all elements of that row correspond to an increment T ji The expression is as follows:
based on the delta expression (14), for each image, the binarized label Y updates the label according to the row maximum delta, namely:
wherein,in order to update the binary label,<·>a logical indicator, a logical true value is 1, otherwise a logical true value is 0.
Step 5: the low-dimensional projection matrix W after the convergence of the objective function (2) can be obtained through the alternate optimization of Y, W and b in the step 4, and the 2 norm values of each row vector of the low-dimensional projection matrix W are calculated j || 2 And ordered in descending order. As can be seen from the sparse regularization term mentioned in step 3, the higher the sparseness of a certain line, i.e. the smaller the 2 norm value of the line, the lower the importance of the pixel represented by the line. Therefore, the 2 normals with the largest h before the image are selected according to the descending order of the ranking values to screen the most important h pixels. Through the screening operation, a more refined image data matrix is finally obtainedIt can be seen that the remaining d-h pixels of the image dataset are all culled.
In the embodiment, as shown in fig. 2, the specific implementation steps of the proposed method for screening key pixels are described by taking an object image data set Coil20 as an example, and the object image data set Coil20 includes 1440 object images with pixel sizes of 32×32, and total 20 objects. The dataset was obtained by taking a picture every 5 degrees horizontally for each object until it was horizontally wrapped around a circle, i.e. 72 images per object, for a total of 1440 images.
Step 1 is implemented: stretching and integrating 1440 images into an image data matrixWhere 1024=32×32 is the total number of pixels of a single image of Coil 20;
step 2 is implemented: for the image data matrix obtained in the last stepBy using eachElement minus corresponding row mean pair ++>Performing a centering process with respect to the pixel dimension such that the row sum of the data matrix is 0, i.e., X1 1440 =0. Recording the image data matrix after the centralization treatment as +.>
Implementing the step 3: randomly initializing a binarized tag based on an image data matrix XInitializing u=i 1024 And giving regularization parameter gamma and norm parameter p;
and 4, implementing the following steps: by g=y (Y T Y) -1/2 Calculating a weighting cluster indication matrix G;
implementing the step 5: fixed G, updating the low-dimensional projection matrix W and the projection deviation b by the following expression:
W * ＝(XX T +γU) -1 XG (31)
implementing step 6: w obtained according to the previous step * Updating the diagonal matrix U:
wherein ε is typically 2×10 -16 ；
Step 7 is implemented: computing a matrix
Implementing step 8: fixing W and b, and sequentially calculating the increment of the row of the corresponding image according to the original image:
wherein y is i And m i The ith column vector of matrices Y and M, respectively. Thus, the optimal solutionCan be obtained by the following formula:
wherein < · > is a logical indicator, logical true then the value is 1, otherwise 0.
Implementing step 9: circularly executing the steps 4 to 8 until the value of the objective function (2) is converged, and outputting a low-dimensional projection matrixThe row vector of the method can represent the importance degree of the corresponding pixels of the original object image. Therefore, 2-range values of the row vectors are calculated and sorted in descending order, pixels corresponding to the first h values are selected as key pixels in the original 1024 pixels, and refined image data +_ is finally obtained>
The validity and importance of the screening image pixels when h=50 of the invention were verified using a K-means clustering method. Then the invention selects 50 most important pixels from 1024 pixels in the Coil20 data set to obtain refined image dataPerforming 10 repeated experiments on X' by adopting a K-means clustering method, and recording the mean value and standard deviation of clustering accuracy, wherein the mean value and the standard deviation are 61.47% and 3.17% respectively; if the original image dataset remains for all pixels +.>The K-means clustering method is adopted to execute 10 repeated experiments, and the average value and standard deviation of clustering accuracy are 57.62% and 5.51% respectively. Therefore, the image screening method provided by the invention not only improves the clustering precision of the image data, but also greatly compresses the data scale despite eliminating a large number of pixel characteristics in the original image data, and verifies the effectiveness of the method.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made without departing from the spirit and scope of the invention.
