CN109063698A - A kind of non-negative feature extraction and face recognition application method, system and storage medium - Google Patents
A kind of non-negative feature extraction and face recognition application method, system and storage medium Download PDFInfo
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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
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Abstract
The present invention provides a kind of non-negative feature extraction and the construction method of face recognition application, include the following steps: that cosine measurement portrays degree of loss step: the degree of loss after portraying matrix decomposition using the cosine measurement between matrix；It constitutes objective function step: degree of loss step being portrayed by cosine measurement, constitutes objective function；It obtains and updates iterative formula step: by objective functionIt is converted, constitutes optimization problem to be solved, the update iterative formula of algorithm is acquired by constructing auxiliary function.The beneficial effects of the present invention are: 1. solve the lighting issues encountered in face recognition process；2. convergence proposed by the invention not only by theoretically being proved using auxiliary function, but also is also verified in an experiment, our algorithm convergence with higher；3. by the face database for having illumination effect compared with related algorithm carries out experiment, the results showed that algorithm of the invention have certain superiority.
Description
Technical field
The present invention relates to technical field of data processing more particularly to a kind of non-negative feature extraction and face recognition application sides
Method, system and storage medium.
Background technique
With the arrival of information age, personal identification identification is carried out using the intrinsic physiological characteristic of human body and behavioural characteristic
Biological identification technology become one of most active research field.In numerous branches of biological identification technology, most hold
A technology being easily accepted is face recognition technology, this is because for other biological identification technology, face
Identification is with no invasive, non-imposed, untouchable and concurrency.
Face recognition technology includes two stages, and the first stage is feature extraction, that is, extracts the people in facial image
Face characteristic information, this stage directly determine the quality of face recognition technology；Second stage is identity authentication, according to extracting
Characteristic information carry out personal identification identification.Principal component analysis (PCA) and singular value decomposition (SVD) are more classical features
Extracting method, but the feature vector that both methods proposes usually contains negative element, therefore is non-negative data in original sample
Under, these methods do not have reasonability and interpretation.Non-negative Matrix Factorization (NMF) is that a kind of feature for handling non-negative data mentions
Method is taken, it is very widely used, such as hyperspectral data processing, facial image identification etc..NMF algorithm is non-in original sample
During negative data matrix decomposition, the feature of extraction is limited with nonnegativity, that is, after decomposing it is important be all it is non-negative,
Non-negative sparse features can thus be extracted.Nonnegative matrix X is namely approximately decomposed into basic image matrix by the essence of NMF algorithm
The product of W and coefficient matrix H, i.e. X ≈ WH, and W and H are nonnegative matrixes.Each column of matrix X in this way can be expressed as square
The non-negative linearity combination of battle array W column vector, this also complies with the construction foundation of NMF algorithm --- to whole perception by whole to forming
(pure additivity) that the perception of the part of body is constituted.Traditional NMF algorithm is to be based on Euclidean distance or KL divergence, different in order to overcome
The interference of constant value, enhances the robustness of algorithm, and has scholar to propose the NMF algorithm (CIM-NMF) based on joint entropy measurement.It examines
Consider a facial image, be denoted as vector x, the illumination of varying strength is equivalent to before vector x multiplied by a coefficient k.
The value of the more strong then k of illumination is bigger, and the value of the more weak then k of illumination is smaller.For Euclidean distance, these three measurements of KL divergence and joint entropy
For, vector x and kx distance are 0 and if only if k=1.When illumination is very strong, i.e., when k value is very big, vector x also becomes with kx distance
Must be very big, so that judging by accident.Similarly, erroneous judgement is also easy to appear when illumination is very weak.Therefore three of the above measurement becomes in illumination
It is fine for changing the recognition effect in apparent face database not.And cosine measurement be for the scaling of scale it is constant, that is, have
There is flexible invariance.No matter k takes any nonzero value, and vector x is remained unchanged with kx COS distance, therefore can overcome recognition of face
Encountered in lighting issues.
Currently available technology mainly has following 3 kinds:
1. the Algorithms of Non-Negative Matrix Factorization (ED-NMF) based on Euclidean distance
Euclidean distance is a kind of common distance metric, it can measure the absolute distance in hyperspace between each point.
