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Bilinear modelling of batch processes. Part I: theoretical discussion
Author(s) -
Camacho José,
Picó Jesús,
Ferrer Alberto
Publication year - 2008
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.1113
Subject(s) - computer science , covariance , process (computing) , partial least squares regression , principal component analysis , bilinear interpolation , range (aeronautics) , variable (mathematics) , data mining , artificial intelligence , machine learning , mathematics , engineering , statistics , mathematical analysis , computer vision , aerospace engineering , operating system
Abstract When studying the principal component analysis (PCA) or partial least squares (PLS) modelling of batch process data, one realizes that there is a wide range of approaches. In many cases, new modelling approaches are presented just because they work properly for a particular application, for example, on‐line monitoring and a given number of processes. A clear understanding of why these approaches perform successfully and which are the advantages and disadvantages in front of the others is seldom supplied. Why does modelling after batch‐wise unfolding capture changing dynamics? What are the consequences of variable‐wise unfolding? Is there any best unfolding method? When should several models for a single process be used? In this paper, it is shown how these and other related questions can be answered by properly analyzing the dynamic covariance structures of the various approaches. Copyright © 2008 John Wiley & Sons, Ltd.