A novel efficient way to estimate the chemical rank of high-way data arrays.
A novel efficient way to estimate the chemical rank of high-way data arrays.
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DOI：
10.1016/j.aca.2007.07.015
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发表时间：
2007-08
影响因子：
6.2
通讯作者：
A-Lin Xia;Hai-Long Wu;Yan Zhang;Shao-Hua Zhu;Qing-Juan Han;R. Yu
中科院分区：
文献类型：
--
作者：
A-Lin Xia;Hai-Long Wu;Yan Zhang;Shao-Hua Zhu;Qing-Juan Han;R. Yu
提出了一种新的高速公路数据阵列化学秩估计方法--伪高速公路数据阵列子空间投影法。该方法通过对原始高速公路数据阵列的切片矩阵进行奇异值分解（SVD）产生伪高速公路数据阵列，并利用原始截断数据集与伪高速公路数据集之差的思想来确定化学秩。与传统方法相比，该方法利用特征向量的信息结合投影残差来估计三路数据阵列的秩，而不是使用特征值。为了验证该方法的优越性能，对模拟和真实的三路数据阵列进行了仿真实验。结果表明，该方法能够准确、快速地确定化合物的化学秩，拟合三线性模型。将该方法与因子指示函数（IND）、ADD-ONE-UP、核心一致性诊断（CORCONDIA）和双模子空间比较（TMSC）等4种因子确定方法进行了比较。研究发现，与许多其他方法相比，该方法可以处理更复杂的、存在严重共线性和痕量浓度的情况，并且在实际应用中表现良好。
A novel method, a subspace projection of pseudo high-way data array (SPPH), was developed for estimating the chemical rank of high-way data arrays. The proposed method determines the chemical rank through performing singular value decomposition (SVD) on the slice matrices of original high-way data array to produce a pseudo high-way data array and employing the idea of the difference of the original truncated data set and the pseudo one. Compared with traditional methods, it uses the information from eigenvectors combined with the projection residual to estimate the rank of the three-way data arrays instead of using the eigenvalue. In order to demonstrate the excellent performance of the new method, simulated and real three-way data arrays were carried out by the proposed method. The results showed that the proposed method could accurately and quickly determine the chemical rank to fit the trilinear model. Moreover, the newly proposed method was compared with the other four factor-determining methods, i.e. factor indicator function (IND), ADD-ONE-UP, core consistency diagnostic (CORCONDIA) and two-mode subspace comparison (TMSC) approaches. It was found that the proposed method can deal with more complex situations with existence of severe collinearity and trace concentration than many other methods can and performs well in practical applications.