CN110287973A - A kind of image characteristic extracting method based on low-rank robust linear discriminant analysis - Google Patents
A kind of image characteristic extracting method based on low-rank robust linear discriminant analysis Download PDFInfo
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Abstract
The invention discloses a kind of image characteristic extracting methods based on low-rank robust linear discriminant analysis, in order to overcome LDA algorithm more sensitive to noise, the problem of inadequate robust, the present invention combines low-rank technology and LDA algorithm, it is proposed a kind of image characteristic extracting method of low-rank robust linear discriminant analysis, for data noisy for one group, the noise separation in data can be come out while the lower-dimensional subspace structure for the data that learn using low-rank representation method.Therefore, low rank analysis is introduced in LDA algorithm, the robustness of algorithm can be improved, make it to insensitive for noise, to further increase the robustness and recognition performance of LDA algorithm.
Description
Technical field
The present invention relates to area of pattern recognition, particularly relate to a kind of characteristics of image based on low-rank robust linear discriminant analysis
Extracting method.
Background technique
In application fields such as pattern-recognition, machine learning, many image datas can be usually encountered.Since image data is general
All be high dimensional data, if directly handled high dimensional data, to the more demanding of computer hardware, and discrimination compared with
It is low.Therefore, classified to image, identify or cluster task before, generally require and dimensionality reduction pretreatment carried out to image, and it is special
It is one of most common dimension reduction method that sign, which extracts,.
Currently, a variety of image feature extraction methods have been had already appeared, such as principal component analysis (Principal
Component Analysis, PCA), linear discriminant analysis (Linear Discriminant Analysis, LDA), part is protected
Hold projection (Locality Preserving Projection, LPP) etc., but the above method all employ to noise and
Heterogeneous data very sensitive Frobenius norm constructs objective function, so that these methods all exist to noise-sensitive, no
The problem of enough robusts.
Summary of the invention
In view of this, it is an object of the invention to propose that a kind of characteristics of image based on low-rank robust linear discriminant analysis mentions
Method is taken, solves the problem of the prior art inadequate robust more sensitive to noise.
Based on a kind of above-mentioned purpose image characteristics extraction side based on low-rank robust linear discriminant analysis provided by the invention
Method, this method include:
The low-rank representation of original image is found out using the Robust Principal Component Analysis algorithm based on low-rank representation；
Feature extraction is carried out using low-rank representation of the linear character discriminatory analysis algorithm to original image；
Classified using nearest neighbor classifier.
Preferably, when finding out the low-rank representation of original image using the Robust Principal Component Analysis algorithm based on low-rank representation,
This method further comprises:
All training samples are obtained, every piece image is stretched by column, so that it becomes the column vector x of d dimensioni∈Rd,
All images are formed a data matrix X={ x by i=1,2, L, N1,x2,L,xN}=[X1,L,Xc]∈Rd×N, wherein c be
The classification number of sample；
All test samples are obtained, every piece image is stretched by column, so that it becomes the column vector y of d dimensioni∈Rd,
All images are formed a data matrix Y={ y by i=1,2, L, M1,y2,L,yM}=[Y1,L,Yc]∈Rd×M；
Initialization: setting initial parameter Y0=sgn (X)/J (sgn (X)), E0=0, μ0=0, ρ > 1, the number of iterations k=0,
Wherein sgn () be sign function, J (sgn (X))=max (| | sgn (X) | |2,λ-1||sgn(X)||∞), λ > 0, | | | |2
For 2 norms, | | | |∞For infinity norm, E is coefficient matrix, it is Lagrange multiplier, is regularization parameter；
It calculatesSingular value decomposition, i.e.,Wherein svd ()
Indicate the singular value decomposition of calculating matrix；
It calculatesFor each of matrix S element Sij, 1≤i≤d, 1≤j≤n has
It calculates
Calculate Yk+1=Yk+μk(X-Ak+1-Ek+1)；μk+1=ρ μk；
Judge whetherIf it is k=k+1 is enabled, initiation parameter, unusual is re-started
Value is decomposed and is calculated；
If otherwise carrying out dimensionality reduction to data matrix A and test sample Y respectively with principal component analysis (PCA) algorithm, obtain
Data matrix A and Y after dimensionality reduction.
