南京大学学报（自然科学版）Issue(2)：219-227,9.DOI:10.13232/j.cnki.jnju.2014.02.014
基于多线性主成分分析的支持高阶张量机
Multilinear principle component analysis based support higher-order tensor machine
摘要
Abstract
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.关键词
支持高阶张量机/多线性主成分分析/张量分解/交替投影张量机Key words
support higher-order tensor machine(SHTM)/multilinear principle component analysis(MPCA)/tensor decomposition/alternating proj ection tensor machine引用本文复制引用
曾奎,何丽芳,杨晓伟..基于多线性主成分分析的支持高阶张量机[J].南京大学学报（自然科学版）,2014,(2):219-227,9.基金项目
国家自然科学基金(61273295),国家社科基金重大项目(11&ZD156) （61273295）
