CN104463211A

CN104463211A - Support vector data description method based on maximum distance between centers of spheres

Info

Publication number: CN104463211A
Application number: CN201410745860.8A
Authority: CN
Inventors: 冀中; 于云龙
Original assignee: Tianjin University
Current assignee: Tianjin University
Priority date: 2014-12-08
Filing date: 2014-12-08
Publication date: 2015-03-25

Abstract

Provided is a support vector data description method based on the maximum distance between the centers of spheres. Objectives with maximized between-class distances are added to an objective optimization function for support vector data description, so that an objective function which makes the radius of each suprasphere minimum and meanwhile makes the distances between different supraspheres maximum is obtained. Between-class information constraints are introduced to multi-class problems on the basis of the support vector data description method for the first time, the suprasphere with the minimum radius is used for surrounding the same class of samples on this basis, and the supraspheres keep away from one another as far as possible. The support vector data description method can solve the problems that classes are unbalanced and recognition dead zones exist in traditional multi-class methods, and the effectiveness of the support vector data description method applied to the multi-class problems is proved through an open set face recognition system with a rejection function. Compared with the traditional methods, the support vector data description method has the advantages of being high in robustness, good in classification effect, and the like. The support vector data description method can be used for solving supervised learning multi-class problems of small sample sets.

Description

A Support Vector Description Method Based on Maximum Center Distance

技术领域technical field

本发明涉及一种支持向量描述方法。特别是涉及一种以所有超球半径的平方和最小及超球体之间的距离最大为目标函数，在核空间中寻找一个超球体将同一类的样本约束在超球体中，并将其他类的样本约束在超球体外，并且使所建立的超球体之间尽可能地分离的基于最大球心距的支持向量描述方法。The invention relates to a support vector description method. In particular, it involves an objective function that takes the minimum sum of the squares of all hypersphere radii and the maximum distance between hyperspheres as the objective function, searches for a hypersphere in the kernel space, constrains the samples of the same class in the hypersphere, and combines the samples of other classes The sample is constrained outside the hypersphere, and the established hyperspheres are separated as much as possible based on the support vector description method of the maximum center-to-center distance.

背景技术Background technique

随着信息技术的快速发展，图像和视频等多媒体数据大量涌现，成为人们获取信息的重要途径之一。如何对获取的信息进行有效地分类是机器学习领域的一个重大挑战。支持向量机(Support Vector Machine,SVM)是一种流行的分类方法，最初由Vapnik等人提出，近年来在其理论研究和算法实现等方面都获得了很大的进展，成为克服“维数灾难”和“过学习”等问题的强有力的手段。其主要思想是找到一个超平面，使其能够尽可能地将两类数据点正确分开，同时使分开的两类数据点距离分类面最远。随着支持向量机和相关支持域技术的提出和完善，二分类问题的理论基础和实现框架都已形成。With the rapid development of information technology, a large number of multimedia data such as images and videos have emerged, which has become one of the important ways for people to obtain information. How to effectively classify the acquired information is a major challenge in the field of machine learning. Support Vector Machine (Support Vector Machine, SVM) is a popular classification method, which was first proposed by Vapnik et al. In recent years, it has made great progress in its theoretical research and algorithm implementation, and has become an important tool for overcoming the "curse of dimensionality". " and "over-learning" issues. The main idea is to find a hyperplane so that it can correctly separate the two types of data points as much as possible, and at the same time make the separated two types of data points farthest from the classification surface. With the introduction and improvement of support vector machine and related support domain technology, the theoretical basis and implementation framework of the binary classification problem have been formed.

