CN110287973B - Image feature extraction method based on low-rank robust linear discriminant analysis - Google Patents

Image feature extraction method based on low-rank robust linear discriminant analysis Download PDF

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CN110287973B
CN110287973B CN201910531905.4A CN201910531905A CN110287973B CN 110287973 B CN110287973 B CN 110287973B CN 201910531905 A CN201910531905 A CN 201910531905A CN 110287973 B CN110287973 B CN 110287973B
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卢桂馥
王勇
唐肝翌
许召辉
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Anhui Polytechnic University
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Abstract

The invention discloses an image feature extraction method based on low-rank robust linear discriminant analysis, which combines a low-rank technology and an LDA algorithm to solve the problems that the LDA algorithm is sensitive to noise and not robust enough. Therefore, low rank analysis is introduced into the LDA algorithm, so that the robustness of the algorithm can be improved, the algorithm is not sensitive to noise, and the robustness and the recognition performance of the LDA algorithm are further improved.

Description

Image feature extraction method based on low-rank robust linear discriminant analysis
Technical Field
The invention relates to the field of pattern recognition, in particular to an image feature extraction method based on low-rank robust linear discriminant analysis.
Background
In the application fields of pattern recognition, machine learning, etc., many image data are often encountered. Because image data is generally high-dimensional data, if the high-dimensional data is directly processed, the requirement on computer hardware is high, and the recognition rate is low. Therefore, before the image is classified, identified or clustered, dimension reduction preprocessing is generally required to be performed on the image, and feature extraction is one of the most common dimension reduction methods.
At present, many image feature extraction methods, such as Principal Component Analysis (PCA), linear Discriminant Analysis (LDA), local Preserving Projection (LPP), etc., have appeared, but all of them use the Frobenius norm, which is very sensitive to noise and heterogeneous data, to construct the objective function, so that they all have the problem of being sensitive to noise and not robust enough.
Disclosure of Invention
In view of this, the invention aims to provide an image feature extraction method based on low-rank robust linear discriminant analysis, which solves the problems of the prior art that the noise is relatively sensitive and the robustness is not enough.
Based on the aim, the invention provides an image feature extraction method based on low-rank robust linear discriminant analysis, which comprises the following steps:
solving low-rank representation of the original image by using a robust principal component analysis algorithm based on the low-rank representation;
performing feature extraction on the low-rank representation of the original image by using a linear feature discrimination analysis algorithm;
and (4) classifying by using a nearest neighbor classifier.
Preferably, when the low rank representation of the original image is obtained by using a robust principal component analysis algorithm based on the low rank representation, the method further comprises:
all training samples are obtained, and each image is stretched according to columns to form a d-dimensional column vector x i ∈R d I =1,2, l, n, all images are grouped into a data matrix X = { X = { X } 1 ,x 2 ,L,x N }＝[X 1 ,L,X c ]∈R d×N Wherein c is the number of classes of the sample;
all test samples are obtained, and each image is stretched column by column to become a d-dimensional column vector y i ∈R d I =1,2,l, m, all images are grouped into a data matrix Y = { Y 1 ,y 2 ,L,y M }＝[Y 1 ,L,Y c ]∈R d×M ；
Initialization: setting an initial parameter Y 0 ＝sgn(X)/J(sgn(X))，E 0 ＝0，μ 0 (= 0,/> 1), number of iterations k =0, where sgn (·) is a sign function, J (sgn (X)) = max (| | sgn (X) | | magnetism), and J (sgn (X)) | magnetism) 2 ,λ -1 ||sgn(X)|| ∞ )，λ＞0，||·|| 2 Is 2 norm, | · caly | | ∞ Infinite norm, E coefficient matrix, lagrange multiplier, regularization parameter;
calculating out
Figure BDA0002100011660000021
Singular value decomposition of, i.e.
Figure BDA0002100011660000022
Wherein svd (·) represents the singular value decomposition of the computation matrix;
computing
Figure BDA0002100011660000023
For each element S in the matrix S ij I is more than or equal to 1 and less than or equal to d, j is more than or equal to 1 and less than or equal to n, has
Figure BDA0002100011660000024
Computing
Figure BDA0002100011660000025
Calculating Y k+1 ＝Y k +μ k (X-A k+1 -E k+1 )；μ k+1 ＝ρμ k ；
Judging whether to use
Figure BDA0002100011660000026
If yes, enabling k = k +1, and re-performing initialization parameters, singular value decomposition and calculation;
and if not, respectively reducing the dimensions of the data matrix A and the test sample Y by using a Principal Component Analysis (PCA) algorithm to obtain the data matrix A and the data matrix Y after dimension reduction.