For Non-negative Matrix Factorization X ≈ WH, ED-NMF needs the optimization problem solved are as follows:
It updates iterative formula are as follows:
2. the Algorithms of Non-Negative Matrix Factorization (KL-NMF) based on Kullback-Leibler divergence
Kullback-Leibler divergence, also referred to as relative entropy, what it was measured is two probability in similar events space
The difference condition of distribution.For Non-negative Matrix Factorization X ≈ WH, KL-NMF needs the optimization problem solved are as follows:
It updates iterative formula are as follows:
Here E is indicated identical as X size, and element is all 1 matrix.
3. the Algorithms of Non-Negative Matrix Factorization (CIM-NMF) based on joint entropy
Joint entropy is commonly used in the noise processed in information theory study.If x, y are n-dimensional vectors, define joint entropy and lure
The measurement (CIM) led are as follows:
Here kσ() indicates kernel function, ei=xi-yiIndicate error.
CIM-NMF is that the measurement of joint entropy induction is designed Algorithms of Non-Negative Matrix Factorization as loss function.For non-
Negative matrix decomposes for X ≈ WH, and CIM-NMF needs the optimization problem solved are as follows:
HereIndicate Gaussian kernel.
The update iterative formula of CIM-NMF are as follows:
It can be seen that: 1, the loss function of traditional Algorithms of Non-Negative Matrix Factorization (NMF) be based on F- norm constructed, so
And F- norm is more sensitive to exceptional value, this makes the stability of algorithm poor.Simultaneously as being stretched since Euclidean distance does not have
Contracting invariance, therefore the variation of illumination in recognition of face cannot be coped with well.2, the Non-negative Matrix Factorization based on joint entropy measurement
(CIM-NMF) stability of traditional Algorithms of Non-Negative Matrix Factorization is improved to a certain extent.It is stretched since joint entropy measurement does not have
Contracting invariance, therefore the recognition effect in the apparent face database of illumination variation is not still fine.
Summary of the invention
The present invention provides a kind of non-negative feature extraction and the construction methods of face recognition application, include the following steps:
Cosine measurement portrays degree of loss step: the degree of loss after portraying matrix decomposition using the cosine measurement between matrix；
It constitutes objective function step: degree of loss step being portrayed by cosine measurement, is constituted objective function F (W, H)；
It obtains and updates iterative formula step: objective function F (W, H) being converted, optimization problem to be solved is constituted,
The update iterative formula of algorithm is acquired by constructing auxiliary function.
As a further improvement of the present invention, which further includes convergence verification step, verifies and walks in convergence
In rapid, prove that algorithm has convergence by construction auxiliary function.
As a further improvement of the present invention, the update iterative formula that algorithm is acquired by constructing auxiliary function are as follows:
Wherein, X indicates that sample matrix, H indicate that coefficient matrix, W indicate that basic image matrix, E indicate and H (or W) size phase
Together, and element be all 1 matrix, the element in s-matrix is
The invention also discloses a kind of non-negative feature extraction and face recognition application method, including training step, the instructions
Practicing step includes:
First step: training sample matrix X, step-up error threshold epsilon, maximum number of iterations are converted by training sample image
Imax, basic image matrix W and coefficient matrix H are initialized；
Second step: using the update iterative formula for acquiring algorithm by constructing auxiliary function, W and H is updated；
Third step: if objective function F (W, H)≤ε or the number of iterations reach Imax, just stop iteration, output matrix W
And H；Otherwise, second step is executed.
As a further improvement of the present invention, a kind of non-negative feature extraction and face recognition application method further include in training
Testing procedure is executed again after step, and the testing procedure includes:
Four steps: the averaged feature vector m of every class in training sample is calculatedj(j=1 ..., c)；
5th step: for test sample y, its feature vector h is calculatedy；
6th step: with respective metric calculation hyTo the averaged feature vector m of every classjDistance, if hyWith mlDistance
Sample y is then attributed to l class by minimum.
As a further improvement of the present invention, the update iterative formula that algorithm is acquired by constructing auxiliary function are as follows:
Wherein, X indicates that sample matrix, H indicate that coefficient matrix, W indicate that basic image matrix, E indicate and H (or W) size phase
Together, and element be all 1 matrix, the element in s-matrix is
The invention also discloses a kind of non-negative feature extraction and the systems of face recognition application, comprising: memory, processor
And it is stored in the computer program on the memory, the realization when computer program is configured to be called by the processor
The step of method described in claim.
