WO2021042328A1 - 自构余弦核空间中人脸数据非负特征表示和识别方法、装置、系统及存储介质 - Google Patents
自构余弦核空间中人脸数据非负特征表示和识别方法、装置、系统及存储介质 Download PDFInfo
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- the invention relates to the technical field of face recognition, in particular a method, device, system and storage medium for non-negative feature representation and recognition of face data in a self-constructed cosine kernel space.
- biometric technology that uses the inherent physiological and behavioral characteristics of the human body for personal identification has become one of the most active research fields.
- face recognition technology the one that is most easily accepted by people is face recognition technology. This is because face recognition is non-invasive, non-mandatory, and non-contact compared with other biometric technologies. And concurrency.
- the face recognition technology consists of two stages.
- the first stage is feature extraction, that is, the extraction of facial feature information in the face image.
- This stage directly determines the quality of the face recognition technology;
- the second stage is identification.
- Principal component analysis (PCA) and singular value decomposition (SVD) are relatively classic feature extraction methods, but the feature vectors proposed by these two methods usually contain negative elements, so when the original sample is non-negative data, these methods do not have Reasonability and interpretability.
- Non-negative matrix factorization is a feature extraction method for processing non-negative data. It has a wide range of applications, such as hyperspectral data processing and face image recognition.
- the NMF algorithm has non-negativity restrictions on the extracted features, that is, all components after decomposition are non-negative, so non-negative sparse features can be extracted.
- the essence of the NMF algorithm is to approximately decompose the non-negative matrix X into the product of the base image matrix W and the coefficient matrix H, that is, X ⁇ WH, and both W and H are non-negative matrices.
- each column of matrix X can be expressed as a non-negative linear combination of matrix W column vectors, which is also in line with the construction basis of the NMF algorithm-the perception of the whole is composed of the perception of the parts that make up the whole (pure additive) .
- NMF neurotrophic factor
- RNMF robust NMF algorithm
- GNMF graph NMF algorithm
- ONMF orthogonal NMF algorithm that introduces orthogonal restrictions.
- these NMF algorithms are linear methods.
- face images become very complicated due to interference factors such as occlusion, lighting, expressions, etc.
- the face recognition problem has become a non-linear problem, so the linear method is no longer applicable.
- the kernel method is an effective method, which provides an elegant theoretical framework for extending linear algorithms to nonlinear algorithms.
- the basic idea of the kernel method is to map the original data to the high-dimensional feature space by using a non-linear mapping function to make the mapped data linearly separable, and then apply the linear algorithm to the mapped data.
- the kernel method the most critical part is the use of kernel techniques.
- the use of nuclear techniques reduces the difficulty of extending the mapping to nuclear space, namely Regenerated Nuclear Hilbert Space (RKHS).
- RKHS Regenerated Nuclear Hilbert Space
- the linear NMF algorithm can be extended to the kernel NMF algorithm (KNMF).
- the main idea of the KNMF algorithm is to pass a nonlinear mapping function Map the sample matrix X to a high-dimensional feature space, and in this feature space, use the NMF algorithm to map the sample matrix Approximate decomposition into two matrices And the product of H, namely In the KNMF method, W and H are called the original image matrix and the characteristic matrix respectively, and both W and H are required to be non-negative matrices.
- KNMF KNNF
- PNMF polynomial kernel non-negative matrix factorization algorithm
- RBFNMF Gaussian kernel non-negative matrix factorization algorithm
- KNMF algorithms have the following problems: (1) The analytical expression of the nonlinear mapping implicit in the kernel function cannot be obtained; (2) The mapped data cannot be guaranteed to be non-negative in the kernel space, so the current The KNMF algorithm can only be regarded as a semi-non-negative matrix factorization; (3) Inaccurate pre-image learning is required; (4) It is not robust to noise.
- this patent first constructs a non-linear mapping (with analytical expressions) that can maintain non-negativity in the kernel space. Based on this, a new cosine kernel function is obtained through construction and proof. This self-constructed cosine nucleus has good properties such as translation invariance and insensitivity to noise. Based on the self-constructed cosine kernel, this patent obtains a new non-negative feature representation and recognition method of face data in the self-constructed cosine kernel space. This method can overcome the above four shortcomings of the current KNMF algorithm. The experimental results show that the cosine kernel NMF face recognition algorithm proposed by this patent has superior performance.
- ⁇ x 1 ,x 2 ,...,x n ⁇ be a set of data in the original sample space.
- the main idea of the kernel method is to pass a nonlinear mapping function The sample is mapped from the original space to a higher-dimensional kernel space, so that the sample is linearly separable in the kernel space. Then use the linear method to classify the mapped data in the kernel space.
- the problem with the kernel method is that the dimensionality of the kernel space is generally very high, and may even be infinite.
- the specific expression of nonlinear mapping is also difficult to obtain. Fortunately, the specific algorithm of the kernel method is generally only related to the inner product of the data after nonlinear mapping. According to the kernel method theory, these inner products can be replaced by a known kernel function k, namely:
- kernel function reflects the degree of similarity between the two samples.