然而，多分类技术仍然不甚成熟。目前对多分类的研究主要有两个方向：间接解决和直接解决。间接解决多分类的方法是将多分类问题转化为二分类问题，即用多个二类分类器组成一个多类分类器。这类方法主要有以下两种：一对多(One-Vs-All，OVA)方法、一对一(One-Vs-One，OVO)方法。OVA是一种很简单的多分类方法，是为每个类构建一个二类分类器,对于N个类别的分类,则要构造N个二类分类器。对第i个类的二类分类器来说,其训练样本集的构成为属于i类的样本为正类,而不属于该类的其他所有样本都为负类，但该方法训练时正负类数据分布不平衡,导致分类精度降低。OVO方法是对多类别数据进行两两区分,为任意两个类构建分类超平面。对于N类数据集,则需要构造N(N-1)/2个二类分类器,这种方法不仅计算量庞大，而且只建立两两类别间的分类器，忽视了与其他类别的信息，并且OVA和OVO多分类方法都存在识别盲区的问题。However, multi-classification techniques are still immature. The current research on multi-classification mainly has two directions: indirect solution and direct solution. The indirect method to solve multi-classification is to transform the multi-classification problem into a two-class classification problem, that is, to use multiple two-class classifiers to form a multi-class classifier. Such methods mainly include the following two types: one-to-many (One-Vs-All, OVA) method and one-to-one (One-Vs-One, OVO) method. OVA is a very simple multi-classification method. It is to construct a two-class classifier for each class. For the classification of N categories, N two-class classifiers must be constructed. For the two-class classifier of the i-th class, the composition of the training sample set is that the samples belonging to the i class are the positive class, and all other samples that do not belong to the class are the negative class, but the method is positive and negative during training. The unbalanced distribution of class data leads to the decrease of classification accuracy. The OVO method is to distinguish between two pairs of multi-category data, and construct a classification hyperplane for any two classes. For N-type data sets, it is necessary to construct N(N-1)/2 two-class classifiers. This method not only has a large amount of calculation, but also only establishes classifiers between two classes, ignoring information related to other classes. And both OVA and OVO multi-classification methods have the problem of identifying blind spots.

最近几年来，不少研究者试图通过设计直接解决多分类问题的SVM来解决多分类问题，同时处理各类数据并考虑各类之间的关联信息。在这类方法中，最著名的是采用支持向量描述(Support Vector Data Description,SVDD)的方法利用K个超球体对K类数据同时进行描述，每个超球体包含同一类的样本数据。SVDD的基本思想是把所有样本映射到特征空间，然后在特征空间中计算包含这组数据的最小超球体边界来获得数据的分布区域，从而对该组数据进行描述,主要用来进行单类分类及去除噪声点或奇异点。和SVM不同的是，SVDD不是寻找一个超平面而是通过计算包含同一类样本的最小超球体边界来对数据的分布范围进行描述。通常位于超球体内部的数据被分类为目标类，位于超球体边界的数据称为支持向量,超球体外的则是非目标样本。In recent years, many researchers have attempted to solve multi-classification problems by designing SVMs that directly solve multi-classification problems, while processing various types of data and considering the correlation information between types. Among these methods, the most famous one is the Support Vector Data Description (SVDD) method, which uses K hyperspheres to simultaneously describe K types of data, and each hypersphere contains sample data of the same type. The basic idea of SVDD is to map all samples to the feature space, and then calculate the minimum hypersphere boundary containing this set of data in the feature space to obtain the distribution area of the data, so as to describe the set of data, mainly used for single-class classification And remove noise points or singular points. Different from SVM, SVDD does not look for a hyperplane but describes the distribution range of data by calculating the boundary of the smallest hypersphere containing samples of the same type. Usually the data located inside the hypersphere is classified as the target class, the data located on the boundary of the hypersphere are called support vectors, and the data outside the hypersphere are non-target samples.