Preferably, when carrying out feature extraction using low-rank representation of the linear character discriminatory analysis algorithm to original image, this
Method further comprises:
Calculate within-class scatter matrix Sw,Wherein NiIndicate the sample for belonging to the i-th class
This subscript collection, ajFor j-th of sample of the i-th class in matrix A, m(i)For the mean value of the i-th class sample；
Calculate between class scatter matrix Sb,Wherein niFor the sample number of the i-th class, m is
The mean value of all samples；
Calculate projection matrix U=[ui], 1≤i≤c-1, uiFor matrixEigenvalue λiCorresponding feature vector, i.e.,
Have1≤i≤c-1, and eigenvalue λiIt arranges from small to large；
It calculatesWith
Preferably, when being classified using nearest neighbor classifier, this method further comprises, in image recognition technology
Nearest neighbor classifier is to matrix after projectionWithCarry out classification processing is carried out, obtains the test sample number being identified, with
The test sample number being identified out calculates algorithm discrimination divided by total test sample number M.
From the above it can be seen that a kind of characteristics of image based on low-rank robust linear discriminant analysis provided by the invention
Extracting method, in order to overcome LDA algorithm more sensitive to noise, the problem of inadequate robust, the present invention calculates low-rank technology and LDA
Method combines, and proposes a kind of image characteristic extracting method of low-rank robust linear discriminant analysis, number noisy for one group
It, can be while the lower-dimensional subspace structure for the data that learn, by the noise in data point using low-rank representation method for
It separates out and.Therefore, low rank analysis is introduced in LDA algorithm, the robustness of algorithm can be improved, and makes it to insensitive for noise, from
And further increase the robustness and recognition performance of LDA algorithm.
Detailed description of the invention
Fig. 1 is that the process of the image characteristic extracting method based on low-rank robust linear discriminant analysis of the embodiment of the present invention is shown
It is intended to；
Fig. 2 is that the logic of the image characteristic extracting method based on low-rank robust linear discriminant analysis of the embodiment of the present invention is shown
It is intended to；
Fig. 3 is the experiment library the ORL parts of images of the embodiment of the present invention.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment, and reference
Attached drawing, the present invention is described in more detail.
It should be noted that all statements for using " first " and " second " are for differentiation two in the embodiment of the present invention
The non-equal entity of a same names or non-equal parameter, it is seen that " first " " second " only for the convenience of statement, does not answer
It is interpreted as the restriction to the embodiment of the present invention, subsequent embodiment no longer illustrates this one by one.
A kind of image characteristic extracting method based on low-rank robust linear discriminant analysis, which is characterized in that as shown in Figure 1,
This method the following steps are included:
101 find out the low-rank representation of original image using the Robust Principal Component Analysis algorithm based on low-rank representation；
102 carry out feature extraction using low-rank representation of the linear character discriminatory analysis algorithm to original image；
103 are classified using nearest neighbor classifier.
In an embodiment of the present invention, original image is found out using the Robust Principal Component Analysis algorithm based on low-rank representation
When low-rank representation, this method further comprises:
Original training image is obtained, by taking ORL image library as an example.The ORL standard faces database is by Olivetti reality
Room creation is tested, which contains 400 width images in total, everyone has the face-image of ten width totally 40 people, and wherein
Some image acquisition times are different.These image scales are entirely 112 × 92 dimensions, comprising 256 gray levels and are carried on the back
Scape is entirely black.These gray level images include facial expression, that is, laugh at or do not laugh at, and illumination condition and face detail are band eye
Mirror perhaps no glasses and open eyes or close one's eyes etc. differences.Arbitrarily select everyone 4 width (or 5 width) image, totally 160 width (or
200 width) image as training sample (salt-pepper noise that intensity is 0.01 is added for the robustness of verification algorithm, in image),
Every piece image is stretched by column, so that it becomes the column vector x of d dimensioni∈Rd, i=1,2, L, N form all images
One data matrix X={ x1,x2,L,xN}=[X1,L,Xc]∈Rd×N, wherein c is the classification number of sample；
Using 240 width (or 200 width) image remaining in the library ORL as test sample, every piece image is stretched by column, is made
Its column vector y for becoming d dimensioni∈Rd, all images are formed a data matrix Y={ y by i=1,2, L, M1,y2,
L,yM}=[Y1,L,Yc]∈Rd×M；
Initialization: setting initial parameter Y0=sgn (X)/J (sgn (X)), E0=0, μ0=0, ρ > 1, the number of iterations k=0,
Wherein sgn () be sign function, J (sgn (X))=max (| | sgn (X) | |2,λ-1||sgn(X)||∞), λ > 0, | | | |2
For 2 norms, | | | |∞For infinity norm；
It calculatesSingular value decomposition, i.e.,Wherein svd ()