The invention also discloses a kind of computer readable storage medium, the computer-readable recording medium storage has calculating
Machine program, when the computer program is configured to be called as processor the step of method described in realization claim.
The beneficial effects of the present invention are: 1. loss by going metric matrix to decompose using cosine measurement substitution F- norm
Degree, solves the lighting issues encountered in face recognition process；2. convergence proposed by the invention, not only passes through benefit
It is theoretically proved with auxiliary function, and is also verified in an experiment, our algorithm receipts with higher
Holding back property；3. by the face database for having illumination effect compared with related algorithm carries out experiment, the results showed that it is of the invention
Algorithm has certain superiority.
Detailed description of the invention
Fig. 1 is algorithm construction process flow diagram flow chart of the invention；
Fig. 2 is algorithm implementation procedure flow chart of the invention；
Fig. 3 is algorithm proposed by the present invention and related algorithm (NMF, CIM-NMF) of the invention
Discrimination on CMU PIE face database compares figure；
Fig. 4 is the convergence curve figure of algorithm of the invention.
Specific embodiment
As shown in Figure 1, the invention discloses a kind of non-negative feature extraction and the construction methods of face recognition application, including such as
Lower step:
Cosine measurement portrays degree of loss step: the degree of loss after portraying matrix decomposition using the cosine measurement between matrix；
It constitutes objective function step: degree of loss step being portrayed by cosine measurement, is constituted objective function F (W, H)；
It obtains and updates iterative formula step: objective function F (W, H) being converted, optimization problem to be solved is constituted,
The update iterative formula of algorithm is acquired by constructing auxiliary function.
The construction method further includes convergence verification step, in convergence verification step, passes through construction auxiliary function card
Bright algorithm has convergence.
A kind of construction method of non-negative feature extraction and face recognition application, it is described to acquire algorithm by constructing auxiliary function
Update iterative formula are as follows:
Wherein, X indicates that sample matrix, H indicate that coefficient matrix, W indicate that basic image matrix, E indicate and H (or W) size phase
Together, and element be all 1 matrix, the element in s-matrix is
As shown in Fig. 2, a kind of non-negative feature extraction and face recognition application method, including training step, the training step
Suddenly include:
First step: training sample matrix X, step-up error threshold epsilon, maximum number of iterations are converted by training sample image
Imax, basic image matrix W and coefficient matrix H are initialized；
Second step: using the update iterative formula for acquiring algorithm by constructing auxiliary function, W and H is updated；
Third step: if objective function F (W, H)≤ε or the number of iterations reach Imax, just stop iteration, output matrix W
And H；Otherwise, second step is executed.
As shown in Fig. 2, a kind of non-negative feature extraction and face recognition application method further include holding again after training step
Row testing procedure, the testing procedure include:
Four steps: the averaged feature vector m of every class in training sample is calculatedj(j=1 ..., c)；
5th step: for test sample y, its feature vector h is calculatedy；
6th step: with respective metric calculation hyTo the averaged feature vector m of every classjDistance, if hyWith mlDistance
Sample y is then attributed to l class by minimum.
A kind of non-negative feature extraction and face recognition application method, the update that algorithm is acquired by constructing auxiliary function
Iterative formula are as follows:
Wherein, X indicates that sample matrix, H indicate that coefficient matrix, W indicate that basic image matrix, E indicate and H (or W) size phase
Together, and element be all 1 matrix, the element in s-matrix is
The system of a kind of non-negative feature extraction and face recognition application, comprising: memory, processor and be stored in described
Computer program on memory is realized described in claim when the computer program is configured to be called as the processor
Method the step of.
A kind of computer readable storage medium, the computer-readable recording medium storage have computer program, the meter
The step of method described in claim is realized when calculation machine program is configured to be called as processor.