由于可以对每一类样本单独使用SVDD，得到各个类别样本的超球体，并以此作为分类边界，因此SVDD可以很容易地扩展为多类分类器来处理处理多分类问题。例如：Zhu等人利用SVDD对多类问题进行分类，提出了一种球结构支持向量机方法，该方法对每一类训练样本求解问题构造一个包含该类样本的最小超球，然后根据测试样本离各个球心的距离来判断测试样本属于哪一类。Lee等人基于贝叶斯决策准则提出了一种求解多类问题的区域描述支持向量分类方法，该方法首先对每一类训练样本求解问题构造-个包含该类样本的最小超球体，然后利用贝叶斯公式计算后验概率来判断测试样本该属于哪一类。Lei等人对Zhu等人提出的方法的判别函数进行修改，当利用测试样本离各个球心距离进行类别判断不明确时就在不明确区域使用最近邻方法进行判别。Hao等人提出了一个求解多分类问题的球型支持向量机，该方法以所有超球体半径的平方和最小为目标函数对每个类构造一个超球体以使该类样本约束在超球体里而将其他样本约束在超球体外，然后根据测试样本离各个球心的距离来判断测试样本属于哪一类。Liu等提出一种基于核空间相对密度的SVDD多类分类算法，该算法首先由SVDD确定包围每类数据的最小超球体，然后计算位于最小超球体重叠区域中每个样本在其同类样本间的相对密度，最后以各类样本相对密度的均值为标准，对重叠区域内的待测样本进行分类。Wang等提出了结构化一类分类(Structured One-Class Classification)算法，是在考虑数据分布的基础上，将一类目标数据用多个超椭球来描述，以获得对目标数据更有效的描述。Since SVDD can be used separately for each class of samples to obtain hyperspheres of samples of each class and use them as classification boundaries, SVDD can be easily extended to multi-class classifiers to deal with multi-class classification problems. For example: Zhu et al. used SVDD to classify multi-class problems, and proposed a ball-structure support vector machine method. This method constructs a minimum hypersphere containing samples of this class for each class of training samples, and then according to the test samples The distance from the center of each sphere is used to determine which category the test sample belongs to. Lee et al. proposed a region description support vector classification method for solving multi-class problems based on Bayesian decision criteria. This method first constructs a minimal hypersphere containing samples of this class for each class of training samples, and then uses The Bayesian formula calculates the posterior probability to determine which class the test sample belongs to. Lei et al. modified the discriminant function of the method proposed by Zhu et al. When the distance between the test sample and the center of each sphere is used to judge the category is not clear, the nearest neighbor method is used for discrimination in the unclear area. Hao et al. proposed a spherical support vector machine for solving multi-classification problems. This method uses the minimum sum of squares of all hypersphere radii as the objective function to construct a hypersphere for each class so that the samples of this class are constrained in the hypersphere. Constrain other samples outside the hypersphere, and then determine which category the test sample belongs to according to the distance between the test sample and the center of each sphere. Liu et al. proposed a SVDD multi-class classification algorithm based on the relative density of the kernel space. The algorithm first determines the smallest hypersphere surrounding each type of data by SVDD, and then calculates the difference between each sample in the overlapping area of the smallest hypersphere among its similar samples. Relative density. Finally, the average value of the relative density of various samples is used as the standard to classify the samples to be tested in the overlapping area. Wang et al. proposed a structured one-class classification (Structured One-Class Classification) algorithm, which is based on considering the data distribution, and describes a class of target data with multiple hyperellipsoids to obtain a more effective description of the target data. .

此外，当前的识别技术大都是针对无拒识的闭集识别，即测试样本一定能与训练数据库中的样本相匹配，但这种情况不符合现实应用的真实情况，而开集识别技术排除了闭集识别中“测试样本一定能与训练数据库的样本相匹配”的假设，能够对与目标库身份不匹配的的异类样本进行拒识，更加符合现实应用中的真实情况。In addition, most of the current recognition technologies are aimed at closed-set recognition without rejection, that is, the test samples must match the samples in the training database, but this situation does not conform to the real situation of practical applications, and the open-set recognition technology excludes The assumption that "test samples must match the samples in the training database" in closed-set recognition can reject heterogeneous samples that do not match the identity of the target database, which is more in line with the real situation in real-world applications.

发明内容Contents of the invention

本发明所要解决的技术问题是，提供一种为每一个类寻求一个包含所有或几乎所有该类目标样本且体积最小的最优超球体，并使超球体之间的距离最大，从而实现多个类别的有效分类，解决多分类问题以及类别之间数据不平衡问题的基于最大球心距的支持向量描述方法。The technical problem to be solved by the present invention is to provide an optimal hypersphere that contains all or almost all target samples of this type and has the smallest volume for each class, and makes the distance between the hyperspheres the largest, thereby realizing multiple hyperspheres. Efficient classification of categories, a support vector description method based on the maximum distance between the centers of spheres to solve multi-category problems and data imbalance problems between categories.

