CAJ | 학술논문

为了处理张量数据,传统的学习算法常常把张量展成向量,但会造成破坏原始数据固有的高阶结构和内在相关性,导致信息丢失,或产生高维向量,使得后期学习过程中容易出现过拟合、维度灾难和小样本问题。近年提出了许多基于张量模式的分类算法,而支持高阶张量机算法是张量分类算法中最有效的方法之一。考虑到张量的高维性和高冗余性,本文提出基于多线性主成分分析的支持高阶张量机分类算法(Multilinear Principle Component Analysis Based Support High-Order Tensor Machine,MPCA+SHTM)。该算法首先利用多线性主成分分析对张量进行降维,然后利用支持高阶张量机对降维后的张量进行学习。在12个张量数据集上的实验表明：MPCA+SHTM在保持测试精度的情况下有效地降低了 SHTM的计算时间。
위료처리장량수거,전통적학습산법상상파장량전성향량,단회조성파배원시수거고유적고계결구화내재상관성,도치신식주실,혹산생고유향량,사득후기학습과정중용역출현과의합、유도재난화소양본문제。근년제출료허다기우장량모식적분류산법,이지지고계장량궤산법시장량분류산법중최유효적방법지일。고필도장량적고유성화고용여성,본문제출기우다선성주성분분석적지지고계장량궤분류산법(Multilinear Principle Component Analysis Based Support High-Order Tensor Machine,MPCA+SHTM)。해산법수선이용다선성주성분분석대장량진행강유,연후이용지지고계장량궤대강유후적장량진행학습。재12개장량수거집상적실험표명：MPCA+SHTM재보지측시정도적정황하유효지강저료 SHTM적계산시간。
In the fields of pattern recognition,computer vision and image processing,data obj ects are typically represented as tensors.For dealing with tensor data,conventional methods usually convert them into feature vectors. However,this may results in the following problems:(1)break the inherent higher-order structure and correlation in the original data and lead to the loss of information;(2)generate the high dimensional feature vectors and thus make the subsequent learning process prone to overfitting,and suffer from the curse of dimensionality and the small sample size problems.In order to overcome these drawbacks,the studies on learning machines whose input patterns are tensors have recently attracted critical attention from the research community.Many tensor based classification algorithms have been proposed.At present,support higher-order tensor machine(SHTM)is one of the most effective algorithms for tensor classification.Considering that tensor obj ects are usually high dimensional and contain large amounts of redundancy,we propose a multilinear principle component analysis based support higher-order tensor machine(MPCA+SHTM)for tensor classification.In the proposed algorithm,multilinear principle component analysis is first used to conduct dimension reduction and preserve the natural structure and correlation in the original tensor data,then support higher-order tensor machine classifier is adopted for further redundancy elimination and classification.The experiments on twelve real tensor datasets show that MPCA+SHTM is faster than SHTM with comparable test accuracy.