- kernel functions are polynomial kernel functions And Gaussian kernel function
- KNMF Kernel non-negative matrix factorization algorithm
- KNMF The main purpose of KNMF is to use the kernel method to solve the nonlinear problem of NMF.
- the NMF algorithm is used to process the mapped data in the high-dimensional kernel space, and the Approximate decomposition into two matrices And the product of H, namely
- the kernel function k( ⁇ , ⁇ ) implicitly defines the high-dimensional kernel space. If the kernel function is not selected properly, it means that the sample data is mapped to a Inappropriate feature space is likely to lead to poor performance.
- PNMF Polynomial kernel non-negative matrix factorization algorithm
- PNMF polynomial kernel non-negative matrix factorization algorithm
- KNMF-RBF Gaussian kernel non-negative matrix factorization algorithm
- KNMF-RBF Gaussian kernel non-negative matrix factorization algorithm
- the non-negative matrix factorization algorithm is a linear algorithm, and many problems in real life are nonlinear, so it is difficult to achieve satisfactory results.
- the current kernel non-negative matrix factorization algorithms generally use polynomial kernel functions or Gaussian kernel functions, but it is difficult to obtain the implicit non-linear mapping analytical expressions.
- the current solution of the original image W of the KNMF algorithm only uses the first three terms expanded by Taylor, so the error is relatively large, and the original image learning is not accurate. Inaccurate pre-images will affect its performance.
- the kernel method based on the polynomial kernel function or the Gaussian kernel function cannot guarantee the non-negativity of the mapped data, in fact it is a semi-non-negative matrix factorization.
- the current nuclear non-negative matrix factorization algorithms are mostly based on polynomial kernel functions or Gaussian kernel functions. These two kernel functions are more sensitive to noise, which makes the algorithm's anti-noise performance poor.
- the present invention provides a non-negative feature representation and recognition method of face data in a self-constructed cosine kernel space, which includes a training step, and the training step includes the following steps:
- the first step transform the training sample image into a training sample matrix X, and normalize each sample to Within, set the error threshold ⁇ and the maximum number of iterations I max ;
- the second step initialize the base image matrix W and the coefficient matrix H;
- the fourth step update the base image matrix W and the coefficient matrix H according to formula (12);
- the sixth step judge whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if yes, then output the base image matrix W and the coefficient matrix H, otherwise perform the fourth step;
- formula (12) is as follows:
- w k ⁇ Rm is the k- th column of the base image matrix W
- r is the number of columns of the base image matrix W, which can be seen by the definition of the present invention
- Parameter t ⁇ [0,1] the inverse function arccos is the inverse cosine function for each element in the vector or matrix.
- the non-negative feature representation and recognition method of face data in the auto-constructed cosine kernel space further includes performing a recognition step after the training step, and the recognition step includes:
- the eighth step normalize all test samples to Inside, input the face image y to be recognized, and calculate its feature vector h y ;
- F , j 1,...,c,
- the tenth step output category P to complete face recognition.
- the present invention also provides a non-negative feature representation and recognition device of face data in self-constructed cosine kernel space, which includes a training module, and the training module includes:
- Input module used to convert training sample images into training sample matrix X, and normalize each sample to Within, set the error threshold ⁇ and the maximum number of iterations I max ;
- Initialization module used to initialize the base image matrix W and coefficient matrix H;
- Update module used to update the base image matrix W and coefficient matrix H according to formula (12);
- Judgment module judge whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if so, output the base image matrix W and the coefficient matrix H, otherwise execute the update module;
- w k ⁇ R m is the k- th column of the base image matrix W
- r is the number of columns of the base image matrix W, as defined by the present invention Knowable Parameter t ⁇ [0,1]
- the inverse function arccos is the inverse cosine function for each element in the vector or matrix.
- the non-negative feature representation and recognition device of face data in the auto-constructed cosine kernel space further includes a recognition module after the training module, and the recognition module includes:
- Feature vector calculation module used to normalize all test samples to , Input the face image y to be recognized, and calculate its feature vector h y ;
- F , j 1,...,c,
- Output module used to output category P to complete face recognition.
- the present invention also discloses a computer-readable storage medium, the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the method of the present invention when called by a processor.
- the present invention also discloses a non-negative feature representation and recognition system of face data in the self-constructed cosine kernel space, which includes a memory, a processor, and a computer program stored on the memory, and the computer program is configured by the The steps of the method of the present invention are implemented when the processor is called.
- the beneficial effects of the present invention are: through experimental comparison with related algorithms in a public face database, the results show that the present invention has certain advantages; through experimental comparison with related algorithms in a noise-added face database, the results show The invention has good robustness.