本发明所采用的技术方案是：一种基于最大球心距的支持向量描述方法，是将类间距离最大化的目标加入到支持向量描述的目标优化函数中，得到在使每一个超球体半径最小的目标下，同时使不同超球体之间的距离最大的目标函数。The technical scheme adopted in the present invention is: a support vector description method based on the maximum center-of-sphere distance, which is to add the target of maximizing the distance between classes into the target optimization function of support vector description, and obtain the radius of each hypersphere Under the minimum objective, the objective function that maximizes the distance between different hyperspheres at the same time.

所述的目标函数的建立，首先设为数据空间中的一个已知训练数据集，其中T为类的个数，t_m为第m类的样本数，得到目标函数：The establishment of the objective function, first set for the data space A known training data set in , where T is the number of classes, t _m is the number of samples of the mth class, and the objective function is obtained:

$\begin{matrix} min min & \underset{m m}{Σ Σ} {R R}_{m m}^{22} - - K K \underset{m m,, n no}{Σ Σ} {d d}_{m m}^{22} + + C C \underset{i i}{Σ Σ} \underset{m m}{Σ Σ} {ξ ξ}_{i i}^{m m} \\ s the s . . t t . . & {| | | | φ φ (({x x}_{i i}^{m m} - - {c c}_{m m})) | | | |}^{22} - - {R R}_{m m} \leq \leq {ξ ξ}_{i i}^{m m},, {ξ ξ}_{i i}^{m m} &GreaterEqual; &Greater Equal; 00,, &ForAll; &ForAll; i i,, m m \end{matrix} - - - - - - ((11))$

其中：R_m为第m类的半径，c_m第m类的球心，d_mn为第m类的球心与第n类球心的距离，m,n∈{1,…,T}，K为调节半径与分离间隔的参数，K≥0，为第m类的第i个样本，C为惩罚参数，用来控制最小包围球半径和错分程度的一个折衷。Among them: R _m is the radius of the m class, c _m is the center of the m class, d _mn is the distance between the m class center and the n class center, m,n∈{1,…,T}, K is the parameter to adjust the radius and separation interval, K≥0, is the i-th sample of the m-th class, and C is a penalty parameter, which is used to control a compromise between the minimum enclosing sphere radius and the degree of misclassification.

本发明的基于最大球心距的支持向量描述方法，在利用训练样本的监督信息的前提下，充分地对每一类的边界进行刻画，并调节建立的超球体之间的距离，使不同类的样本尽可能的分离。充分地利用了类内和类间的信息。本发明首次在支持向量描述的方法的基础上引入类间信息约束到多分类问题中，并在此基础上利用一个半径最小的超球体将同一类样本包围，并使超球体之间尽可能的远离。本发明可以避免传统多分类方法中存在的类别不平衡问题以及识别盲区问题，通过有拒识的开集人脸识别系统证明了该发明用于多分类问题的有效性。本发明与传统方法相比,具有鲁棒性强、分类效果好等优点。可以用于解决小样本集的监督学习多分类问题。The support vector description method based on the maximum center-of-sphere distance of the present invention fully describes the boundary of each class under the premise of using the supervision information of the training samples, and adjusts the distance between the established hyperspheres so that different classes The samples were separated as much as possible. The intra-class and inter-class information is fully utilized. The present invention introduces inter-class information constraints into multi-classification problems for the first time on the basis of the support vector description method, and on this basis, uses a hypersphere with the smallest radius to surround the same class of samples, and makes the hyperspheres as close as possible keep away. The invention can avoid the category imbalance problem and the identification blind area problem existing in the traditional multi-classification method, and the effectiveness of the invention for the multi-classification problem is proved by an open-set face recognition system with recognition rejection. Compared with the traditional method, the present invention has the advantages of strong robustness, good classification effect and the like. It can be used to solve supervised learning multi-classification problems with small sample sets.

