CN114821181A - Image classification method - Google Patents
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Abstract
The invention relates to an image classification method, firstly, extracting the characteristics of original image data to obtain the characteristic data of the original image, and generating a representative anchor point in the characteristic data by adopting a K-Means algorithm; secondly, establishing a correlation matrix between the anchor points and the data points by adopting a probability neighbor-based method, and obtaining a similarity matrix between the data points; and finally, obtaining a discrete class indication matrix according to the corresponding relation between the neighbor graph and the class indication matrix by adopting a coordinate ascending method. The method selects representative anchor points, constructs a two-step graph between the anchor points and the sample points, and constructs a neighbor graph between the sample points, thereby reducing the calculation amount of excavating neighbor relation between images. And (3) directly solving a label matrix in a clustering algorithm by adopting a coordinate ascending method to directly obtain an image classification result, and accelerating the calculation speed of image classification.
Description
Technical Field
The invention belongs to the field of image classification and machine learning, and particularly relates to an image classification method.
Background
Clustering algorithms are one of the important research subjects in the field of machine learning, and have been widely used in the fields of pattern recognition, data analysis, image processing, and the like. In image classification, image data is firstly subjected to feature extraction, and common image features include color features, shape features, texture features, edge features, features obtained through a neural network and the like. Along with the development of acquisition equipment, more and more data are acquired, so that data annotation is difficult and high in cost. The clustering algorithm reveals the intrinsic properties and rules of data by learning the unlabeled data and divides the data into different clusters, so that the same types are as identical as possible and the different types are as different as possible. By utilizing the advantage of no need of labels, the clustering algorithm is widely applied to image classification. The spectral clustering is a typical clustering algorithm and mainly comprises two steps, firstly, a neighbor graph is established according to the distance between data, a low-dimensional indication matrix is obtained by carrying out eigenvalue decomposition on a Laplacian matrix based on the neighbor graph, and since the low-dimensional indication matrix possibly contains negative values and can not represent the sample class, the low-dimensional indication matrix needs to be subjected to K-Means clustering or spectral rotation again to obtain a final discrete class indication matrix. However, the computation complexity is high when feature decomposition is performed, and the K-Means clustering performed on the low-dimensional indication matrix again may affect the real category of the sample point, increase the computation complexity, and be difficult to compute and expand on large-scale data.
Aiming at the two problems, Ni Zhongyuan and Liu Jing Rele (Ni Zhongyuan, Liu Jing Rele. fast spectral clustering based on graph filtering [ J/OL ]. Shanxi university school newspaper (nature science edition): 1-14[2022-01-22]. DOI:10.13451/j.sxu.ns.2021058.) provide a fast spectral clustering algorithm based on graph filtering, which overcomes the difficulty of feature decomposition of a Laplace matrix by generating a pseudo feature vector, reduces the data scale by a sampling method and accelerates the subsequent K-Means clustering calculation process. Although the time complexity of spectral clustering is improved and errors are reduced by using an optimization process, the main calculation process of spectral clustering is still maintained, only relevant steps are optimized, and the original structure of data can be changed due to the adoption of a sampling method to reduce the data size.
Disclosure of Invention
Technical problem to be solved
The invention provides an image classification method, which can solve the problem that the existing unsupervised learning method has high calculation complexity when applied to an image classification task, and aims to solve the problems that the eigenvalue decomposition calculation amount in the existing spectral clustering algorithm is too large, and a class indication matrix cannot be directly obtained and cannot be better applied to image classification.
Technical scheme
An image classification method is characterized by comprising the following steps:
s1: inputting a classified image;
s2: extracting image features to obtain feature data
Wherein x is i Is the ith data point, d is the dimension of the feature, and n is the number of image data points;
s3: selecting m anchor points by adopting a balance K mean value method of variable anchor point numbers to obtain an anchor point set U;
s4: constructing a similarity matrix A between data points according to the anchor points;
s5: constructing a model according to the similarity matrix A and the label relation;
s6: and solving the model by adopting a coordinate ascending method to obtain a label of the characteristic data, and finishing image classification.
The further technical scheme of the invention is as follows: the step S4 is divided into the following two steps:
s41: constructing a correlation relation matrix B between the data points and the anchor points by adopting a similarity self-learning method;
s42: and calculating to obtain a sample neighbor graph A and a similarity matrix A according to the correlation matrix B.
