输入为张量的回归问题和分类问题算法研究

发布时间：2019-03-18 12:58

【摘要】：张量类型的数据已经极大的引起了人们的注意.近期,一些张量学习的方法出现了,但是它们中的大多处理张量学习问题的方法致力于研究将原张量直接向量化.而直接将张量向量化可能会导致很多问题.第一,张量的结构信息被破坏.第二,直接将张量向量化可能会产生一个维数很高的向量,而这可能会导致较高的计算复杂度,过拟合问题以及较大的内存需要.因此,研究出更佳有效的解决张量的回归问题和分类问题的算法是很有意义的.本文主要从两个方面出发研究了一些输入是张量的回归问题和分类问题的算法.第一,尽可能多的保留和利用张量的结构信息;第二,将张量向量化成维数尽可能小的向量.从第一方面出发,首先我们受到彩色照片和灰色照片之间的关系的启发,我们重新构造了训练集并形成了新的基于张量子矩阵片的最小二乘支持张量回归机模型来求解张量的回归问题.通过引入投影矩阵和另一个固定点连续算法,我们把基于张量子矩阵片的最小二乘支持张量回归机模型转换成一些列的最小二乘支持矩阵回归机模型,然后用提出了一个固定点连续算法对这些最小二乘支持矩阵回归机模型进行求解.其次,我们知道矩阵的核范数可以看成是矩阵的秩的一个刻画,因此自然的能够想到用张量的核范数来刻画张量的秩,因此,通过选取张量的核范数的定义,建立了一个基于张量的核范数的支持张量机来求解张量的分类问题.从第二方面出发,我们通过将输入张量进行张量的T-svd分解来对原始数据进行预处理,得到一个维数相对较小的向量,再用解向量回归或者分类的算法来进行计算.后文的实验结果表明,我们提出的处理张量回归问题和分类问题的算法均具有较好的实验表现.
[Abstract]:Zhang Liang's type of data has greatly attracted people's attention. Recently, a number of Zhang Liang learning methods have emerged, but most of them deal with Zhang Liang learning methods devoted to the direct vectorization of Zhang Liang. And the direct Zhang Liang vectorization may lead to a lot of problems. First, Zhang Liang's structural information was destroyed. Second, the direct vectorization of Zhang Liang may produce a vector with a high dimension, which may lead to higher computational complexity, over-fitting problems and large memory requirements. Therefore, it is meaningful to study a better and more effective algorithm to solve Zhang Liang's regression problem and classification problem. In this paper, we mainly study some algorithms of Zhang Liang's regression problem and classification problem from two aspects. First, keep and make use of Zhang Liang's structure information as much as possible; second, quantify Zhang Liang vector into vector with as small dimension as possible. First of all, we're inspired by the relationship between color and gray, We re-construct the training set and form a new least square support Zhang Liang regression model based on Zhang quantum matrix to solve Zhang Liang's regression problem. By introducing projection matrix and another fixed-point continuous algorithm, we transform the least square support Zhang Liang regression model based on tensor quantum matrix slice into the least square support matrix regression model of some columns. Then a fixed-point continuous algorithm is proposed to solve these least square support matrix regression models. Secondly, we know that the kernel norm of a matrix can be regarded as a characterization of the rank of a matrix, so we can naturally think of using Zhang Liang's kernel norm to characterize Zhang Liang's rank. Therefore, by selecting the definition of Zhang Liang's kernel norm, A support Zhang machine based on Zhang Liang's kernel norm is established to solve Zhang Liang's classification problem. From the second aspect, we preprocess the original data by decomposing Zhang Liang into Zhang Liang's T-svd, and get a vector with relatively small dimension. Then we use the algorithm of solution vector regression or classification to calculate the original data. The experimental results show that the proposed algorithms to deal with the Zhang Liang regression problem and the classification problem have good experimental performance.
【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】：O183.2

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