CN111611963A - Face recognition method based on neighbor preserving canonical correlation analysis - Google Patents

Face recognition method based on neighbor preserving canonical correlation analysis Download PDF

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CN111611963A
CN111611963A CN202010473892.2A CN202010473892A CN111611963A CN 111611963 A CN111611963 A CN 111611963A CN 202010473892 A CN202010473892 A CN 202010473892A CN 111611963 A CN111611963 A CN 111611963A
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neighbor
correlation analysis
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face recognition
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CN111611963B (en
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袁运浩
张超
张晖
李云
强继朋
李斌
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Yangzhou University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V40/00—Recognition of biometric, human-related or animal-related patterns in image or video data
    • G06V40/10—Human or animal bodies, e.g. vehicle occupants or pedestrians; Body parts, e.g. hands
    • G06V40/16—Human faces, e.g. facial parts, sketches or expressions
    • G06V40/168—Feature extraction; Face representation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/214—Generating training patterns; Bootstrap methods, e.g. bagging or boosting
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/241—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2413—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on distances to training or reference patterns
    • G06F18/24147—Distances to closest patterns, e.g. nearest neighbour classification
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/25—Fusion techniques
    • G06F18/253—Fusion techniques of extracted features
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V40/00—Recognition of biometric, human-related or animal-related patterns in image or video data
    • G06V40/10—Human or animal bodies, e.g. vehicle occupants or pedestrians; Body parts, e.g. hands
    • G06V40/16—Human faces, e.g. facial parts, sketches or expressions
    • G06V40/172—Classification, e.g. identification

Abstract

The invention discloses a face recognition method based on neighbor preserving canonical correlation analysis, which comprises the following steps of 1, inputting a face training data set X ∈ Rm×N，Y∈Rn×NCalculating a neighbor weight reconstruction matrix U of the image by neighbor preserving learningxAnd Uy(ii) a 2: finding two sets of projection vectors w using canonical correlation analysisxAnd wyKeeping the neighbors into the frame of typical correlation analysis by an optimization method, and calculating a projection matrix W by utilizing generalized eigenvalue decompositionxAnd Wy(ii) a 3: low-dimensional projection of test face image by adopting two feature fusion strategies
Figure DDA0002515179950000011
And
Figure DDA0002515179950000012
carrying out fusion; 4: and using the fused features for face recognition by using a nearest neighbor classifier. The invention learns the face adjacent weight reconstruction matrix through adjacent maintenance, introduces the adjacent maintenance into a typical correlation analysis frame by an optimization method, and then utilizes the label information of the face, so that the extracted face characteristics not only maximize the correlation among different faces, but also maintain the neighborhood structure of the face to the greatest extent, and improve the face recognition capability and stability.

Description

Face recognition method based on neighbor preserving canonical correlation analysis
Technical Field
The invention relates to the field of classification and recognition in machine learning, in particular to a face recognition method based on neighbor preserving canonical correlation analysis.
Background
With the rapid development of modern information technology, the technology for identity authentication is moving to the level of biological characteristics. Modern biological recognition technology is mainly characterized in that personal identity is identified by closely combining a computer with a high-tech means and utilizing inherent physiological characteristics and behavior characteristics of a human body. The face recognition refers to the distribution of facial features and contours of a person, and the distribution features are different from person to person and are inherent. Face recognition is a technique that is performed based on facial feature information of a person. The method comprises the steps of collecting images or video streams containing human faces by using a camera or a pick-up head, automatically detecting and tracking the human faces in the images, and then determining one person or a plurality of persons in a scene by using an existing human face database. The current research scope of face recognition mainly comprises several aspects: face detection and positioning, face feature representation, face recognition, expression and posture analysis and physiological analysis and classification. At present, the research methods of face recognition include a method based on geometric features, a local feature analysis method, a characteristic face method and a latest neural network method. It is also one of the trends to study face recognition from a three-dimensional perspective in the future.