The further technical scheme of the invention is as follows: the method for constructing the correlation matrix between the data points and the anchor points by adopting the similarity self-learning method comprises the following specific steps:
obtaining a correlation matrix B between the data point X and the anchor point U by a similarity self-learning method,
a correlation relation matrix between the sample point and the anchor point is obtained; for the ith sample point, the model is as follows:
wherein, b ij Is the ith row and jth column element in B,
in row i of B, γ is a regularization coefficient. Is provided with
Is the euclidean distance between the ith sample point and the jth anchor point,
is a vector whose j-th element is k ij Then the above optimization problem can be written in the form of a vector as follows
Let b be i In which there are l (l is less than or equal to m) non-zero elements, for k i Reordering is performed, assuming after the ordering
Corresponding to b i Is composed of
Then
Is expressed as
The invention further adopts the technical scheme that: calculating according to the correlation matrix B to obtain a sample neighbor graph A, wherein the similarity matrix A is as follows:
after B is obtained, the similarity between the sample points is constructed through the similarity between the sample points and the anchor points
A＝BΔ -1 B T
Wherein the content of the first and second substances,
is a diagonal matrix whose i-th element is calculated as
Order to
At this time
A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the above-described method.
A computer-readable storage medium having stored thereon computer-executable instructions for performing the above-described method when executed.
A computer program comprising computer executable instructions which when executed perform the method described above.
Advantageous effects
Firstly, carrying out feature extraction on original image data to obtain feature data of the original image, and generating representative anchor points in the feature data by adopting a balanced K-means method with variable anchor point number; secondly, establishing a correlation matrix between the anchor points and the data points by adopting a probability neighbor-based method, and obtaining a similarity matrix between the data points; and finally, obtaining a discrete class indication matrix according to the corresponding relation between the neighbor graph and the class indication matrix by adopting a coordinate ascending method.
Compared with the prior art, the invention has the following beneficial effects:
(1) by selecting representative anchor points and constructing a two-step graph between the anchor points and the sample points, a neighbor graph between the sample points is constructed, so that the calculation amount of mining neighbor relations between images is reduced.
(2) And (3) directly solving the label matrix in the clustering algorithm by adopting a coordinate ascending method to directly obtain an image classification result, so that the calculation speed of image classification is accelerated.
(3) The method has a linear relationship between the calculation complexity and the number of samples, and is suitable for the classification of large-scale image data.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a flow chart of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the respective embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention relates to an image classification method, a basic flow chart of which is shown in figure 1, and the method comprises the following specific steps:
step 1: generating representative anchor points
Assume that the image corresponds to feature data of
Wherein x is i Is the ith data point, d is the dimension of the feature, and n is the number of image data points. Using variable number of anchor pointsGenerating m representative anchor points from original n data by a balanced K mean value method to obtain an anchor point matrix
Wherein u is i Is the ith anchor point, and m is the number of anchor points. In the traditional balanced K-means algorithm, the data are continuously divided into two by adopting K-means, and if the dividing times is q, the number of the anchor points is 2 q The method has the defects that the number of anchor points can only be the power of 2, and the method for balancing the K mean value of the variable number of the anchor points can select any number of anchor points, and has the following specific operation steps. Suppose that m anchor points need to be selected, and m cannot be represented as 2 q In the form of (1), then calculate q first min And q is max Both of them satisfy
First select
Sorting the clusters where the anchor points are located according to the variance, and taking the first
And (4) dividing the cluster with the largest variance into two parts to obtain m anchor points.
Step 2: constructing an adaptive neighbor graph from representative anchor points
Step 2.1: constructing a correlation relation matrix between representative anchor points and data points
Obtaining a correlation matrix B between the data point X and the anchor point U by a similarity self-learning method,
is a correlation matrix between the sample point and the anchor point. For the ith sample point, the model is as follows:
wherein, b ij Is the ith row and jth column element in B,
in row i of B, γ is a regularization coefficient. Is provided with
Is the euclidean distance between the ith sample point and the jth anchor point,
is a vector whose j-th element is k ij Then the above optimization problem can be written in the form of a vector as follows
Let b be i In which there are l (l is less than or equal to m) non-zero elements. To k is paired i Reordering is performed, assuming after the ordering
Corresponding to b i Is composed of
Then
Is expressed as
Step 2.2: constructing similarity matrix between samples
After B is obtained, the similarity between the sample points is constructed through the similarity between the sample points and the anchor points
A＝BΔ -1 B T
Wherein the content of the first and second substances,
is a diagonal matrix whose i-th element is calculated as
For a more concise expression A, let
At this time
And step 3: solution of optimization problem
The invention is realized by minimizing A and FF T The distance between the two matrixes is used for solving the label matrix, and considering that the two matrixes possibly have scale difference, the matrix S is added to balance the difference, so that the general optimization problem is as follows
Where Ind denotes that the matrix F is a discrete value and S can be a scalar, a diagonal matrix, or a symmetric matrix. The solution of the problem is discussed in three cases below.