Preferably, when the linear feature discrimination analysis algorithm is used to perform feature extraction on the low-rank representation of the original image, the method further includes:
computing intra-class scatter matrices S w ，
Figure BDA0002100011660000027
Wherein N is i Subscript set representing samples belonging to class i, a j For the jth sample, m, of the ith class in matrix A (i) The mean value of the ith sample is obtained;
computing classInter-scatter matrix S b ，
Figure BDA0002100011660000031
Wherein n is i The number of samples in the ith class, and m is the mean value of all samples;
calculating projection matrix U = [ U ] i ]，1≤i≤c-1，u i Is a matrix
Figure BDA0002100011660000032
Characteristic value λ of i Corresponding feature vectors, i.e. having
Figure BDA0002100011660000033
I is more than or equal to 1 and less than or equal to c-1, and the characteristic value lambda i Arranging from small to large;
computing
Figure BDA0002100011660000034
And
Figure BDA0002100011660000035
preferably, when the classification is performed by using the nearest neighbor classifier, the method further comprises the step of using the nearest neighbor classifier in the image recognition technology to perform the classification on the projected matrix
Figure BDA0002100011660000036
And with
Figure BDA0002100011660000037
And performing classification processing to obtain the number of the identified test samples, and dividing the number of the identified test samples by the total number M of the test samples to calculate the algorithm identification rate.
From the above, it can be seen that, in order to overcome the problem that the LDA algorithm is relatively sensitive to noise and is not robust enough, the image feature extraction method based on the low-rank robust linear discriminant analysis provided by the invention combines the low-rank technology and the LDA algorithm, and provides an image feature extraction method based on the low-rank robust linear discriminant analysis. Therefore, low rank analysis is introduced into the LDA algorithm, so that the robustness of the algorithm can be improved, the algorithm is not sensitive to noise, and the robustness and the recognition performance of the LDA algorithm are further improved.
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FIG. 1 is a schematic flow chart of an image feature extraction method based on low-rank robust linear discriminant analysis according to an embodiment of the present invention;
FIG. 2 is a logic diagram of an image feature extraction method based on low-rank robust linear discriminant analysis according to an embodiment of the present invention;
FIG. 3 is an image of an ORL library for use in experiments according to embodiments 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 is further described in detail with reference to the following embodiments and the accompanying drawings.
It should be noted that all expressions using "first" and "second" in the embodiments of the present invention are used for distinguishing two entities with the same name but different names or different parameters, and it should be noted that "first" and "second" are merely for convenience of description and should not be construed as limitations of the embodiments of the present invention, and they are not described in any more detail in the following embodiments.
An image feature extraction method based on low-rank robust linear discriminant analysis is characterized in that, as shown in fig. 1, the method comprises the following steps:
101, solving the low-rank representation of an original image by using a robust principal component analysis algorithm based on the low-rank representation;
102, performing feature extraction on the low-rank representation of the original image by using a linear feature discrimination analysis algorithm;
103 are classified using nearest neighbor classifiers.
In an embodiment of the present invention, when the low-rank representation of the original image is obtained by using a robust principal component analysis algorithm based on the low-rank representation, the method further includes:
an original training image is acquired and,take the ORL image library as an example. The ORL standard face database was created by the Olivetti laboratory and contained a total of 400 images, ten face images for a total of 40 people per person, and some of the image acquisition times were different. These images are all 112 x 92 dimensional, contain 256 gray levels and the background is all black. These gray scale images include facial expressions, i.e., laughing or not, lighting conditions and facial details, i.e., with or without glasses, and open or closed eyes, among others. Arbitrarily selecting 4 (or 5) images of each person, using 160 (or 200) images as training samples (adding salt-pepper noise with intensity of 0.01 into the images in order to verify the robustness of the algorithm), stretching each image according to columns to change the image into a column vector x with d dimension i ∈R d I =1,2, l, n, all images are grouped into a data matrix X = { X = { X } 1 ,x 2 ,L,x N }＝[X 1 ,L,X c ]∈R d×N Wherein c is the number of classes of the sample;
using the remaining 240 (or 200) images in ORL library as test samples, and stretching each image column by column to obtain a d-dimensional column vector y i ∈R d I =1,2,l, m, all images are grouped into a data matrix Y = { Y = { Y } 1 ,y 2 ,L,y M }＝[Y 1 ,L,Y c ]∈R d×M ；
Initialization: setting an initial parameter Y 0 ＝sgn(X)/J(sgn(X))，E 0 ＝0，μ 0 (= 0,/> 1), number of iterations k =0, where sgn (·) is a sign function, J (sgn (X)) = max (| | sgn (X) | | magnetism), and J (sgn (X)) | magnetism) 2 ,λ -1 ||sgn(X)|| ∞ )，λ＞0，||·|| 2 Is 2 norm, | ·| luminance ∞ Is an infinite norm;
computing
Figure BDA0002100011660000051
Singular value decomposition of, i.e.
