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Slice transform‐based weight updating strategy for PLS
Author(s) -
Bi Yiming,
Xie Qiong,
Peng Silong,
Lu Weiying
Publication year - 2012
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2479
Subject(s) - mathematics , wilcoxon signed rank test , rank (graph theory) , partial least squares regression , piecewise , piecewise linear function , algorithm , representation (politics) , weight , statistics , combinatorics , mathematical analysis , geometry , lie algebra , politics , political science , pure mathematics , law , mann–whitney u test
A modified partial least squares (PLS) algorithm is presented on the basis of a novel weight updating strategy. The new weight can handle situations with directions in X space having large variance unrelated to Y , whereas the linear PLS may not work well. In the proposed algorithm, the slice transform technique is introduced to provide a piecewise linear representation of the weight vectors. Then, the corresponding mapping functions are estimated by a least square criterion of the inner relation between the observed variables and the score of response variables. At last, weight vectors are updated by the obtained mapping functions, and the corresponding scores and loadings are calculated with the new weights. An optimal piecewise linear replacements of the PLS weights are achieved by the proposed method. The predictive performances of the new approach and other methods are compared statistically using the Wilcoxon signed rank test. Experimental results show that the proposed method can achieve simpler models, whereas the model performances are at least comparable with PLS and other methods. Copyright © 2012 John Wiley & Sons, Ltd.