附图说明Description of drawings

图1是测试样本仅落入某一超球体中的示意图；Figure 1 is a schematic diagram of a test sample only falling into a certain hypersphere;

图2是测试样本落入多个超球体中的示意图；Figure 2 is a schematic diagram of a test sample falling into multiple hyperspheres;

图3是测试样本落在所有超球体之外的示意图；Figure 3 is a schematic diagram of the test sample falling outside all hyperspheres;

图4是本发明的方法应用于开集人脸识别的流程图。Fig. 4 is a flow chart of the method of the present invention applied to open-set face recognition.

具体实施方式Detailed ways

下面结合实施例和附图对本发明的基于最大球心距的支持向量描述方法做出详细说明。The method for describing support vectors based on the maximum center-to-center distance of the present invention will be described in detail below with reference to the embodiments and the accompanying drawings.

本发明的基于最大球心距的支持向量描述方法，是将类间距离最大化的目标加入到支持向量描述的目标优化函数中，得到在使每一个超球体半径最小的目标下，同时使不同超球体之间的距离最大的目标函数。The support vector description method based on the maximum center distance of the present invention is to add the object of maximizing the inter-class distance into the objective optimization function of the support vector description, and obtain the minimum object of each hypersphere radius, and simultaneously make different The objective function for maximizing the distance between hyperspheres.

本发明所述的目标函数可以通过求解拉格朗日函数的鞍点得到：The objective function of the present invention can obtain by solving the saddle point of Lagrangian function:

引入拉格朗日乘子α_i≥0，β_i≥0，相应的拉格朗日函数为：Introducing Lagrangian multipliers α _i ≥ 0, β _i ≥ 0, the corresponding Lagrangian function is:

$L L = = \underset{m m}{Σ Σ} {R R}_{m m}^{22} - - K K \underset{mn mn}{Σ Σ} {d d}_{mn mn}^{22} + + C C \underset{i i,, m m}{Σ Σ} {ξ ξ}_{i i}^{m m} - - \underset{i i,, m m}{Σ Σ} {α α}_{i i}^{m m} (({ξ ξ}_{i i}^{m m} + + {R R}_{m m}^{22} - - {| | | | φ φ (({x x}_{i i}^{m m})) - - {c c}_{m m} | | | |}^{22})) - - \underset{i i,, m m}{Σ Σ} {β β}_{i i}^{m m} {ξ ξ}_{i i}^{m m} - - - - - - ((22))$

由于计算的复杂性，一般不直接进行求解，而是依据拉格朗日对偶理论求解其对偶问题，所以求L关于R_m、c_m、的偏导，并令其等于零得：Due to the complexity of the calculation, it is generally not directly solved, but the dual problem is solved according to the Lagrangian dual theory, so the relationship between L and R _m , c _m , and setting it equal to zero gives:

$\frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {R R}_{m m}} = = 22 {R R}_{m m} - - 22 {R R}_{m m} \underset{i i}{Σ Σ} {α α}_{i i}^{m m} = = 00 &DoubleRightArrow; &DoubleRightArrow; \underset{i i}{Σ Σ} {α α}_{i i}^{m m} = = 11 - - - - - - ((33))$

$\frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {ξ ξ}_{i i}^{m m}} = = C C - - {α α}_{i i}^{m m} - - {β β}_{i i}^{m m} = = 00 &DoubleRightArrow; &DoubleRightArrow; C C = = {α α}_{i i}^{m m} + + {β β}_{i i}^{m m} - - - - - - ((44))$

$\frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {c c}_{m m}} = = 22 K K \underset{n no}{Σ Σ} (({c c}_{n no} - - {c c}_{m m})) - - 22 \underset{i i}{Σ Σ} {α α}_{i i}^{m m} ((φ φ (({x x}_{i i}^{m m})) - - {c c}_{m m})) = = 00 - - - - - - ((55))$

$&DoubleRightArrow; &DoubleRightArrow; \underset{m m}{Σ Σ} {c c}_{m m} = = \underset{i i,, m m}{Σ Σ} {α α}_{i i}^{m m} φ φ (({x x}_{i i}^{m m}))$