One, keyword explain (note: illustrate the present invention relates to some key words concept)
1. symbol description
X matrix
A, b vector
XijI-th j element of matrix X
XTThe transposition of X
The product of matrix A and corresponding element in B
The quotient of matrix A and corresponding element in B
AdThe d power of each element in matrix A
2. Non-negative Matrix Factorization (Non-negative Matrix Factorization, NMF)
The basic thought of NMF is by a non-negative sample matrixIt is approximately decomposed into the product of two nonnegative matrixes,
That is:
X≈WH
Wherein,WithIt is known respectively as basic image matrix and coefficient matrix.Also, pass through building damage
The approximation ratio between function measurement X and WH is lost, ordinary loss function is defined based on F- norm, are as follows:
F (W, H)=| | X-WH | |2
Here | | | | indicate F- norm.
3. cosine similarity (Cosine Similarity)
Cosine similarity be use two vectorial angle cosine values as measure two inter-individual differences size measurement,
It more focuses on difference of two vectors on direction than Euclidean distance.Cosine phase for any vector a and b, between them
Like degree is defined as:
Similar, for Arbitrary Matrix A and B, we define the cosine similarity between them are as follows:
It is constant for the rotation of coordinate system and the scaling of scale it can be seen from the definition of cosine similarity.
Present invention is generally directed to the lighting issues encountered in recognition of face, propose a kind of NMF based on cosine measurement
Algorithm (CSNMF).Compared to other measurements, cosine measurement is more that difference is distinguished from direction, and not to absolute numerical value
Sensitivity, therefore illumination effect encountered in recognition of face can be eliminated.We demonstrate the receipts of algorithm by constructing auxiliary function
Holding back property, and pass through the experimental verification validity of algorithm.
The main object of the present invention has:
1, a kind of new non-negative feature extraction algorithm based on cosine measurement is proposed, can be overcome based on F- norm, phase
Close the defect of the NMF algorithms of loss functions such as entropy measurement.
2, since cosine measurement has constant characteristic of stretching, therefore illumination encountered in recognition of face can be overcome to ask
Topic.
The it is proposed of 1.CSNMF
The building of objective function
In order to overcome the influence of illumination in recognition of face, the present invention portrays loss function using cosine measurement, it may be assumed that
Then optimization problem is writeable are as follows:
min F(W,H)s.t.W≥0,H≥0 (2)
In order to solve two unknown nonnegative matrix W and H in the objective function (1), we convert two for objective function
A sub- objective function, is respectively as follows:
Then problem (2) has also evolved into two sub-problems, is respectively as follows:
min f1(H)s.t.H≥0 (5)
min f2(W)s.t.W≥0 (6)
We obtain following update iterative formula by the method for construction auxiliary function, are as follows:
Wherein, X indicates that sample matrix, H indicate that coefficient matrix, W indicate that basic image matrix, E indicate and H (or W) size phase
Together, and element be all 1 matrix, the element in s-matrix isAlthough there is minus sign in our iterative formula,
But it can be proved that the iterative formula still meets the nonnegativity requirement of decomposition.
2. convergence proves
Since the convergence of W and H are proved to be all fours, below we only the convergence of H is proved.Firstly,
We will introduce the definition of auxiliary function.
Define 1: for arbitrary matrix H and H(t)If meeting condition
G(H,H(t)) >=f (H), and G (H(t),H(t))=f (H(t))
Then claim G (H, H(t)) be function f (H) an auxiliary function.
Lemma 1: if G (H, H(t)) be f (H) an auxiliary function, then f (H) is single under following update rule
What tune did not increased,
Lemma 2: A is set as a non-negative symmetrical matrix, then to arbitrary integer k, is set up just like lower inequality:
Next, we prove that the new algorithm that the present invention constructs has convergence by construction auxiliary function.
Theorem 1: function
It is f1(H) auxiliary function.
It proves: obviously, G (H(t),H(t))=f1(H(t))。
Enable A=WTW, P2=H has by lemma 2 it is found that arbitrary integer k
Therefore have
F can be obtained1(H)≤G(H,H(t))。
According to 1 and lemma 1 is defined, we know function G (H, H(t)) it is function f1(H) a upper limit, andG (H, H in order to obtain(t)) minimum value, we solve its derivative and it are enabled to have for 0
It is equivalent to
Thus formula can solve HabUpdate iterative formula:
Due to
Therefore update H under iterative formula herein and still meet nonnegativity, the f known to lemma 11(H) in the update iterative formula
Under be non-increasing.