The research of the face recognition system started in the 60 s of the 20 th century, and the development of computer technology and optical imaging technology was improved after the 80 s, while the real entering into the first stage of application was in the later 90 s, and the technology implementation in the united states, germany and japan was the main. The key to the success of the face recognition system is whether the face recognition system has a core algorithm with a sharp end or not, and the recognition result has practical recognition rate and recognition speed. The face recognition system integrates various professional technologies such as artificial intelligence, pattern recognition, machine learning, model theory, expert system, video image processing and the like, and simultaneously needs to combine the theory and realization of intermediate value processing, is the latest application of biological feature recognition, realizes the core technology of the face recognition system, and shows the conversion from weak artificial intelligence to strong artificial intelligence.
Unlike the traditional fusion method that multiple groups of features are initially juxtaposed to form a high-dimensional feature, the CCA (Canonical Correlation Analysis) achieves the purpose of feature fusion by maximizing the Correlation between two groups of features after projection, and has been successfully applied to the field of pattern recognition, such as face recognition, expression recognition, image processing, digital character recognition, and the like. However, like PCA, canonical correlation analysis can only extract linear features of the pattern, and as an unsupervised learning method, the classification effect is often poor, and then many researchers have proposed various improved methods on the basis of canonical correlation analysis, for example, Kernel Canonical Correlation Analysis (KCCA) combines canonical correlation analysis with kernel methods to extract nonlinear features of the pattern; sparse Canonical Correlation Analysis (SCCA) can preserve sparse reconstruction relationships of samples. Besides, researchers introduce supervision and Semi-supervision technologies into the canonical correlation analysis, and propose Discriminant Canonical Correlation Analysis (DCCA) and Semi-supervised canonical correlation score (Semi-CCA), and on the basis, researchers introduce pairwise constraint information among samples, and propose a supervised canonical correlation analysis algorithm using relative strength.
In recent years, manifold learning is applied to the field of face recognition due to the characteristics of nonlinearity, capability of revealing an intrinsic structure of a data set and maintaining local geometric characteristics of data and the like. The main manifold learning algorithm includes equal scale mapping, local linear embedding, laplacian feature mapping and local tangential spatial arrangement. Because the implicit mapping established by the manifold learning algorithms between the high-dimensional observation space and the internal low-dimensional space is defined on the training data set, new observation data points cannot be directly mapped, and therefore the implicit mapping cannot be directly used in face recognition, two new dimension reduction methods, namely local preserving projection and neighbor preserving embedding, are proposed to solve the problem. The traditional CCA face recognition method is an unsupervised method, label information of a good face is not utilized, and sometimes, the data volume of a face image is too large, so that the recognition speed and the recognition effect are influenced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a face recognition method based on neighbor preserving canonical correlation analysis, wherein the extracted face features not only maximize the correlation between different face data, but also optimally save the adjacent structure of the face, thereby improving the face recognition capability and stability.
The purpose of the invention is realized as follows: a face recognition method based on neighbor preserving canonical correlation analysis comprises the following steps:
step 1, inputting a face training data set X ∈ Rm×N，Y∈Rn×NCalculating a neighbor weight reconstruction matrix U of the image by neighbor preserving learningxAnd Uy；
Step 2: finding two sets of projection vectors w using canonical correlation analysisxAnd wyKeeping the neighbors into the frame of typical correlation analysis by an optimization method, and calculating a projection matrix W by utilizing generalized eigenvalue decompositionxAnd Wy；
And step 3: in the feature fusion stage, two feature fusion strategies are adopted to perform low-dimensional projection on the tested face image
Figure BDA0002515179930000031
And
Figure BDA0002515179930000032
carrying out fusion;
and 4, step 4: and using the fused features for face recognition by using a nearest neighbor classifier.