Claims (3)
1. A rapid image pixel screening method based on sparse discrimination K-means is characterized by comprising the following steps:
step 1: elongating a dataset comprising n a x b pixel-scale images into an image data matrixWhere n is the number of images and d=a×b is the total number of pixels of a single image;
step 2: matrix by subtracting corresponding row mean value from each elementPerforming a centering process with respect to the pixel dimension such that the row sum of the processed data matrices is 0, i.e., X1 n =0, where 1 n Is an n-dimensional full 1 vector; recording the image data matrix after the centralization treatment as +.>
Step 3: on the X basis after the centralization treatment, adopting a discrimination K-means model based on a regression model to construct an objective function of a feature selection method so as to directly optimize a binary label; first, the formulation of the discrimination K-means model objective function based on the regression model is expressed as follows:
wherein,representing a low-dimensional projection matrix, c being the true category number,/->For each class of linear projection deviations, +.>A binarized label, i.e., ind (Index), representing each sample, with γ > 0 being the regularization parameter of the second term from left to right; as can be seen from equation (1), the matrix G satisfies the relationship G T G＝I c Wherein I c For a c-dimensional unit matrix, the column vectors in the matrix are orthogonal in pairs and are called a weighted cluster indication matrix, and the matrix aims to avoid meaningless solutions generated when Y and W are optimized simultaneously, namely W=O;
to perform the feature selection task, the F-norm in equation (1) is replaced with a sparse regularization term, l 2,p The norm is used to satisfy the row sparsity of the low-dimensional projection matrix W, and the objective function to be solved is expressed as follows:
step 4: alternately iterating and optimizing the objective function (2) constructed in the step 3;
step 5: the low-dimensional projection matrix W after the convergence of the objective function (2) can be obtained through the alternate optimization of Y, W and b in the step 4, and the 2 norm values of each row vector of the low-dimensional projection matrix W are calculated j || 2 And sorted in descending order; as can be seen from the sparse regularization term mentioned in step 3, the higher the sparseness of a certain line, that is, the smaller the 2-norm value of the line, the lower the importance of the pixel represented by the line; therefore, selecting the 2 normals with the larger h before the image according to the descending order of the sorting values to screen the most important h pixels; through the screening operation, a more refined image data matrix is finally obtainedIt can be seen that the remaining d-h pixels of the image dataset are all culled.
2. The rapid image pixel screening method based on sparse discriminant K-means of claim 1, wherein step 4 is specifically as follows:
(1) fixing the binarized label Y, and updating the linear low-dimensional projection matrix W and the deviation b:
when Y is fixed, problem (2) is equivalent to:
the conversion into trace representation is as follows:
wherein,a d-dimensional diagonal matrix; the j (j is not less than 1 and not more than d) element U of U jj Is represented as follows
Wherein U is according to d-dimensional unit array I d Initial settings are made and ε is intended to prevent the optimization procedure from being performed as w j || 2 When zero, singular operation occurs;
therefore, the lagrangian function corresponding to the problem (4) is constructed as follows:
in order to find the optimal W and b, the bias of the function L (W, b) to both W and b variables needs to be zero, then:
note that the original image data matrix in step 2Is subjected to a centring treatment, i.e. X1 n =0, therefore, the operations of the formulas (7) and (8) can be simplified and the following optimum W can be obtained * And b * ：
W * ＝(XX T +γU) -1 XG (9)
Since the matrix U is closely related to W, W is obtained * Then, U is updated by the following formula (5);
(2) fixing the linear low-dimensional projection matrix W and the deviation b, and updating the binarization label Y:
when W and b are fixed, problem (2) is equivalent to:
by further simplification, formula (11) is equivalent to the following problem:
wherein, the constant matrixSince equation (12) is a discrete problem, it is converted into the following vector representation:
wherein y is i And m i The ith column vector of the matrix Y and M, respectively; aiming at the problem (13), adopting a coordinate descent method based on incremental calculation to solve the problem; more specifically, for the binarized tag Y, optimization is performed with a policy that updates one row to fix other rows, assuming that the jth row is fixed, i.e., for the jth image, then all elements of that row correspond to an increment T ji The expression is as follows:
based on the delta expression (14), for each image, the binarized label Y updates the label according to the row maximum delta, namely:
wherein,in order to update the binary label,<·>a logical indicator, a logical true value is 1, otherwise a logical true value is 0.
3. The method for rapidly screening image pixels based on sparse discriminant K-means of claim 2, wherein ε is set to 2×10 -16 。
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| WO2019174377A1 (en) * | 2018-03-14 | 2019-09-19 | 大连理工大学 | Monocular camera-based three-dimensional scene dense reconstruction method |
| CN110364264A (en) * | 2019-06-24 | 2019-10-22 | 南京理工大学 | Medical data collection feature dimension reduction method based on sub-space learning |
| CN113869454A (en) * | 2021-10-12 | 2021-12-31 | 西北工业大学 | Hyperspectral image sparse feature selection method based on fast embedded spectral analysis |
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