- FIG. 1 is a flowchart of the algorithm construction process of the present invention
- Figure 2 is a flow chart of the method of the present invention
- FIG. 3 is a comparison diagram of the recognition rate of the non-negative feature representation and recognition method of face data and related algorithms (PNMF, KNMF-RBF) on the FERET face database in the self-constructed cosine kernel space proposed by the present invention
- PNMF non-negative feature representation and recognition method and related algorithms
- Fig. 5 is a convergence curve diagram of the non-negative feature representation and recognition method of face data in the self-constructed cosine kernel space of the present invention.
- the invention discloses a non-negative feature representation and recognition method of face data in a self-constructed cosine kernel space.
- the main purposes of the invention are as follows:
- NMF non-negative sample matrix
- the loss function is defined based on the F-norm, as:
- ⁇ be the input space
- k( ⁇ , ⁇ ) is a symmetric function defined on ⁇
- Gram matrix K is always positive semi-definite:
- the objective function of the new KNMF is defined as follows:
- the selection step vector is:
- This update iteration formula can be transformed into a matrix form, and there are the following theorems.
- Theorem 2 Fixed matrix W, when the coefficient matrix H in sub-problem (3) is updated in the following iterative manner
- the selection step size is:
- the above iterative formula can be expressed as (14) in matrix form.
- Theorem 3 Fixed matrix H, the objective function f 2 (H) is non-increasing, when the base image matrix W in the sub-problem (4) is updated in the following iterative manner:
- Definition 1 For any vector w and w (t) , if the conditions are met
- the specific construction process of the non-negative feature representation and recognition method of face data in the self-constructed cosine kernel space of the present invention is as follows:
- the present invention provides a non-negative feature representation and recognition method of face data in a self-constructed cosine kernel space, which includes a training step, and the training step includes the following steps:
- the first step transform the training sample image into a training sample matrix X, and normalize each sample to Within, set the error threshold ⁇ and the maximum number of iterations I max ;
- the second step initialize the base image matrix W and the coefficient matrix H;
- the fourth step update the base image matrix W and the coefficient matrix H according to formula (12);
- the sixth step judge whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if yes, then output the base image matrix W and the coefficient matrix H, otherwise perform the fourth step;
- the non-negative feature representation and recognition method of face data in the auto-constructed cosine kernel space further includes performing a recognition step after the training step, and the recognition step includes:
- the eighth step normalize all test samples to , Input the face image y to be recognized, and calculate its feature vector h y ;
- F , j 1,...,c,
- the tenth step output category P to complete face recognition.
- the output category P indicates that the face image y to be recognized is recognized as the P-th face category, so after the category P is output, the face recognition is completed.
- the present invention also provides a non-negative feature representation and recognition device of face data in self-constructed cosine kernel space, which includes a training module, and the training module includes:
- Input module used to convert training sample images into training sample matrix X, and normalize each sample to Within, set the error threshold ⁇ and the maximum number of iterations I max ;
- Initialization module used to initialize the base image matrix W and coefficient matrix H;
- Update module used to update the base image matrix W and coefficient matrix H according to formula (12);
- Judgment module judge whether the objective function F(W,H) ⁇ or the number of iterations n reaches the maximum number of iterations I max , if so, output the base image matrix W and the coefficient matrix H, otherwise execute the update module;
- the device for expressing and identifying the non-negative features of face data in the self-constructed cosine kernel space further includes a recognition module that executes after the training module, and the recognition module includes:
- Feature vector calculation module used to normalize all test samples to , Input the face image y to be recognized, and calculate its feature vector h y ;
- F , j 1,...,c,
- Output module used to output category P to complete face recognition.
- the present invention also discloses a computer-readable storage medium, the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the method of the present invention when called by a processor.
- the present invention also discloses a non-negative feature representation and recognition system of face data in the self-constructed cosine kernel space, which includes a memory, a processor, and a computer program stored on the memory, and the computer program is configured by the The steps of the method of the present invention are implemented when the processor is called.
- Table 1 compares the recognition rate (%) of the method (Our Method) proposed by this patent with the polynomial kernel non-negative matrix factorization (PNMF) and Gaussian kernel non-negative matrix factorization (KNMF-RBF) on the FERET face database.
