SIMPLS - AN ALTERNATIVE APPROACH TO PARTIAL LEAST-SQUARES REGRESSION
SIMPLS - AN ALTERNATIVE APPROACH TO PARTIAL LEAST-SQUARES REGRESSION
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DOI：
10.1016/0169-7439(93)85002-x
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发表时间：
1993-03-01
影响因子：
3.9
通讯作者：
DEJONG, S
中科院分区：
文献类型：
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作者：
DEJONG, S
提出了一种新的偏最小二乘（PLS）回归算法SIMPLS，它直接将PLS因子作为原始变量的线性组合来计算。PLS因子被确定为使得协方差准则最大化，同时遵守某些正交性和归一化限制。这种方法遵循其他传统的多变量方法。避免了非线性迭代偏最小二乘（NIPALS）-PLS算法中构造收缩数据矩阵的问题。对于单变量y，SIMPLS等价于PLS 1，并且与现有的双对角化算法密切相关。这是根据Krylov序列对PLS 1回归的分析得出的。对于多变量Y，SIMPLS方法和NIPALS-PLS 2之间存在轻微差异。在实践中，SIMPLS算法似乎是快速和易于解释，因为它不涉及数据集的故障。
A novel algorithm for partial least squares (PLS) regression, SIMPLS, is proposed which calculates the PLS factors directly as linear combinations of the original variables. The PLS factors are determined such as to maximize a covariance criterion, while obeying certain orthogonality and normalization restrictions. This approach follows that of other traditional multivariate methods. The construction of deflated data matrices as in the nonlinear iterative partial least squares (NIPALS)-PLS algorithm is avoided. For univariate y SIMPLS is equivalent to PLS1 and closely related to existing bidiagonalization algorithms. This follows from an analysis of PLS1 regression in terms of Krylov sequences. For multivariate Y there is a slight difference between the SIMPLS approach and NIPALS-PLS2. In practice the SIMPLS algorithm appears to be fast and easy to interpret as it does not involve a breakdown of the data sets.