As a further limitation of the present invention, the step 1 specifically includes inputting face training data X ═ X1,x2,...,xN]∈Rm×NAnd Y ═ Y1,y2,...,yN]∈Rn×NCalculating k-neighbor reconstruction weight matrix U of training samplexAnd Uy，UxAnd UyCan be obtained by minimizing the following objective function:
Figure BDA0002515179930000033
Figure BDA0002515179930000034
and
Figure BDA0002515179930000035
Figure BDA0002515179930000036
wherein
Figure BDA0002515179930000041
And
Figure BDA0002515179930000042
respectively representing face samples xiAnd yiK-nearest neighbor samples of (1) are calculated to obtain Ux＝(ux,ij) And Uy＝(uy,ij)。
As a further limitation of the present invention, the step 2 specifically includes: establishing an optimization function of a neighbor preserving canonical correlation analysis:
Figure BDA0002515179930000043
wherein Sxy＝XYTA cross-covariance matrix representing X and Y, describing the correlation between two sets of variables; swRepresenting the intra-class correlation matrix, SbAn inter-class correlation matrix is represented in which,
Figure BDA0002515179930000044
Figure BDA0002515179930000045
m represents a same type of face sample set, C represents a different type of face sample set,
Figure BDA0002515179930000046
and
Figure BDA0002515179930000047
a local linear reconstruction error matrix is represented, which is defined as follows:
Figure BDA0002515179930000048
wherein U isxAnd UyReconstructing a weight matrix for the neighbor, wherein I is an identity matrix;
using the merit function method, the optimization function (1) can be transformed into the following optimization function (2):
Figure BDA0002515179930000049
by adopting Lagrange multiplier method, the optimization function (2) can be converted into the following two generalized eigenvalue problems:
Figure BDA0002515179930000051
in actual calculation, only d eigenvectors corresponding to the first d largest non-zero eigenvalues of one generalized eigenvalue problem need to be solved, and then the other set of projection directions are solved by using the following relation:
Figure BDA0002515179930000052
obtaining projection matrix of two groups of human face characteristics X and Y
Figure BDA0002515179930000053
And
Figure BDA0002515179930000054
as a further limitation of the present invention, said step 3 specifically comprises, for any one of the test samples [ x ]T,yT]TA low-dimensional projection thereof can be obtained as
Figure BDA0002515179930000055
And
Figure BDA0002515179930000056
and fusing by adopting two characteristic combination strategies, wherein the two characteristic combination strategies comprise a characteristic fusion strategy 1:
Figure BDA0002515179930000057
feature fusion strategy 2:
Figure BDA0002515179930000058
compared with the prior art, the invention has the beneficial effects that: aiming at label information and local information of a face which are not introduced in the traditional typical correlation analysis face recognition, the method provides the method which meets the requirement that the extracted two groups of face features have the maximum correlation coefficient, and simultaneously requires that the local linear reconstruction errors in the two face feature sets after projection are as small as possible. In order to better utilize face label information, improve the identification capability of extracting face features, maximize the correlation between the same face features and minimize the correlation between different face features, when a neighbor weight reconstruction matrix of an image is calculated, the label information is introduced, and neighbor points are selected from the face images of the same type. In the feature fusion stage, two feature fusion strategies are adopted. The face neighborhood weight reconstruction matrix is learned through neighborhood maintenance, the neighborhood maintenance is introduced into a typical correlation analysis frame by an optimization method, and the label information of the face is utilized, so that the extracted face features not only maximize the correlation among different faces, but also maintain the neighborhood structure of the face to the greatest extent, and improve the face recognition capability and stability.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention.
Fig. 2 is an ORL face recognition rate diagram under the feature fusion strategy 1.
Fig. 3 is an ORL face recognition rate diagram under the feature fusion policy 2.
Fig. 4 is a diagram of the Yale face recognition rate in the feature fusion strategy 1.
Fig. 5 is a diagram of the Yale face recognition rate under the feature fusion strategy 2.
