对于矩阵数据分类的双支持矩阵机

发布时间：2018-08-26 18:19

【摘要】：如今,张量作为一种常见的形式被越来越广泛地应用在各种领域中.如何对张量数据进行分类是一个重要的研究课题,例如人脸识别,视觉识别,医学图像等等.矩阵,是一个二阶张量,可以用来建立向量与张量之间的桥梁.高阶张量也可以展开成矩阵的形式,因此如何对矩阵数据分类也具有重要的研究意义。在本文中,一个巧妙的学习框架多秩多线性双支持矩阵分类机,作为双支持向量机的扩展被提出来.而与双支持向量机不同的是,多秩多线性双支持矩阵分类机用两对投影矩阵来构建一对函数.这对函数是用来建立决策函数的.与基于向量输入的方法相比,基于矩阵的方法不仅能够保持矩阵数据的结构,而且还能降低计算复杂度.另外,我们加入一个正则项来提升多秩多线性双支持矩阵分类机的表现,并且还介绍了对于多秩多线性双支持矩阵分类机巧妙的算法.关于不同方法在分类正确率,收敛性,计算时间的实验结果将被展示出来。高维矩阵输入不仅本身占用内存较大并且在计算过程中也需要较大的运行内存.为了提高对于高维矩阵输入的存储和计算能力,本文基于奇异值分解对多秩多线性双支持矩阵分类机进行了改进.在多秩多线性双支持矩阵分类机的基础上,建立了一个基于奇异值分解双支持矩阵分类机.对于矩阵输入,我们基于矩阵奇异值分解定义了一个矩阵映射函数,用来处理矩阵输入,降低数据维数并形成一个新的训练集.通过学习新的训练集,分类正确率将会升高,训练时间将会减少.对五组数据集进行训练,通过与其他分类方法相比,基于奇异值分解双支持矩阵分类机是一个有效的分类器。
[Abstract]:Nowadays, Zhang Liang as a common form is more and more widely used in various fields. How to classify Zhang Liang data is an important research topic, such as face recognition, visual recognition, medical image and so on. Matrix, is a second-order Zhang Liang, can be used to build a vector and Zhang Liang between the bridge. High order Zhang Liang can also expand into matrix form, so how to classify matrix data has important significance. In this paper, a clever learning framework is proposed as an extension of the double support vector machine (DSVM). Different from the double support vector machine, the multi-rank multi-linear double support matrix classifier uses two pairs of projection matrices to construct a pair of functions. This pair of functions is used to establish a decision function. Compared with the method based on vector input, the method based on matrix can not only preserve the structure of matrix data, but also reduce the computational complexity. In addition, we add a regular term to improve the performance of multi-rank multi-linear bilinear support matrix classifier, and introduce a clever algorithm for multi-rank multi-linear bilinear support matrix classifier. Experimental results on the classification accuracy, convergence and computation time of different methods will be shown. The input of high dimensional matrix not only occupies a large amount of memory, but also needs a large amount of running memory in the process of calculation. In order to improve the ability of storing and computing the input of high-dimensional matrix, this paper improves the multi-rank and multi-linear bilinear support matrix classifier based on singular value decomposition (SVD). On the basis of multi-rank multi-linear bilinear support matrix classifier, a two-support matrix classifier based on singular value decomposition (SVD) is established. For matrix input, we define a matrix mapping function based on matrix singular value decomposition, which is used to deal with matrix input, reduce data dimension and form a new training set. By learning the new training set, the classification accuracy will increase and the training time will be reduced. Five groups of data sets are trained. Compared with other classification methods, the dual support matrix classifier based on singular value decomposition is an effective classifier.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21;O183.2

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