- PNMF polynomial kernel non-negative matrix factorization
- KNMF-RBF Gaussian kernel non-negative matrix factorization
- Table 2 is the recognition rate (%) of the method proposed by this patent (Our Method), polynomial kernel non-negative matrix factorization (PNMF) and Gaussian kernel non-negative matrix factorization (KNMF-RBF) on the ORL face database with Gaussian noise added Comparison ( ⁇ represents additive Gaussian noise variance)
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Abstract
一种自构余弦核空间中人脸数据非负特征表示和识别方法、装置、系统及存储介质,该自构余弦核空间中人脸数据非负特征表示和识别方法包括训练步骤和识别步骤。通过在公开的人脸数据库中与相关算法进行实验比较,结果表明具有一定的优越性;通过在添加噪声的人脸数据库中与相关算法进行实验比较,结果表明具有很好的鲁棒性。
Description
本发明涉及人脸识别技术领域,尤其一种自构余弦核空间中人脸数据非负特征表示和识别方法、装置、系统及存储介质。
随着信息化时代的到来,利用人体固有的生理特征和行为特征进行个人身份鉴定的生物识别技术成为了一个最活跃的研究领域之一。在生物识别技术的众多分支中,最容易被人们接受的一个技术是人脸识别技术,这是由于相对于其他生物识别技术而言,人脸识别具有无侵害性、非强制性、非接触性和并发性。
人脸识别技术包含两个阶段,第一阶段是特征提取,也就是提取人脸图像中的人脸特征信息,这一阶段直接决定了人脸识别技术的好坏;第二阶段是身份鉴定,根据提取出的特征信息进行个人身份鉴定。主成分分析(PCA)与奇异值分解(SVD)都是较为经典的特征提取方法,但是这两种方法提出的特征向量通常含有负元素,因此在原始样本为非负数据下,这些方法不具有合理性与可解释性。非负矩阵分解(NMF)是一种处理非负数据的特征提取方法,它的应用非常广泛,比如高光谱数据处理、人脸图像识别等。NMF算法在原始样本非负数据矩阵分解过程中,对提取的特征具有非负性限制,即分解后的所有分量都是非负的,因而可以提取非负的稀疏特征。NMF算法的实质也就是将非负矩阵X近似分解为基图像矩阵W和系数矩阵H的乘积,即X≈WH,且W和H都是非负矩阵。这样矩阵X的每一列就可以表示成矩阵W列向量的非负线性组合,这也符合NMF算法的构造依据——对整体的感知是由对组成整体的部分的感知构成的(纯加性)。近年来,学者们提出了许多对NMF变形的算法,例如,增强算法鲁棒性的鲁棒NMF算法(RNMF)、保持局部特征的图NMF算法(GNMF)、引入正交限制的正交NMF算法(ONMF)。然而,这些NMF算法都是线性方法。在人脸识别过程中,由于包含遮挡,光照,表情等干扰因素,导致脸部图像变得十分复杂。此时的人脸识别问题变成了一个非线性的问题,故线性方法不再适用。
对于处理非线性问题,核方法是一种有效方法,它为将线性算法拓展 为非线性算法提供了一个精美的理论框架。核方法的基本思想是通过使用一个非线性映射函数将原始数据映射到高维特征空间中,使得被映射后的数据线性可分,然后将线性算法应用到被映射后的数据上。在核方法中,最关键的部分是核技巧的使用,通过利用核函数取代被映射数据的内积,因而不需要知道非线性映射函数的具体解析式。核技巧的使用降低了将映射扩展到核空间即再生核希尔伯特空间(RKHS)的难度。利用核方法,可以将线性NMF算法推广为核NMF算法(KNMF)。KNMF算法的主要思路是是通过非线性映射函数
将样本矩阵X映射到高维特征空间中,并在这个特征空间中,利用NMF算法,将映射后的样本矩阵
近似分解为两个矩阵
与H的乘积,即
在KNMF方法中W和H分别称为原像矩阵和特征矩阵,并要求W和H均为非负矩阵。
目前的KNMF算法大都是基于多项式核和高斯核,即这些KNNF算法主要可分为两类:多项式核非负矩阵分解算法(PNMF)和高斯核非负矩阵分解算法(RBFNMF)。但这些KNMF算法大都存在如下问题:(1)不能得到隐含在核函数中的非线性映射的解析表达式;(2)不能保证映射后的数据在核空间中具有非负性,因而目前的KNMF算法只能算是半非负矩阵分解;(3)需要进行不精确的原像学习;(4)对噪声不具有鲁棒性。为了解决这些问题,本专利首先构造了一种在核空间中能够保持非负性的非线性映射(具有解析表达式),据此通过构造和证明得到了一种新的余弦核函数。这种自构余弦核具有平移不变性和对噪声不敏感等良好性能。基于自构余弦核,本专利得到了一种新的自构余弦核空间中人脸数据非负特征表示和识别方法。该方法可以克服目前KNMF算法的如上四个缺陷。实验结果表明,本专利提出的余弦核NMF人脸识别算法具有优越的性能。