Detailed Description
A face recognition method based on neighbor preserving canonical correlation analysis as shown in fig. 1 includes the following steps:
step 1, inputting a face training data set X ∈ Rm×N，Y∈Rn×NCalculating a neighbor weight reconstruction matrix U of the image by neighbor preserving learningxAnd Uy；
Input face training data X ═ X1,x2,...,xN]∈Rm×NAnd Y ═ Y1,y2,...,yN]∈Rn×NCalculating k-neighbor reconstruction weight matrix U of training samplexAnd Uy，UxAnd UyCan be obtained by minimizing the following objective function:
Figure BDA0002515179930000061
Figure BDA0002515179930000062
and
Figure BDA0002515179930000063
Figure BDA0002515179930000064
wherein
Figure BDA0002515179930000071
And
Figure BDA0002515179930000072
respectively representing face samples xiAnd yiK-nearest neighbor samples of (1) are calculated to obtain Ux＝(ux,ij) And Uy＝(uy,ij)。
Step 2: finding two sets of projection vectors w using canonical correlation analysisxAnd wyKeeping the neighbors into the frame of typical correlation analysis by an optimization method, and calculating a projection matrix W by utilizing generalized eigenvalue decompositionxAnd Wy；
Establishing an optimization function of a neighbor preserving canonical correlation analysis:
Figure BDA0002515179930000073
wherein Sxy＝XYTA cross-covariance matrix representing X and Y, describing the correlation between two sets of variables; swRepresenting the intra-class correlation matrix, SbAn inter-class correlation matrix is represented in which,
Figure BDA0002515179930000074
Figure BDA0002515179930000075
m represents a same type of face sample set, C represents a different type of face sample set,
Figure BDA0002515179930000076
and
Figure BDA0002515179930000077
a local linear reconstruction error matrix is represented, which is defined as follows:
Figure BDA0002515179930000078
wherein U isxAnd UyReconstructing a weight matrix for the neighbor, wherein I is an identity matrix;
using the merit function method, the optimization function (1) can be transformed into the following optimization function (2):
Figure BDA0002515179930000081
by adopting Lagrange multiplier method, the optimization function (2) can be converted into the following two generalized eigenvalue problems:
Figure BDA0002515179930000082
in actual calculation, only d eigenvectors corresponding to the first d largest non-zero eigenvalues of one generalized eigenvalue problem need to be solved, and then the other set of projection directions are solved by using the following relation:
Figure BDA0002515179930000083
obtaining projection matrix of two groups of human face characteristics X and Y
Figure BDA0002515179930000084
And
Figure BDA0002515179930000085
and step 3: in the feature fusion stage, two feature fusion strategies are adopted to perform low-dimensional projection on the tested face image
Figure BDA0002515179930000086
And
Figure BDA0002515179930000087
carrying out fusion;
for any one test sample xT,yT]TA low-dimensional projection thereof can be obtained as
Figure BDA0002515179930000088
And
Figure BDA0002515179930000089
and fusing by adopting two characteristic combination strategies, wherein the two characteristic combination strategies comprise a characteristic fusion strategy 1:
Figure BDA00025151799300000810
feature fusion strategy 2:
Figure BDA00025151799300000811
and 4, step 4: and using the fused features for face recognition by using a nearest neighbor classifier.
To test the effectiveness of the present invention, the following experiments were performed, first performing experimental parameter settings:
ORL face database: the database contains 400 face images of 40 people, 10 images per person, each image having a resolution of 92 x 112. These facial images contain changes in expression, changes in pose, and the like. During the experiment, the first 5 images of each person are selected as training samples, the second 5 images are selected as test samples, and wavelet 4-level decomposition is carried out on the original face images to obtain low-frequency components as a second feature set; in addition, the Principal Component Analysis (PCA) is adopted to reduce the dimension of the face image, and the calculation complexity is reduced.
Yale face database: the database contains 165 gray-scale face images of 15 persons, and the resolution of each image is 120 x 91. Each person had 11 images containing three different lighting directions left, right and front, and eye, expression changes (normal, happy, sad, sleepy, surprised and blinking); in the experiment, each person selects the first 5 images as a training set, the rest 6 images as a test set, wavelet 4-level decomposition is carried out on the original face image to obtain a low-frequency component as a second feature set, and PCA is adopted for dimension reduction, so that the calculation complexity is reduced.
The experiment adopts a nearest neighbor classifier for classification, the performance measurement parameter is identification accuracy (A), and the formula is as follows:
Figure BDA0002515179930000091
experiment 1ORL face database recognition rate analysis
As shown in fig. 2 and fig. 3, the classification recognition rate of the ORL face database of cambridge university in england under different feature fusion strategies is shown, the abscissa shows the feature dimension after projection, and the ordinate shows the classification recognition accuracy. The experimental results show that the classification recognition rate of a plurality of algorithms increases along with the increase of the feature dimension, and when the feature dimension increases to a certain dimension, the recognition rate can be maintained at a stable level.
