交替加权四线性分解算法用于处理非五线性五维数阵  

A new alternating weighted quadrilinear decomposition algorithm with application for analysis of non-quinquelinear five-way data arrays

作　　者：卿湘东[1,2] 吴海龙[1] 张喜华[1] 李勇[1] 谷惠文[1] 文瑾[2] 申湘忠[2] 俞汝勤[1] 

机构地区：[1]化学生物传感与计量学国家重点实验室,湖南大学化学化工学院,长沙410082 [2]湖南人文科技学院化学与材料科学系,娄底417000

出　　处：《中国科学：化学》2016年第4期401-408,共8页SCIENTIA SINICA Chimica

基　　金：国家自然科学基金(编号:21175041,21221003);湖南人文科技学院引进人才启动项目(编号:8250139)资助

摘　　要：针对获得的非五线性五维数阵,采用一种先拓展后处理的思路,即将该数阵沿着不具有线性的一维铺展成四线性四维数阵,然后采用四维平行因子分析(4-PARAFAC)、交替加权残差约束四线性分解(AWRCQLD)和新发展的交替加权四线性分解(AWQLD)算法来对其进行解析.在处理实验数据之前,还通过2组模拟数据对提出的方法进行了验证.结果表明,新发展的AWQLD算法给出了与AWRCQLD和4-PARAFAC相似甚至更好的结果,为处理非多线性多维数阵又提供了一种很有潜力的分析方法.In the work, a new method based on firstly expanding before processing was proposed to investigate the non-quinquelinear five-way data produced in the study. The five-way data array was firstly rearranged into an expanded four-way data array along the non-linear way, then it was decomposed by four-way calibration based on four way-PARAFAC, alternating weighted residue constraint quadrilinear decomposition（AWRCQLD） and newly presented alternating weighted quadrilinear decomposition（AWQLD）. Before processing real data, a simulated fluorescence data and a simulated chromatographic data were used to verify the proposed method. It was found that the results of AWQLD were similar to or ever better than the ones of PARAFAC and AWRCQLD. These results indicated that the developed method possessed great potential to deal with non-multilinear multidimensional data.

关 键 词：交替加权四线性分解 四维校正 非五线性五维数阵 平行因子分析 色谱 

分 类 号：O657.7[理学—分析化学] TQ450.1[理学—化学]