In conclusion the specific building process of face recognition algorithms of the invention is as follows:
(1) degree of loss after matrix decomposition is portrayed using the cosine measurement between matrix；
(2) the update iterative formula of algorithm is acquired by constructing auxiliary function, as shown in figure 4, and demonstrating of the invention
Convergence theoretically ensure that the reasonability of algorithm.
As shown in Figure 3 and Table 1, it algorithm (Our Method) proposed by the present invention and Non-negative Matrix Factorization (NMF) and is based on
Discrimination (%) of the Non-negative Matrix Factorization (CIM-NMF) of joint entropy on CMU PIE face database compares
(3) (number of training that TN indicates every one kind)
The loss function for the Algorithms of Non-Negative Matrix Factorization that the present invention constructs is to measure to construct based on cosine, due to cosine degree
Amount is constant for the scaling of scale, therefore can overcome the illumination effect in recognition of face.
The invention proposes a kind of new non-negative feature extraction algorithms with preferable constringency performance and recognition performance, and
Successful application and recognition of face.
The beneficial effects of the present invention are: 1. loss by going metric matrix to decompose using cosine measurement substitution F- norm
Degree, solves the lighting issues encountered in face recognition process；2. convergence proposed by the invention, not only passes through benefit
It is theoretically proved with auxiliary function, and is also verified in an experiment, our algorithm receipts with higher
Holding back property；3. by the face database for having illumination effect compared with related algorithm carries out experiment, the results showed that it is of the invention
Algorithm has certain superiority.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
Claims (8)
1. the construction method of a kind of non-negative feature extraction and face recognition application, which comprises the steps of:
Cosine measurement portrays degree of loss step: the degree of loss after portraying matrix decomposition using the cosine measurement between matrix；
It constitutes objective function step: degree of loss step being portrayed by cosine measurement, is constituted objective function F (W, H)；
It obtains and updates iterative formula step: objective function F (W, H) being converted, optimization problem to be solved is constituted, passes through
Construction auxiliary function acquires the update iterative formula of algorithm.
2. construction method according to claim 1, which is characterized in that the construction method further includes convergence verification step,
In convergence verification step, prove that algorithm has convergence by construction auxiliary function.
3. the method according to claim 1, wherein the update for acquiring algorithm by constructing auxiliary function changes
For formula are as follows:
Wherein, X indicates that sample matrix, H indicate that coefficient matrix, W indicate that basic image matrix, E indicate identical as H (or W) size, and
Element is all 1 matrix, and the element in s-matrix is
4. a kind of non-negative feature extraction and face recognition application method, which is characterized in that including training step, the training step
Include:
First step: training sample matrix X, step-up error threshold epsilon, maximum number of iterations I are converted by training sample imagemax,
Basic image matrix W and coefficient matrix H are initialized；
Second step: using the update iterative formula for acquiring algorithm by constructing auxiliary function, W and H is updated；
Third step: if objective function F (W, H)≤ε or the number of iterations reach Imax, just stop iteration, output matrix W and H；
Otherwise, second step is executed.
5. a kind of non-negative feature extraction according to claim 4 and face recognition application method, which is characterized in that this method
It further include executing testing procedure again after training step, the testing procedure includes:
Four steps: the averaged feature vector m of every class in training sample is calculatedj(j=1 ..., c)；
5th step: for test sample y, its feature vector h is calculatedy；
6th step: with respective metric calculation hyTo the averaged feature vector m of every classjDistance, if hyWith mlDistance it is minimum,
Sample y is then attributed to l class.
6. a kind of non-negative feature extraction according to claim 4 and face recognition application method, which is characterized in that described logical
Cross the update iterative formula that construction auxiliary function acquires algorithm are as follows:
Wherein, X indicates that sample matrix, H indicate that coefficient matrix, W indicate that basic image matrix, E indicate identical as H (or W) size, and
Element is all 1 matrix, and the element in s-matrix is
7. the system of a kind of non-negative feature extraction and face recognition application characterized by comprising memory, processor and
The computer program being stored on the memory, the computer program are configured to realize right when being called by the processor
It is required that the step of method described in any one of 4-6.
8. a kind of computer readable storage medium, which is characterized in that the computer-readable recording medium storage has computer journey
Sequence, when the computer program is configured to be called as processor the step of method described in any one of realization claim 4-6.
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| WO2020082315A2 (en) | 2020-04-30 |
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