相关技术的技术方案:
1.核方法
设{x
1,x
2,…,x
n}是原始样本空间中的一组数据。核方法的主要思想是通过一个非线性映射函数
将样本从原始空间映射到一个更高维的核空间中,使得样本在核空间中线性可分。然后在核空间里使用线性方法对映射后的数据进行分类。核方法的问题在于核空间的维数一般很高,甚至可能是无穷维的。另外,非线性映射的具体表达式也很难得到。幸运的是,核方法的具体算法一般只与非线性映射后数据的内积有关。根据核方法理论,这些内积可以用一个已知的核函数k来取代,即:
(RBF)k(x
i,x
j)=exp(-||x
i-x
j||
2/(2δ
2))。
2.核非负矩阵分解算法(KNMF)
KNMF的主要目的是利用核方法解决NMF的非线性问题。首先利用非线性映射函数
将原始空间中的非负样本数据
映射到一个高维特征空间中,得到被映射的样本数据
然后,在高维核空间中利用NMF算法处理被映射的数据,将
近似分解为两个矩阵
与H的乘积,即
这里损失函数F(W,H)定义如下:
在KNMF算法中,最主要的影响因素是核函数k(·,·)的选择,核函数隐式地定义了高维核空间,若核函数选择不合适,那么意味着将样本数据映射到了一个不合适的特征空间,很可能导致性能不佳。
3.多项式核非负矩阵分解算法(PNMF)
多项式核非负矩阵分解算法(PNMF)是基于多项式核函数来求解优化问题(1),其得到W和H的更新迭代公式为:
4.高斯核非负矩阵分解算法(KNMF-RBF)
高斯核非负矩阵分解算法(KNMF-RBF)是基于高斯核函数来求解优化问题(1),其得到W和H的更新迭代公式为:
相关技术的缺点:
1、非负矩阵分解算法是一种线性的算法,而现实生活中许多问题都是非线性的,故难以取得让人满意的效果。
2、目前核非负矩阵分解算法一般使用基于多项式核函数或者高斯核函数,但很难求得其所隐含的非线性映射的解析表达式。另外,目前KNMF算法原像W的求解只使用了Taylor展开的前三项,因而误差较大,其原像学习是不精确的。不精确的原像会影响其性能。
3、基于多项式核函数或者高斯核函数的核方法不能保证映射后的数据的非负性,事实上为半非负矩阵分解。
4、目前核非负矩阵分解算法大都是基于多项式核函数或者高斯核函数,这两种核函数对噪声比较敏感,这使得算法的抗噪性较差。
发明内容
本发明提供了一种自构余弦核空间中人脸数据非负特征表示和识别方法,包括训练步骤,所述训练步骤包括如下步骤:
第二步骤:对基图像矩阵W和系数矩阵H进行初始化;
第三步骤:设置迭代次数n=0;
第四步骤:根据公式(12)更新基图像矩阵W和系数矩阵H;
第五步骤:使n=n+1;
第六步骤:判断目标函数F(W,H)≤ε或迭代次数n是否达到最大迭代次数I
max,如果是,那么输出基图像矩阵W和系数矩阵H,否则执行第四步骤;
在第四步骤中,公式(12)如下:
其中w
k∈Rm是基图像矩阵W的第k列,m是向量w
k(k=1,2,…,r)的维数,r是基图像矩阵W的列的数目,由本发明定义可知
参数t∈[0,1],反函数arccos是对向量或矩阵中的每个元素求余弦反函数。
作为本发明的进一步改进:该自构余弦核空间中人脸数据非负特征表示和识别方法还包括在训练步骤之后再执行识别步骤,所述识别步骤包括:
第七步骤:计算训练样本中每类的平均特征向量m
j(j=1,2,…,c),c为不同人脸类别数,j为第j类的标记数;
第九步骤:计算待识别人脸图像的特征向量h
y到第j类平均特征向量m
j的距离d
j=||h
y-m
j||
F,j=1,…,c,||·||
F为Frobenius范数,若h
y与第p类样本的平均特征向量m
p的距离d
p最小,即
则将待识别人脸图像y归于第p类;
第十步骤:输出类别P,从而完成人脸识别。
本发明还提供了一种自构余弦核空间中人脸数据非负特征表示和识别装置,包括训练模块,所述训练模块包括:
初始化模块:用于对基图像矩阵W和系数矩阵H进行初始化;
赋值模块:用于设置迭代次数n=0;
更新模块:用于根据公式(12)更新基图像矩阵W和系数矩阵H;
计数模块:使n=n+1;
判断模块:判断目标函数F(W,H)≤ε或迭代次数n是否达到最大迭代次数I
max,如果是,那么输出基图像矩阵W和系数矩阵H,否则执行更新模块;
在更新模块中,公式(12)如下:
其中w
k∈R
m是基图像矩阵W的第k列,m是向量w
k(k=1,2,…,r)的维数,r是基图像矩阵W的列的数目,由本发明定义可知
参数t∈[0,1],反函数arccos是对向量或矩阵中的每个元素求余弦反函数。