The first condition is as follows: when s is a number
The optimization problem can be transformed as follows:
the objective function contains two variables of F and s, s is unconstrained, s is directly differentiated, and J is ordered 1 ＝2sTr(F T AF)-s 2 Tr(FF T FF T ) Is obtained by
Substituting the expression of s into the original optimization problem, the optimization problem can be changed into
Wherein the content of the first and second substances,
let F be the matrix obtained in the previous step, whose column I is
Row ith and column ith elements of
When updating ith row and ith column of F, the variation of the objective function is calculated as follows
Wherein g is il For the ith row and the ith column element of the matrix G, f is optimal i Is composed of
Wherein < > indicates that the value of the parameter is 1 if it is true and 0 if it is false.
Case two: when S is a diagonal matrix
When S is a diagonal matrix, the original problem is
At this time, the optimization problem is written in the form of summation
The optimization problem for each s jj Are independent and therefore can solve for s individually jj To s to jj Obtaining the partial derivative, and making the partial derivative value be 0 to obtain s jj Is solved as
Handle s jj Substituting the expression into the original optimization problem, the optimization problem becomes
Updating F line by adopting a coordinate ascending method, namely when a certain line is updated, other lines are all fixed, and the currently obtained optimal is assumed
When updating the ith row and the ith element of the ith row is changed from 0 to 1, the increment of the objective function can be calculated as
Then
Wherein < > operation means that the value of the inside is 1 if true, and 0 if not.
Case three: when S is a symmetric matrix
An objective function of
Let J equal 2Tr (F) T AFS)-Tr(FSF T FSF T ) Since S is not constrained, the derivation of S is derived to have a derivative value of 0
F T AF＝F T FSF T F
Can be pushed out
S＝(F T F) -1 F T AF(F T F) -1
Substituting the above into the expression of J can result in
J＝Tr(F T AFS)
＝Tr(F T AF(F T F) -1 F T AF(F T F) -1 )
After the objective function is derived from S, the original objective function is substituted to obtain:
J＝Tr(F T AF(F T F) -1 F T AF(F T F) -1 )
let P be F T AF(F T F) -1 The objective function becomes:
wherein the content of the first and second substances,
can be substituted to obtain
Updating F by adopting a coordinate descent method, wherein when the ith row and the ith column of the F are updated, F il Is changed, J is in and f il Relevant part J 1 Is expressed as
Let A ═ a 1 ,a 2 ,...,a i ,...,a n ]Wherein a is i Line i of A, a j Line j of A. Then, when the coordinate-ascent method is used, when updating the ith row and the ith column of F,optimum f i Is composed of
Wherein the content of the first and second substances,<>the operation indicates that the value of the internal is 1 if the internal is true, and is 0 and q if the internal is not true il Is expressed as
Example 1:
taking clustering of a Yale image data set recognized by a certain face as an example, the Yale image data set comprises 165 images, the length and the width of each image are 32 pixels, 15 categories are provided, each category comprises 11 sample points, and the number of selected anchor points is 64.
Step 1: generating representative anchor points
The gray feature of the image is used as the data feature of the image, the pixel gray value of each image is straightened into a vector, the dimension of the vector is 1024, and the feature data corresponding to the image is 1024
Wherein x is i For the ith data point, d is 1024, which is the dimension of the feature, and n is 165, which is the number of image data points. Generating 64 representative anchor points from 165 data by adopting a balance K-means method of variable anchor point number to obtain an anchor point matrix
Wherein u is i And m is the number of the anchor points, and is 64.
