Basic Concepts of Evolving Factor Analysis

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Basic Concepts of Evolving Factor Analysis
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Factor Analysis
Factor Analysis (FA) started as a method to find
out the underlying structure in data matrices,
i.e. to know how many sources of variation
(factors) are needed to describe the data sets
and, if possible, to identify the chemical nature
of these factors. The first step in this process
is called abstract factor analysis or PCA. The
second and more important step links theses PCs
with chemical sources of variation.
Factor Analysis in Chemistry E. R.
Malinowski, 3th edition, Wiley-Interscience,
2002
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Evolutionary Processes
The fact that the rows (or columns) of a data
matrix follow a certain logical sequence may be
explained for finding the pure row (or column)
factor.
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Variance
xP yP
xQ yQ
xR yR
OP2 xP2 yP2
yP
OQ2 xQ2 yQ2
yQ
OR2 xR2 yR2
yR
OP2 OQ2 OR2
xP2 yP2 xQ2 yQ2
xR2 yR2
xQ
xR
Sum squared of all elements of a matrix is a
criterion for variance in that matrix
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Variance can be measured as a function of
evolution
D1 0.1 0.2
VD1 (0.1)2 (0.2)2 0.05
VD2 (0.1)2 (0.2)2 (0.2)2 (0.4)2 0.25
VD (0.1)2 (0.2)2 (0.2)2 (0.4)2
(0.3)2 (0.6)2 0.70
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Elution of a sample containing one component
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Forward and backward evolutionary variation in
variance
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Elution of a sample containing two components
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Forward and backward evolutionary variation in
variance
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Show distribution of spectra in three wavelength
absorbance space for one components and two
component HPLC systems
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Principal Component Analysis (PCA)