Indicate the singular value decomposition of calculating matrix；
It calculatesFor each of matrix S element Sij, 1≤i≤d, 1≤j≤n has
It calculates
Calculate Yk+1=Yk+μk(X-Ak+1-Ek+1)；μk+1=ρ μk；
Judge whetherIf it is k=k+1 is enabled, initiation parameter, unusual is re-started
Value is decomposed and is calculated；
If otherwise carrying out dimensionality reduction to data matrix A and test sample Y respectively with principal component analysis (PCA) algorithm, obtain
Data matrix A and Y after dimensionality reduction；
In an embodiment of the present invention, it is carried out using low-rank representation of the linear character discriminatory analysis algorithm to original image special
When sign extracts, this method further comprises:
Calculate within-class scatter matrix Sw,Wherein NiIndicate the sample for belonging to the i-th class
This subscript collection, ajFor j-th of sample of the i-th class in matrix A, m(i)For the mean value of the i-th class sample；
Calculate between class scatter matrix Sb,Wherein niFor the sample number of the i-th class, m
For the mean value of all samples；
Calculate projection matrix U=[ui], 1≤i≤c-1, uiFor matrixEigenvalue λiCorresponding feature vector, i.e.,
Have1≤i≤c-1, and eigenvalue λiIt arranges from small to large；
It calculatesWith
In an embodiment of the present invention, when being classified using nearest neighbor classifier, this method further comprises:
With nearest neighbor classifier widely used in image recognition technology to matrix after projectionWithClassify
Processing, can obtain the test sample number being identified, with the test sample number being identified obtained divided by total test sample number
M, so that it may calculate algorithm discrimination.
In application fields such as pattern-recognition, machine learning, many image datas can be usually encountered.Since image data is general
All be high dimensional data, if directly handled high dimensional data, to the more demanding of computer hardware, and discrimination compared with
It is low.Therefore, classified to image, identify or cluster task before, generally require and dimensionality reduction pretreatment carried out to image, and it is special
It is one of most common dimension reduction method that sign, which extracts,.
Currently, a variety of image feature extraction methods have been had already appeared, such as principal component analysis (Principal
Component Analysis, PCA), linear discriminant analysis (Linear Discriminant Analysis, LDA), part is protected
Hold projection (Locality Preserving Projection, LPP) etc..The basic thought of PCA algorithm is to find out most represent
The projecting direction of initial data.PCA algorithm is a kind of Feature Extraction Algorithm of classics, it has also become a kind of base of field of image recognition
Quasi- algorithm, but PCA algorithm is a kind of unsupervised algorithm, can not utilize the classification information of sample.It is different from PCA algorithm, LDA
Algorithm is a kind of Feature Extraction Algorithm for having supervision.The core concept of LDA algorithm is to find such one group of projection vector, so that not
Similar sample is separate as far as possible after passing through projection, and of a sort sample connects as far as possible after projection
Closely.That is, it is maximum to make between class distance, and inter- object distance is minimum.PCA and LDA algorithm are all Global Algorithms, are not examined
Consider the local geometry between sample.The basic thought of LPP is: initial data can be kept after projection in lower dimensional space
Its local geometry in higher dimensional space.Since LPP algorithm considers local geometry, so that it often compares LDA algorithm
There is better discrimination.
But the above method all employs the Frobenius norm very sensitive to noise and heterogeneous data to construct
Objective function so that these methods all have the defects that it is certain.In recent years, it was discovered by researchers that image often has low-rank knot
Structure, using low-rank representation technology, what researcher can be convenient finds out the lower-dimensional subspace structure being embedded in data.For one
For the noisy data of group, it can will be counted while the lower-dimensional subspace structure for the data that learn using low-rank representation method
Noise separation in comes out.
In order to overcome LDA algorithm more sensitive to noise, the problem of inadequate robust, the present invention calculates low-rank technology and LDA
Method combines, and proposes a kind of image characteristic extracting method of low-rank robust linear discriminant analysis, to further increase LDA calculation
The robustness and recognition performance of method.
In the present invention, low-rank structure is introduced in LDA algorithm, compared with existing PCA, LDA and LPP algorithm, is had such as
Lower advantage:
It, can be in the lower-dimensional subspace knot for the data that learn using low-rank representation method for data noisy for one group
While structure, the noise separation in data is come out.Therefore, low rank analysis is introduced in LDA algorithm, and the Shandong of algorithm can be improved
Stick makes it to insensitive for noise；
By the experiment in ORL facial image database, the superiority of the relatively other algorithms of this algorithm is demonstrated.Fig. 2 is experiment
With the library ORL parts of images (increasing the salt-pepper noise that intensity is 0.01 in image).
