朴素支持张量机的算法研究综述

A review of algorithms for Naive-supported tensor machines

大部分数据的自然表示形式是向量、矩阵或者更高维的数据,支持向量机可以较好地处理向量形式的数据,但是对于高维数据,传统的机器学习算法在将多维数据转化成向量形式时会损失大量的结构信息。因此,研究者提出朴素支持张量机这一类分类器,将多维数据输入进行训练,利用SMO算法求解。其中利用CP分解、Tucker分解或者张量核函数等来获取数据的结构信息,这样不但能够获取数据的大部分信息,还可以节省时间成本,减少计算量,又可以求得凸优化函数的全局最优解。本文对这一类分类器的一个算法研究综述,同时指出了算法的优缺点和未来发展的方向。

Most of the natural representation forms of data are vectors,matrices or higher-dimensional data.Support vector machines can handle the data in vector form better,but for high-dimensional data,traditional machine learning algorithms will lose a lot of structural information when transforming multidimensional data into vector form.Therefore,the researchers proposed a classifier such as naive support tensor,trained multidimensional data input,and solved it by SMO algorithm,in which CP decomposition,Tucker decomposition or tensor kernel function were used to obtain the structural information of the data.In this way,most of the information of the data can be obtained,the time cost can be saved,the computation can be reduced,and the global optimal solution of convex optimization function can be obtained.This paper is an overview of the algorithm research of this kind of classifier,and points out the advantages and disadvantages of the algorithm and the future development direction.