作为本发明的进一步改进:该自构余弦核空间中人脸数据非负特征表示和识别装置还包括在训练模块之后再执行识别模块,所述识别模块包括:
平均特征向量计算模块:用于计算训练样本中每类的平均特征向量m
j(j=1,2,…,c),c为不同人脸类别数,j为第j类的标记数;
距离计算模块:计算待识别人脸图像的特征向量h
y到第j类平均特征向量m
j的距离d
j=||h
y-m
j||
F,j=1,…,c,||·||
F为Frobenius范数,若h
y与第p类样本的平均特征向量m
p的距离d
p最小,即
则将待识别人脸图像y归于第p类;
输出模块:用于输出类别P,从而完成人脸识别。
本发明还公开了一种计算机可读存储介质,所述计算机可读存储介质存储有计算机程序,所述计算机程序配置为由处理器调用时实现本发明所述的方法的步骤。
本发明还公开了一种自构余弦核空间中人脸数据非负特征表示和识别系统,包括:存储器、处理器以及存储在所述存储器上的计算机程序,所述计算机程序配置为由所述处理器调用时实现本发明所述的方法的步骤。
本发明的有益效果是:通过在公开的人脸数据库中与相关算法进行实验比较,结果表明本发明具有一定的优越性;通过在添加噪声的人脸数据库中与相关算法进行实验比较,结果表明本发明具有很好的鲁棒性。
图1是本发明的算法构造过程流程图;
图2是本发明的方法流程图;
图3是本发明提出的自构余弦核空间中人脸数据非负特征表示和识别方法与相关算法(PNMF,KNMF-RBF)在FERET人脸数据库上的识别率比较图;
图4是本发明提出的自构余弦核空间中人脸数据非负特征表示和识别方法与相关算法(PNMF,KNMF-RBF)在添加高斯噪声的ORL人脸数据库上的识别率比较图;
图5是本发明的自构余弦核空间中人脸数据非负特征表示和识别方法的收敛曲线图。
本发明公开了一种自构余弦核空间中人脸数据非负特征表示和识别方法,本发明的主要目的有:
1、克服目前KNMF算法的不精确原像学习问题;
2、保证映射到核空间中的数据的非负性,克服目前KNMF算法在核空间中的半非负分解问题;
3、构建了一种可以写出显式的非线性映射,进而构造出一种新的具有平移不变性和抗噪性的余弦核函数;
4、构建一个具有抗噪性的高识别性能的核非负矩阵分解人脸识别方法。
一.关键词解释:
1.符号说明
X 矩阵
x
j 矩阵X的第j列
x
ij 矩阵X的第ij个元素
max(x) 列向量x中最大的元素的值
cos x 列向量x中元素的余弦列向量
sin x 列向量x中元素的正弦列向量
A⊙B 矩阵A与B中Hadamard乘积
2.非负矩阵分解(Non-negative Matrix Factorization,NMF)
X≈WH,
3.核函数(Kernel Function)
令χ为输入空间,k(·,·)是定义在χ×χ上的对称函数,则k是核函数当且仅当对于任意数据D={x
1,x
2,…,x
n},Gram矩阵K总是半正定的:
4.余弦函数的性质(Properties of cosine functions)
二.具体技术方案:
容易证明k是一个核函数。我们称此函数为自构余弦核函数。
考虑一张人脸图像数据x=(x
1,x
2,…,x
i,…,x
m)
T,如果x
i由于噪声的干扰变为x
i+a,即
则
当m足够大的时候k(x,x
*)≈1。这表明自构余弦核在噪声下依然能保持较高的样本相似度。因此在人脸识别中,自构余弦核能够有效克服噪声的影响,增强算法的鲁棒性。为了方便,在本专利推导中取t=1,即
1.自构余弦核非负矩阵算法(CKNMF)的提出
预处理
在本算法中,我们将所有的非负数据x*均进行如下预处理
目标函数的构建
新KNMF的目标函数定义如下:
为了利用新构建的余弦核函数求解目标函数(2)中的两个未知非负矩阵W和H,我们将目标函数转化为两个子目标函数,分别为:
则问题(2)也转化为两个子问题,分别为:
min f
1(H)s.t.H≥0, (3)
1)对系数矩阵H的学习
由(2)有f
1(H)=tr(K
XX-2K
XWH+H
TK
WWH)。对于子问题(3),采用梯度下降法对系数矩阵H的第k列h
k进行求解,有:
将公式(6)带入公式(5)中有
为了保证h
k的非负性,令:
因此,选择步长向量为:
可将此更新迭代公式转化为矩阵形式,且有以下定理。
定理2:固定矩阵W,当子问题(3)中的系数矩阵H按以下迭代方式更新时
则目标函数f
1(H)是单调非增的。
2)对原像矩阵W的学习
将公式(9)带入公式(8),得到
因此,选择步长为:
上述迭代式用矩阵形式可表示为(14)。
定理3:固定矩阵H,目标函数f
2(H)是非增的,当子问题(4)中的基图像矩阵W按以下迭代方式更新:
综上所述,通过定理1和定理2,可以得到本专利提出的余弦核非负矩阵分解的更新迭代公式,为:
2.收敛性证明