Step 2: constructing an adaptive neighbor graph from representative anchor points
Step 2.1: constructing a correlation relation matrix between the representative anchor point and the data point
Obtaining the correlation relationship moment between the data point X and the anchor point U by a similarity self-learning methodThe matrix B is a matrix B in which the matrix B is a matrix,
is a correlation matrix between the sample point and the anchor point. For the ith sample point, the model is as follows:
wherein, b ij Is the ith row and jth column element in B,
in row i of B, γ is a regularization coefficient. Is provided with
Is the euclidean distance between the ith sample point and the jth anchor point,
is a vector whose j-th element is k ij Then the above optimization problem can be written in the form of a vector as follows
Let b be i In which there are l (l is less than or equal to m) non-zero elements. To k is paired i Reordering is performed, assuming after the ordering
Corresponding to b i Is composed of
Then
Is expressed as
Step 2.2: constructing similarity matrix between samples
After B is obtained, the similarity between the sample points is constructed through the similarity between the sample points and the anchor points
A＝BΔ -1 B T
Wherein the content of the first and second substances,
is a diagonal matrix whose i-th element is calculated as
For a more concise expression A, let
At this time
And 3, step 3: solution of optimization problem
The method proposed by the present invention is described herein by taking s as an example. The optimization problem is now
The objective function contains two variables of F and s, s is unconstrained, s is directly differentiated, and J is ordered 1 ＝2sTr(F T AF)-s 2 Tr(FF T FF T ) Is obtained by
Substituting the expression of s into the original optimization problem, the optimization problem can be changed into
Wherein the content of the first and second substances,
when updating ith row and ith column of F, the variation of the objective function is as follows
Wherein g is il Is the ith row and the ith column element of the matrix G, then f is optimal i Is composed of
Wherein < > indicates that the value of the parameter is 1 if it is true and 0 if it is false.
The optimal discrete label matrix can be obtained through iterative calculation, the clustering precision can be 43.64 percent by comparing the label matrix obtained through the comparison calculation with the sample real label, the clustering precision is improved by 11.52 percent compared with spectral clustering in precision, the time is less than 0.0026s compared with spectral clustering, and the image classification task of the invention has advantages.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.
Claims (7)
1. An image classification method is characterized by comprising the following steps:
s1: inputting a classified image;
s2: extracting image features to obtain feature data
Wherein x is i Is the ith data point, d is the dimension of the feature, and n is the number of image data points;
s3: selecting m anchor points by adopting a balance K mean value method of variable anchor point numbers to obtain an anchor point set U;
s4: constructing a similarity matrix A between data points according to the anchor points;
s5: constructing a model according to the similarity matrix A and the label relation;
s6: and solving the model by adopting a coordinate lifting method to obtain a label of the characteristic data, and finishing image classification.
2. An image classification method according to claim 1, characterized in that said S4 is divided into the following two steps:
s41: constructing a correlation relation matrix B between the data points and the anchor points by adopting a similarity self-learning method;
s42: and calculating to obtain a sample neighbor graph A and a similarity matrix A according to the correlation matrix B.
3. An image classification method according to claim 2, characterized in that: the method for constructing the correlation matrix between the data points and the anchor points by adopting the similarity self-learning method comprises the following specific steps:
obtaining a correlation matrix B between the data point X and the anchor point U by a similarity self-learning method,
a correlation relation matrix between the sample point and the anchor point is obtained; for the ith sample point, the model is as follows:
wherein, b ij Is the ith row and jth column element in B,
for row i in B, γ is the regularization coefficient. Is provided with
Is the euclidean distance between the ith sample point and the jth anchor point,
is a vector whose j-th element is k ij Then the above optimization problem can be written in the form of a vector as follows
Let b be i In which there are l (l is less than or equal to m) non-zero elements, for k i Reordering is performed, assuming after the ordering
Corresponding to b i Is composed of
Then
Is expressed as
4. An image classification method according to claim 3, characterized in that: calculating according to the correlation matrix B to obtain a sample neighbor graph A, wherein the similarity matrix A is as follows:
after B is obtained, the similarity between the sample points is constructed through the similarity between the sample points and the anchor points
A＝BΔ -1 B T
Wherein the content of the first and second substances,
is a diagonal matrix whose i-th element is calculated as
Order to
At this time
5. A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of any of claims 1-4.
6. A computer-readable storage medium having stored thereon computer-executable instructions for performing the method of any of claims 1-4 when executed.
7. A computer program comprising computer executable instructions which when executed perform the method of any one of claims 1 to 4.
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| CN116310452B (en) * | 2023-02-16 | 2024-03-19 | 广东能哥知识科技有限公司 | Multi-view clustering method and system |
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