Experiment 2Yale face database recognition rate analysis
As shown in fig. 4 and 5, the classification recognition rate of the Yale face database under different feature fusion strategies is shown, the abscissa shows the feature dimension after projection, and the ordinate shows the recognition rate. From experimental results, because the Yale face training samples are fewer and 165 faces are counted, under the characteristic fusion strategies 1 and 2, the face identification information extracted by the algorithm is weaker, the recognition rate fluctuation is larger, the recognition result is reduced compared with an ORL face database, but the recognition rate is still higher than that of other algorithms.
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.

Claims (4)

1. A face recognition method based on neighbor preserving canonical correlation analysis is characterized by comprising the following steps:
step 1, inputting a face training data set X ∈ Rm×N，Y∈Rn×NCalculating a neighbor weight reconstruction matrix U of the image by neighbor preserving learningxAnd Uy；
Step 2: finding two sets of projection vectors w using canonical correlation analysisxAnd wyKeeping the neighbors into the frame of typical correlation analysis by an optimization method, and calculating a projection matrix W by utilizing generalized eigenvalue decompositionxAnd Wy；
And step 3: in the feature fusion stage, two feature fusion strategies are adopted to perform low-dimensional projection on the tested face image
Figure FDA0002515179920000018
And
Figure FDA0002515179920000017
carrying out fusion;
and 4, step 4: and using the fused features for face recognition by using a nearest neighbor classifier.
2. The face recognition method based on nearest neighbor preserving canonical correlation analysis according to claim 1, wherein the step 1 specifically includes inputting face training data X ═ X1,x2,...,xN]∈Rm×NAnd Y ═ Y1,y2,...,yN]∈Rn×NCalculating k-neighbor reconstruction weight matrix U of training samplexAnd Uy，UxAnd UyCan be obtained by minimizing the following objective function:
Figure FDA0002515179920000011
Figure FDA0002515179920000012
and
Figure FDA0002515179920000013
Figure FDA0002515179920000014
wherein
Figure FDA0002515179920000015
And
Figure FDA0002515179920000016
respectively representing face samples xiAnd yiK-nearest neighbor samples of (1) are calculated to obtain Ux＝(ux,ij) And Uy＝(uy,ij)。
3. The face recognition method based on neighbor preserving canonical correlation analysis according to claim 1, wherein the step 2 specifically includes: establishing an optimization function of a neighbor preserving canonical correlation analysis:
Figure FDA0002515179920000021
wherein Sxy＝XYTA cross-covariance matrix representing X and Y, describing the correlation between two sets of variables; swRepresenting the intra-class correlation matrix, SbAn inter-class correlation matrix is represented in which,
Figure FDA0002515179920000022
Figure FDA0002515179920000023
m represents a same type of face sample set, C represents a different type of face sample set,
Figure FDA0002515179920000024
and
Figure FDA0002515179920000025
a local linear reconstruction error matrix is represented, which is defined as follows:
Figure FDA0002515179920000026
wherein U isxAnd UyReconstructing a weight matrix for the neighbor, wherein I is an identity matrix;
using the merit function method, the optimization function (1) can be transformed into the following optimization function (2):
Figure FDA0002515179920000027
by adopting Lagrange multiplier method, the optimization function (2) can be converted into the following two generalized eigenvalue problems:
Figure FDA0002515179920000031
in actual calculation, only d eigenvectors corresponding to the first d largest non-zero eigenvalues of one generalized eigenvalue problem need to be solved, and then the other set of projection directions are solved by using the following relation:
Figure FDA0002515179920000032
obtaining projection matrix of two groups of human face characteristics X and Y
Figure FDA0002515179920000033
And
Figure FDA0002515179920000034
4. the face recognition method based on neighbor preserving canonical correlation analysis according to claim 1, wherein the step 3 specifically includes: for any one test sample xT,yT]TA low-dimensional projection thereof can be obtained as
Figure FDA0002515179920000035
And
Figure FDA0002515179920000036
and fusing by adopting two characteristic combination strategies, wherein the two characteristic combination strategies comprise a characteristic fusion strategy 1:
Figure FDA0002515179920000037
feature fusion strategy 2:
Figure FDA0002515179920000038
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