${c c}_{m m} = = \frac{11}{TK TK - - 11} ((K K \underset{i i,, m m}{Σ Σ} {α α}_{i i}^{m m} φ φ (({x x}_{i i}^{m m})) - - \underset{i i}{Σ Σ} {α α}_{i i}^{m m} φ φ (({x x}_{i i}^{m m})))) - - - - - - ((66))$

将(3)-(6)代入到(2)中，可得其对偶问题为：Substituting (3)-(6) into (2), the dual problem can be obtained as:

$\begin{matrix} max max & \underset{i i,, m m}{Σ Σ} {α α}_{i i}^{m m} K K (({x x}_{i i}^{m m},, {x x}_{i i}^{m m})) - - \frac{K K}{TK TK - - 11} \underset{i i,, j j,, m m,, n no = = 11}{Σ Σ} {α α}_{i i}^{m m},, {α α}_{j j}^{n no} K K (({α α}_{i i}^{m m},, {α α}_{j j}^{n no})) + + \frac{11}{TK TK - - 11} \underset{i i,, j j,, m m}{Σ Σ} {α α}_{i i}^{m m} {α α}_{j j}^{m m} K K (({x x}_{i i}^{m m},, {x x}_{j j}^{m m})) \\ s the s . . t t . . & \underset{i i}{Σ Σ} {α α}_{i i}^{m m} = = 1,0 1,0 \leq \leq {α α}_{i i}^{m m} \leq \leq C C \end{matrix} - - - - - - ((77))$

利用核函数的思想，K(x_i,x_j)＝φ(x_i)·φ(x_j)，“·”表示内积，在本发明中利用径向基(RBF)核函数，即：K(x_i,x_j)＝exp(-q||x_i-x_j||²)。Utilize the idea of kernel function, K(x _i , x _j )=φ(x _i ) φ(x _j ), “ ” represents the inner product, utilizes radial basis (RBF) kernel function in the present invention, namely: K(x _i , x _j )=exp(-q|| _xi -x _j || ² ).

以上的目标函数是线性约束的凸规划问题，利用二次规划算法进行求解，得到每个类的球心可以通过公式(6)得到，对于每一个超球体的球心，由KKT(Karush-Kuhn-Tucker)条件知：The above objective function is a convex programming problem with linear constraints, and it is solved by using the quadratic programming algorithm to obtain The center of each class can be obtained by formula (6). For the center of each hypersphere, it is known by the KKT (Karush-Kuhn-Tucker) condition:

$\begin{matrix} {α α}_{i i}^{m m} (({| | | | φ φ (({x x}_{i i})) - - {c c}_{m m} | | | |}^{22} - - {R R}_{m m}^{22} - - {ξ ξ}_{i i}^{m m})) = = 00,, {β β}_{i i}^{m m} {ξ ξ}_{i i}^{m m} = = 00 \\ {| | | | φ φ (({x x}_{i i})) - - {c c}_{m m} | | | |}^{22} \leq \leq {R R}_{m m}^{22} + + {ξ ξ}_{i i}^{m m},, C C - - {α α}_{i i}^{m m} - - {β β}_{i i}^{m m} = = 00,, {ξ ξ}_{i i}^{m m} &GreaterEqual; &Greater Equal; 00 . . \end{matrix}$

当 $0 < α_{i}^{m} < C$ 时， ${| | φ (x_{i}) - c_{m} | |}^{2} - R_{m}^{2} - ξ_{i}^{m} = 0, β_{i}^{m} > 0, ξ_{i}^{m} = 0,$ when $0 < α_{i}^{m} < C$ hour, ${| | φ (x_{i}) - c_{m} | |}^{2} - R_{m}^{2} - ξ_{i}^{m} = 0, β_{i}^{m} > 0, ξ_{i}^{m} = 0,$

因此对于对应的x_i有：Therefore for The corresponding x _i are:

${R R}_{m m}^{22} = = {| | | | φ φ (({x x}_{i i})) - - {c c}_{m m} | | | |}^{22}$

其中对应的x_i是支持向量。in The corresponding _xi are support vectors.