Table 1 is PCA, and (training sample is difference to the discrimination of LDA, LPP and algorithm designed by the present invention in the library ORL
Discrimination when being 4 and 5).
Discrimination of 1 algorithms of different of table in the library ORL
It should be understood by those ordinary skilled in the art that: the discussion of any of the above embodiment is exemplary only, not
It is intended to imply that the scope of the present disclosure (including claim) is limited to these examples；Under thinking of the invention, above embodiments
Or can also be combined between the technical characteristic in different embodiments, step can be realized with random order, and be existed such as
Many other variations of the upper different aspect of the invention, for simplicity, they are not provided in details.
The embodiment of the present invention be intended to cover fall into all such replacements within the broad range of appended claims,
Modifications and variations.Therefore, all within the spirits and principles of the present invention, any omission, modification, equivalent replacement, the improvement made
Deng should all be included in the protection scope of the present invention.
Claims (4)
1. a kind of image characteristic extracting method based on low-rank robust linear discriminant analysis, which is characterized in that the described method includes:
The low-rank representation of original image is found out using the Robust Principal Component Analysis algorithm based on low-rank representation；
Feature extraction is carried out using low-rank representation of the linear character discriminatory analysis algorithm to original image；
Classified using nearest neighbor classifier.
2. the image characteristic extracting method according to claim 1 based on low-rank robust linear discriminant analysis, feature exist
In when finding out the low-rank representation of original image using the Robust Principal Component Analysis algorithm based on low-rank representation, this method is further
Include:
All training samples are obtained, every piece image is stretched by column, so that it becomes the column vector x of d dimensioni∈Rd, i=
All images are formed a data matrix X={ x by 1,2, L, N1,x2,L,xN}=[X1,L,Xc]∈Rd×N, wherein c is sample
This classification number；
All test samples are obtained, every piece image is stretched by column, so that it becomes the column vector y of d dimensioni∈Rd, i=
All images are formed a data matrix Y={ y by 1,2, L, M1,y2,L,yM}=[Y1,L,Yc]∈Rd×M；
Initialization: setting initial parameter Y0=sgn (X)/J (sgn (X)), E0=0, μ0=0, ρ > 1, the number of iterations k=0, wherein
Sgn () be sign function, J (sgn (X))=max (| | sgn (X) | |2,λ-1||sgn(X)||∞), λ > 0, | | | |2For 2 models
Number, | | | |∞For infinity norm, E is coefficient matrix, it is Lagrange multiplier, is regularization parameter；
It calculatesSingular value decomposition, i.e.,Wherein svd () is indicated
The singular value decomposition of calculating matrix；
It calculatesFor each of matrix S elements Sij, 1≤i≤d, 1≤j≤n has
It calculates
Calculate Yk+1=Yk+μk(X-Ak+1-Ek+1)；μk+1=ρ μk；
Judge whetherIf it is k=k+1 is enabled, initiation parameter, singular value point are re-started
Solution and calculating；
If otherwise carrying out dimensionality reduction to data matrix A and test sample Y respectively with principal component analysis (PCA) algorithm, dimensionality reduction is obtained
Data matrix A and Y afterwards.
3. the image characteristic extracting method according to claim 1 based on low-rank robust linear discriminant analysis, feature exist
In when carrying out feature extraction using low-rank representation of the linear character discriminatory analysis algorithm to original image, this method is further wrapped
It includes:
Calculate within-class scatter matrix Sw,Wherein NiIndicate the sample for belonging to the i-th class
Subscript collection, ajFor j-th of sample of the i-th class in matrix A, m(i)For the mean value of the i-th class sample；
Calculate between class scatter matrix Sb,Wherein niFor the sample number of the i-th class, m is all
The mean value of sample；
Calculate projection matrix U=[ui], 1≤i≤c-1, uiFor matrixEigenvalue λiCorresponding feature vector, that is, haveAnd eigenvalue λiIt arranges from small to large；
It calculatesWith
4. the image characteristic extracting method according to claim 1 based on low-rank robust linear discriminant analysis, feature exist
In when being classified using nearest neighbor classifier, this method further comprises, with the nearest neighbor classifier in image recognition technology
To matrix after projectionWithCarry out classification processing is carried out, the test sample number being identified is obtained, is identified with what is obtained
Test sample number divided by total test sample number M, calculate algorithm discrimination.
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