这里我们主要讨论迭代公式(13)与(14)的收敛性,迭代公式(7)的收敛性可类似证明。为此需要利用辅助函数的定义和性质:
定义1:对于任意的向量w和w
(t),若满足条件
G(w,w
(t))≥f(w),且G(w
(t),w
(t))=f(w
(t)),
则称G(w,w
(t))为函数f(w)的一个辅助函数。
引理1:如果G(w,w
(t))是f(w)的一个辅助函数,那么f(w)在如下的更新法则下是单调不增的,
接下来,我们通过构造辅助函数证明定理3的成立,也就是证明本专利构造的新算法具有收敛性。
那么,函数
可以很明显的看出,当W=W
(t)时,G(W
(t),W
(t))=g(W
(t))。又因为
可得,G(W,W
(t))-g(W)≥0,G(W,W
(t))是g(W)的辅助函数,证毕。
设矩阵W的第k列w
k未知,其他列都是已知的,对辅助函数G(W,W
(t))关于w
k求导,可得
通过计算,可得
将其转化为矩阵形式可得公式(11),因此定理3成立。
3.特征提取
即,
其中K
Wy为一个核向量。因此,特征h
y可以求出为
其中,
是矩阵K
WW的广义逆。类似的,我们可以得到训练样本的平均特征向量。假设原始空间中有c类样本,其中第j类的训练样本数为n
j(j=1,2,…,c),训练样本矩阵为X
j,那么第j类的平均特征向量可以表示为:
综上,本发明自构余弦核空间中人脸数据非负特征表示和识别方法具体构建过程如下:
(1)在本专利的算法中引入我们构建的具有显式非线性映射的余弦核函数;
(2)通过利用梯度下降法及推导出本专利算法的更新迭代公式;
(3)通过构造辅助函数,证明了本专利算法的收敛性,从理论上保证了算法的合理性。
如图2所示,本发明提供了一种自构余弦核空间中人脸数据非负特征表示和识别方法,包括训练步骤,所述训练步骤包括如下步骤:
第二步骤:对基图像矩阵W和系数矩阵H进行初始化;
第三步骤:设置迭代次数n=0;
第四步骤:根据公式(12)更新基图像矩阵W和系数矩阵H;
第五步骤:使n=n+1;
第六步骤:判断目标函数F(W,H)≤ε或迭代次数n是否达到最大迭代次数I
max,如果是,那么输出基图像矩阵W和系数矩阵H,否则执行第四步骤;
在第四步骤中,公式(12)如下:计算公式为:
该自构余弦核空间中人脸数据非负特征表示和识别方法还包括在训练步骤之后再执行识别步骤,所述识别步骤包括:
第七步骤:计算训练样本中每类的平均特征向量m
j(j=1,2,…,c),c为不同人脸类别数,j为第j类的标记数;
第九步骤:计算待识别人脸图像的特征向量h
y到第j类平均特征向量m
j的距离d
j=||h
y-m
j||
F,j=1,…,c,||·||
F为Frobenius范数,若h
y与第p类样本的平均特征向量m
p的距离d
p最小,即
则将待识别人脸图像y归于第p类;
第十步骤:输出类别P,从而完成人脸识别。
输出类别P,表示待识别人脸图像y被识别为第P个人脸类别,所以输出类别P后,人脸识别就完成了。
本发明还提供了一种自构余弦核空间中人脸数据非负特征表示和识别装置,包括训练模块,所述训练模块包括:
初始化模块:用于对基图像矩阵W和系数矩阵H进行初始化;
赋值模块:用于设置迭代次数n=0;
更新模块:用于根据公式(12)更新基图像矩阵W和系数矩阵H;
计数模块:使n=n+1;
判断模块:判断目标函数F(W,H)≤ε或迭代次数n是否达到最大迭代次数I
max,如果是,那么输出基图像矩阵W和系数矩阵H,否则执行更新模块;
在更新模块中,公式(12)如下:
该自构余弦核空间中人脸数据非负特征表示和识别装置还包括在训练模块之后再执行识别模块,所述识别模块包括:
平均特征向量计算模块:用于计算训练样本中每类的平均特征向量m
j(j=1,2,…,c),c为不同人脸类别数,j为第j类的标记数;
距离计算模块:计算待识别人脸图像的特征向量h
y到第j类平均特征向量m
j的距离d
j=||h
y-m
j||
F,j=1,…,c,||·||
F为Frobenius范数,若h
y与第p类样本的平均特征向量m
p的距离d
p最小,即
则将待识别人脸图像y归于第p类;
输出模块:用于输出类别P,从而完成人脸识别。
本发明还公开了一种计算机可读存储介质,所述计算机可读存储介质存储有计算机程序,所述计算机程序配置为由处理器调用时实现本发明所述的方法的步骤。
本发明还公开了一种自构余弦核空间中人脸数据非负特征表示和识别系统,包括:存储器、处理器以及存储在所述存储器上的计算机程序,所述计算机程序配置为由所述处理器调用时实现本发明所述的方法的步骤。
表1是本专利提出的方法(Our Method)与多项式核非负矩阵分解(PNMF)和高斯核非负矩阵分解(KNMF-RBF)在FERET人脸数据库上的识别率(%)比较
(TN表示每一类的训练样本数)
TN | 2 | 3 | 4 | 5 |
PNMF | 51.77 | 56.63 | 63.04 | 62.75 |