测试样本x到第m个超球体的球心的距离为：The distance from the test sample x to the center of the mth hypersphere is:

$\begin{matrix} {d d}_{m m}^{22} = = {| | | | φ φ ((x x)) - - {c c}_{m m} | | | |}^{22} \\ = = K K ((x x,, x x)) - - \frac{22 K K}{TK TK - - 11} \underset{i i,, m m}{Σ Σ} {α α}_{i i}^{m m} K K (({x x}_{i i}^{m m},, x x)) + + \frac{22}{TK TK - - 11} \underset{i i}{Σ Σ} {α α}_{i i}^{m m} K K (({x x}_{i i}^{m m},, x x)) + + {c c}_{m m}^{22} \end{matrix}$

对于测试样本的判别准则是，判断测试样本是否落入超球体之中，如果落入超球体中，则判断测试样本属于目标类，否则测试样本属于非目标类。所以判别函数为：The judgment criterion for the test sample is to judge whether the test sample falls into the hypersphere, if it falls into the hypersphere, then it is judged that the test sample belongs to the target class, otherwise the test sample belongs to the non-target class. So the discriminant function is:

$f f ((x x)) = = sign sign (({R R}_{m m}^{22} - - {d d}_{m m}^{22})) . .$

当f(x)>0时，测试样本x落入第m个超球体中，否则落在超球体之外。When f(x)>0, the test sample x falls into the mth hypersphere, otherwise it falls outside the hypersphere.

对于多分类问题，测试样本与所建立的超球体之间的关系有三种关系：For multi-classification problems, there are three relationships between the test sample and the established hypersphere:

(1)测试样本仅落入某一超球体中，如图1所示，图中x表示测试样本，A表示超球体。(1) The test sample only falls into a certain hypersphere, as shown in Figure 1, where x in the figure represents the test sample, and A represents the hypersphere.

(2)测试样本落入多个超球体中，如图2所示，图中x表示测试样本，B、C表示超球体。(2) The test sample falls into multiple hyperspheres, as shown in Figure 2, where x in the figure represents the test sample, and B and C represent the hyperspheres.

(3)测试样本落在所有超球体之外，如图3所示，图中x表示测试样本，D、E、F表示超球体。(3) The test sample falls outside all hyperspheres, as shown in Figure 3, where x in the figure represents the test sample, and D, E, and F represent the hyperspheres.

闭集识别中，对于关系(2)、(3)中出现的情况，在本发明中利用K近邻来确定该样本类别的归属。而对于开集识别，针对关系(2)中出现的情况，利用K近邻来确定该测试样本类别的归属，而对于关系(3)中测试样本，则判定其为异类样本，模型将予以拒绝。In the closed set recognition, for the situations appearing in the relation (2) and (3), in the present invention, K-nearest neighbors are used to determine the attribution of the sample category. For open set recognition, for the situation in relation (2), K-nearest neighbors are used to determine the attribution of the test sample category, while for the test sample in relation (3), it is judged to be a heterogeneous sample, and the model will reject it.

与传统的“一对多”，“一对一”多分类技术不同的是，本发明以所有超球半径的平方和最小及超球体之间的距离最大为目标函数，利用一个半径最小的超球将同一类的样本包围，同时使超球体之间的距离最远，是“一次性”建立多个超球体，而不是设计多个二分类器实现多分类的目的。本发明充分考虑类别之间的关系，避免了类别不平衡的问题；同时模型是以建立超球体为目标，可以有效解决识别盲区的问题。Different from the traditional "one-to-many" and "one-to-one" multi-classification techniques, the present invention takes the minimum sum of squares of all hypersphere radii and the maximum distance between hyperspheres as the objective function, and utilizes a hypersphere with the smallest radius The ball surrounds the samples of the same class, and at the same time makes the distance between the hyperspheres the farthest. It is to establish multiple hyperspheres "at once", rather than designing multiple binary classifiers to achieve multi-classification. The invention fully considers the relationship between categories and avoids the problem of unbalanced categories; at the same time, the model aims to establish a hypersphere, which can effectively solve the problem of identifying blind spots.