Figure BDA0002100011660000052
Wherein svd (·) represents the singular value decomposition of the computation matrix;
calculating out
Figure BDA0002100011660000053
For each element S in the matrix S ij I is more than or equal to 1 and less than or equal to d, j is more than or equal to 1 and less than or equal to n, has
Figure BDA0002100011660000054
Computing
Figure BDA0002100011660000055
Calculating Y k+1 ＝Y k +μ k (X-A k+1 -E k+1 )；μ k+1 ＝ρμ k ；
Determine whether or not
Figure BDA0002100011660000056
If yes, enabling k = k +1, and re-performing initialization parameters, singular value decomposition and calculation;
if not, using a Principal Component Analysis (PCA) algorithm to respectively reduce the dimensions of the data matrix A and the test sample Y to obtain the data matrix A and the data matrix Y after dimension reduction;
in an embodiment of the present invention, when performing feature extraction on a low-rank representation of an original image by using a linear feature discriminant analysis algorithm, the method further includes:
computing an intra-class scatter matrix S w ，
Figure BDA0002100011660000057
Wherein N is i Subscript set representing samples belonging to class i, a j For the jth sample, m, of the ith class in matrix A (i) The mean value of the ith sample is obtained;
computing an inter-class scatter matrix S b ，
Figure BDA0002100011660000058
Wherein n is i The number of samples in the ith class is m is the mean value of all samples;
calculating projection matrix U = [ U ] i ]，1≤i≤c-1，u i Is a matrix
Figure BDA0002100011660000059
Characteristic value λ of i Corresponding feature vectors, i.e. having
Figure BDA00021000116600000510
I is more than or equal to 1 and less than or equal to c-1, and the characteristic value lambda i Arranging from small to large;
computing
Figure BDA00021000116600000511
And
Figure BDA00021000116600000512
in an embodiment of the present invention, when the classification is performed by using the nearest neighbor classifier, the method further includes:
projection matrix pair using nearest neighbor classifier widely used in image recognition technology
Figure BDA0002100011660000061
And
Figure BDA0002100011660000062
the algorithm identification rate can be calculated by classifying the test samples to obtain the number of the identified test samples and dividing the number of the identified test samples by the total number M of the test samples.
In the application fields of pattern recognition, machine learning, etc., many image data are often encountered. Since image data is generally high-dimensional data, if the high-dimensional data is directly processed, the requirement on computer hardware is high, and the recognition rate is low. Therefore, before the image is classified, identified or clustered, dimension reduction preprocessing is generally required to be performed on the image, and feature extraction is one of the most common dimension reduction methods.
At present, many image feature extraction methods have appeared, such as Principal Component Analysis (PCA), linear Discriminant Analysis (LDA), local Preserving Projection (LPP), and the like. The basic idea of the PCA algorithm is to find the projection direction that best represents the raw data. The PCA algorithm is a classic feature extraction algorithm and becomes a benchmark algorithm in the field of image recognition, but the PCA algorithm is an unsupervised algorithm and cannot utilize the class information of samples. Unlike the PCA algorithm, the LDA algorithm is a supervised feature extraction algorithm. The core idea of the LDA algorithm is to find a set of projection vectors such that samples of different classes are as far apart as possible after projection, while samples of the same class are as close as possible after projection. That is, the inter-class distance is maximized and the intra-class distance is minimized. Both PCA and LDA algorithms are global algorithms and do not take into account local geometry between samples. The basic idea of LPP is: after projection, the original data can keep the local geometric structure of the original data in a high-dimensional space in a low-dimensional space. Because the LPP algorithm considers the local geometry, the LPP algorithm has better recognition rate than the LDA algorithm.
However, the methods use the Frobenius norm which is very sensitive to noise and heterogeneous data to construct the objective function, so that the methods have certain defects. In recent years, researchers find that images often have low-rank structures, and by using a low-rank representation technology, the researchers can conveniently find out the low-dimensional subspace structures embedded in data. For a group of noisy data, the low rank representation method can be used for separating the noise in the data while learning the low-dimensional subspace structure of the data.
In order to solve the problems that an LDA algorithm is sensitive to noise and not robust enough, the invention combines a low-rank technology and the LDA algorithm, and provides an image feature extraction method for low-rank robust linear discriminant analysis, thereby further improving the robustness and the recognition performance of the LDA algorithm.
