349
12.3.4 Component Identification by Canberra Distance
and Second Order Analysis
In an effort to improve the results of the previous method, we assumed that some
problems may come from the subtraction of background from the spectra. the
curve enclosing background was drawn manually and for some intervals of wavenumbers we were not sure how to define it exactly. If we assume that this curve
varies slowly in comparison with the curve representing the spectrum then it is useful to consider second order derivatives of spectra. Since the spectra are given by
sequences of measured data points, the derivatives must be calculated numerically.
to this end we used Savitzky- golay filtering, which relies on fitting a polynomial
of some degree to successive local windows of data points. the value of the second
derivative of the polynomial in the middle of a window is approximately equal to
the second derivative of the function representing the spectrum. this time we try to
find the optimum scaling coefficients of the reconstructed spectrum minimizing the
following function:
Table 12.5 Identification results by the correlation function of measured mixture spectra denoted
by letters; see table 12.4. All amino acids in the second column were identified correctly using
mechanical stop condition of the iterative algorithm (see Sect. 12.3.3). the third column shows the
false positive cases, i.e., the components identified but not present in the mixture. the last column
shows false negative cases, i.e., the components not identified but present in the mixture
mixture
Identified correctly
False positives
False negatives
a
Phe
Ala
b
his Arg Pro
c
tyr Asn
d
gly thr Ser gln Leu
e
trp glu gln
Ile
f
Ser Arg thr
Ala
g
met Ala gly his
Pro
Leu
h
glu Leu Ile
i
his gly
Pro
Leu
j
glu met
Lys
k
gly tyr his Pro
l
thr Ala
m
Asn
n
met val Leu Ile
o
Phe
trp Ser
gln
p
tyr thr Asn Pro Asp
q
gly glu
Ala
r
tyr trp Arg his
Ser
s
trp Asp
t
tyr Cys Phe Ser his
thr
Leu Ile
12 Raman Spectra of Solid Aminoacids: Spectral Correlation Analysis …
12.3.4 Component Identification by Canberra Distance
and Second Order Analysis
In an effort to improve the results of the previous method, we assumed that some
problems may come from the subtraction of background from the spectra. the
curve enclosing background was drawn manually and for some intervals of wavenumbers we were not sure how to define it exactly. If we assume that this curve
varies slowly in comparison with the curve representing the spectrum then it is useful to consider second order derivatives of spectra. Since the spectra are given by
sequences of measured data points, the derivatives must be calculated numerically.
to this end we used Savitzky- golay filtering, which relies on fitting a polynomial
of some degree to successive local windows of data points. the value of the second
derivative of the polynomial in the middle of a window is approximately equal to
the second derivative of the function representing the spectrum. this time we try to
find the optimum scaling coefficients of the reconstructed spectrum minimizing the
following function:
Table 12.5 Identification results by the correlation function of measured mixture spectra denoted
by letters; see table 12.4. All amino acids in the second column were identified correctly using
mechanical stop condition of the iterative algorithm (see Sect. 12.3.3). the third column shows the
false positive cases, i.e., the components identified but not present in the mixture. the last column
shows false negative cases, i.e., the components not identified but present in the mixture
mixture
Identified correctly
False positives
False negatives
a
Phe
Ala
b
his Arg Pro
c
tyr Asn
d
gly thr Ser gln Leu
e
trp glu gln
Ile
f
Ser Arg thr
Ala
g
met Ala gly his
Pro
Leu
h
glu Leu Ile
i
his gly
Pro
Leu
j
glu met
Lys
k
gly tyr his Pro
l
thr Ala
m
Asn
n
met val Leu Ile
o
Phe
trp Ser
gln
p
tyr thr Asn Pro Asp
q
gly glu
Ala
r
tyr trp Arg his
Ser
s
trp Asp
t
tyr Cys Phe Ser his
thr
Leu Ile
12 Raman Spectra of Solid Aminoacids: Spectral Correlation Analysis …