KNMF-RBF | 57.93 | 65.36 | 71.04 | 73.50 |
Our Method | 66.38 | 72.25 | 78.08 | 80.33 |
表1
表2是本专利提出的方法(Our Method)与多项式核非负矩阵分解(PNMF)和高斯核非负矩阵分解(KNMF-RBF)在添加高斯噪声的ORL人脸数据库上的识别率(%)比较(σ表示加性高斯噪声方差)
σ | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 |
PNMF | 88.06 | 85.00 | 80.00 | 75.50 | 68.62 |
KNMF-RBF | 45.19 | 40.56 | 29.81 | 29.81 | 26.44 |
Our Method | 89.68 | 86.43 | 84.75 | 80.38 | 78.81 |
表2
本发明的有益效果:
1.通过构建的具有抗噪性的余弦核函数,得到了一种具有抗噪性的核非负矩阵分解算法。实验结果表明,我们的算法对噪声具有鲁棒性。
2.本专利所提出的算法的收敛性,不仅通过利用辅助函数在理论上进行了证明,而且在实验中也得到了验证,我们的算法具有较高的收敛性。
3.通过在公开的人脸数据库中与相关算法进行实验比较,结果表明本专利开发的方法具有一定的优越性。
4.通过在添加噪声的人脸数据库中与相关算法进行实验比较,结果表明本专利开发的方法具有很好的鲁棒性。
以上内容是结合具体的优选实施方式对本发明所作的进一步详细说明,不能认定本发明的具体实施只局限于这些说明。对于本发明所属技术领域的普通技术人员来说,在不脱离本发明构思的前提下,还可以做出若 干简单推演或替换,都应当视为属于本发明的保护范围。
Claims (6)
- 一种自构余弦核空间中人脸数据非负特征表示和识别方法,其特征在于,包括训练步骤,所述训练步骤包括如下步骤:第二步骤:对基图像矩阵W和系数矩阵H进行初始化;第三步骤:设置迭代次数n=0;第四步骤:根据公式(12)更新基图像矩阵W和系数矩阵H;第五步骤:使n=n+1;第六步骤:判断目标函数F(W,H)≤ε或迭代次数n是否达到最大迭代次数I max,如果是,那么输出基图像矩阵W和系数矩阵H,否则执行第四步骤;在第四步骤中,公式(12)如下:
- 根据权利要求1所述的自构余弦核空间中人脸数据非负特征表示和识别方法,其特征在于,该自构余弦核空间中人脸数据非负特征表示和识别方法还包括在训练步骤之后再执行识别步骤,所述识别步骤包括:第七步骤:计算训练样本中每类的平均特征向量m j(j=1,2,…,c),c为不同人脸类别数,j为第j类的标记数;第九步骤:计算待识别人脸图像的特征向量h y到第j类平均特征向量m j的距离d j=||h y-m j|| F,j=1,…,c,||·|| F为Frobenius范数,若h y与第p类样本 的平均特征向量m p的距离d p最小,即 则将待识别人脸图像y归于第p类;第十步骤:输出类别P,从而完成人脸识别。
- 一种自构余弦核空间中人脸数据非负特征表示和识别装置,其特征在于,包括训练模块,所述训练模块包括:初始化模块:用于对基图像矩阵W和系数矩阵H进行初始化;赋值模块:用于设置迭代次数n=0;更新模块:用于根据公式(12)更新基图像矩阵W和系数矩阵H;计数模块:使n=n+1;判断模块:判断目标函数F(W,H)≤ε或迭代次数n是否达到最大迭代次数I max,如果是,那么输出基图像矩阵W和系数矩阵H,否则执行更新模块;在更新模块中,公式(12)如下:
- 根据权利要求3所述的自构余弦核空间中人脸数据非负特征表示和识别装置,其特征在于,该自构余弦核空间中人脸数据非负特征表示和识别装置还包括在训练模块之后再执行识别模块,所述识别模块包括:平均特征向量计算模块:用于计算训练样本中每类的平均特征向量m j(j=1,2,…,c),c为不同人脸类别数,j为第j类的标记数;距离计算模块:计算待识别人脸图像的特征向量h y到第j类平均特征向量m j的距离d j=||h y-m j|| F,j=1,…,c,||·|| F为Frobenius范数,若h y与第p类样本的平均特征向量m p的距离d p最小,即 则将待识别人脸图像y归于第p类;输出模块:用于输出类别P,从而完成人脸识别。
- 一种计算机可读存储介质,其特征在于,所述计算机可读存储介质存储有计算机程序,所述计算机程序配置为由处理器调用时实现权利要求1-2中任一项所述的方法的步骤。
- 一种自构余弦核空间中人脸数据非负特征表示和识别系统,其特征在于,包括:存储器、处理器以及存储在所述存储器上的计算机程序,所述计算机程序配置为由所述处理器调用时实现权利要求1-2中任一项所述的方法的步骤。
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