In the invention, a low-rank structure is introduced into the LDA algorithm, and compared with the existing PCA, LDA and LPP algorithms, the LDA and LPP algorithm has the following advantages:
for a group of noisy data, the low rank representation method can be used for separating the noise in the data while learning the low-dimensional subspace structure of the data. Therefore, low-rank analysis is introduced into the LDA algorithm, so that the robustness of the algorithm can be improved, and the algorithm is not sensitive to noise;
the superiority of the algorithm compared with other algorithms is verified through experiments in an ORL face image library. Fig. 2 is an image of an ORL library image for experiment (image with impulse noise of 0.01 added).
Table 1 shows the recognition rates of PCA, LDA, LPP and the algorithm designed by the present invention in ORL library (the recognition rates of training samples are 4 and 5, respectively).
Table 1 recognition rates of different algorithms in ORL library.
Figure BDA0002100011660000071
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances which fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (3)

1. An image feature extraction method based on low-rank robust linear discriminant analysis, the method comprising:
solving low-rank representation of the original image by using a robust principal component analysis algorithm based on the low-rank representation;
performing feature extraction on the low-rank representation of the original image by using a linear feature discrimination analysis algorithm;
classifying by using a nearest neighbor classifier;
when the low-rank representation of the original image is solved by using a robust principal component analysis algorithm based on the low-rank representation, the method further comprises the following steps:
all training samples are obtained, and each image is stretched according to columns to form a d-dimensional column vector
Figure IMAGE002
，
Figure IMAGE004
Combining all images into a data matrix
Figure IMAGE006
Wherein c is the number of classes of the sample;
all test samples are obtained, and each image is stretched in columns to become a d-dimensional column vector
Figure IMAGE008
，
Figure IMAGE010
Forming a data matrix from all images
Figure IMAGE012
；
Initialization: setting initial parameters
Figure IMAGE014
，
Figure IMAGE016
，
Figure IMAGE018
，
Figure IMAGE020
Number of iterations
Figure IMAGE022
Wherein
Figure IMAGE024
In the form of a function of the sign,
Figure IMAGE026
，
Figure IMAGE028
，
Figure IMAGE030
is a norm of 2, and is,
Figure IMAGE032
infinite norm, E coefficient matrix, lagrange multiplier, regularization parameter;
computing
Figure IMAGE034
Singular value decomposition of, i.e.
Figure IMAGE036
Wherein
Figure IMAGE038
A singular value decomposition representing a computational matrix;
computing
Figure IMAGE040
For each element in the matrix S
Figure IMAGE042
，
Figure IMAGE044
，
Figure IMAGE046
Is provided with
Figure IMAGE048
；
Computing
Figure IMAGE050
；
Calculating out
Figure IMAGE052
;
Figure IMAGE054
;
Judging whether to use
Figure IMAGE056
If yes, then order
Figure IMAGE058
Carrying out initialization parameter, singular value decomposition and calculation again;
and if not, respectively reducing the dimensions of the data matrix A and the test sample Y by using a Principal Component Analysis (PCA) algorithm to obtain the data matrix A and the data matrix Y after dimension reduction.
2. The method for extracting image features based on low-rank robust linear discriminant analysis as claimed in claim 1, wherein when performing feature extraction on the low-rank representation of the original image by using a linear feature discriminant analysis algorithm, the method further comprises:
computing intra-class scatter matrices
Figure IMAGE060
，
Figure IMAGE062
Wherein
Figure IMAGE064
A subscript set indicating samples belonging to the ith class,
Figure IMAGE066
for the jth sample of the ith class in matrix a,
Figure IMAGE068
the mean value of the ith sample is obtained;
computing inter-class scatter matrices
Figure IMAGE070
，
Figure IMAGE072
In which
Figure IMAGE074
Is the number of samples in the i-th class,
Figure IMAGE076
is the mean of all samples;
computing a projection matrix
Figure IMAGE078
，
Figure IMAGE080
，
Figure IMAGE082
Is a matrix
Figure IMAGE084
Characteristic value of
Figure IMAGE086
Corresponding feature vector, i.e. having
Figure IMAGE088
，
Figure IMAGE080
And a characteristic value
Figure IMAGE086
Arranged from small to large；
Computing
Figure IMAGE090
And
Figure IMAGE092
。
3. the method for extracting image features based on low-rank robust Linear Discriminant Analysis (LDA) of claim 1, wherein when the classification is performed by using a nearest neighbor classifier, the method further comprises using the nearest neighbor classifier in an image recognition technology to perform projection matrix analysis
Figure IMAGE094
And with
Figure IMAGE096
Performing classification to obtain the number of recognized test samples, and dividing the number of recognized test samples by the total number of test samplesMAnd calculating the algorithm recognition rate.
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