下面结合图4说明本发明在有拒识的开集人脸识别的应用。需要说明的是，本发明不仅可以应用在开集人脸识别中，也可以应用在其他生物特征的开集识别中。The application of the present invention in open-set face recognition with rejection will be described below in conjunction with FIG. 4 . It should be noted that the present invention can be applied not only in open-set face recognition, but also in open-set recognition of other biological features.

(1)图像预处理和特征提取(1) Image preprocessing and feature extraction

首先对人脸图像进行对齐，光照归一化等预处理操作，然后提取人脸图像的特征；First, pre-processing operations such as alignment and illumination normalization are performed on the face image, and then the features of the face image are extracted;

(2)特征变换(2) Feature transformation

为了更好地对样本数据进行描述，对提取的人脸图像的原始数据特征进行特征变换，可以采用基于核的方法、基于子空间的方法、基于流形学习的方法等；In order to better describe the sample data, the feature transformation of the original data features of the extracted face image can be performed using a kernel-based method, a subspace-based method, a manifold learning-based method, etc.;

(3)利用本发明的方法建立有拒识的开集人脸分类模型(3) Utilize the method of the present invention to set up the open set human face classification model that rejects recognition

利用本发明的多分类模型将每一类人脸样本用一个半径最小的超球体包围，并使不同的人脸类之间距离最大，达到不同的类尽可能分离的目的；Utilize the multi-classification model of the present invention to surround each type of face sample with a hypersphere with the smallest radius, and make the distance between different face classes the largest, so as to achieve the purpose of separating different classes as much as possible;

(4)对待测人脸样本进行测试(4) Test the face samples to be tested

对待测人脸样本进行预处理并提取特征，经过特征转换后将提取的高维特征转化为具有判别信息的低维特征，若待测人脸样本落到某个超球体中，则将此待测样本归为此类；当多个超球体同时包含测试样本时根据测试样本周围各类样本核空间的相对密度均值的大小来判定它的归属；如果待测人脸样本落在所有超球体之外则认为此待测人脸样本不属于目标集内人脸样本，并将其拒绝。Preprocess the face sample to be tested and extract features. After feature conversion, the extracted high-dimensional features are transformed into low-dimensional features with discriminative information. If the face sample to be tested falls into a hypersphere, the waiting The test sample is classified into this category; when multiple hyperspheres contain the test sample at the same time, it is determined according to the size of the relative density average of the various sample kernel spaces around the test sample; if the face sample to be tested falls between all hyperspheres Otherwise, it is considered that the face sample to be tested does not belong to the face sample in the target set, and it is rejected.

Claims

1. A support vector description method based on the maximum center-of-sphere distance, characterized in that, the object of maximizing the inter-class distance is added to the objective optimization function described by the support vector, and the object of making each hypersphere radius minimum is obtained Under , the objective function that maximizes the distance between different hyperspheres at the same time.

2. the support vector description method based on maximum center-of-sphere distance according to claim 1, is characterized in that, the establishment of described objective function, at first set for the data space A known training data set in , where T is the number of classes, t _m is the number of samples of the mth class, and the objective function is obtained:

min min \underset{m m}{Σ Σ} {R R}_{m m}^{22} - - K K \underset{m m,, n no}{Σ Σ} {d d}_{mn mn}^{22} + + C C \underset{i i}{Σ Σ} \underset{m m}{Σ Σ} {ξ ξ}_{i i}^{m m} - - - - - - ((11))

\begin{matrix} s the s . . t t . . & {| | | | φ φ (({x x}_{i i}^{m m} - - {c c}_{m m})) | | | |}^{22} - - {R R}_{m m} \leq \leq {ξ ξ}_{i i}^{m m} & {ξ ξ}_{i i}^{m m} &GreaterEqual; &Greater Equal; 00 & &ForAll; &ForAll; i i,, m m \end{matrix}

Among them: R _m is the radius of the m class, c _m is the center of the m class, d _mn is the distance between the m class center and the n class center, m,n∈{1,…,T}, K is the parameter to adjust the radius and separation interval, K≥0, is the i-th sample of the m-th class, and C is a penalty parameter, which is used to control a compromise between the minimum enclosing sphere radius and the degree of misclassification.