A. H. Carrieri (Arthur.Carrieri@SBCCOM.apgea.army.mil) is with the U.S. Army Soldier Biological Chemical Command, Edgewood Chemical and Biological Center, Research and Technology Directorate, Aberdeen Proving Ground, Maryland 21010-5424.
Arthur H. Carrieri, "Neural network pattern recognition by means of differential absorption
Mueller matrix spectroscopy," Appl. Opt. 38, 3759-3766 (1999)
Artificial neural network systems were built for detecting amino acids, sugars, and
other solid organic matter by pattern recognition of their polarized light scattering
signatures in the form of a Mueller matrix. Backward-error propagation and adaptive
gradient descent methods perform network training. The product of the training is a
weight matrix that, when applied as a filter, discerns the presence of the analytes
on the basis of their cued susceptive Mueller matrix difference elements. This filter
function can be implemented as a software or a hardware module to a future
differential absorption Mueller matrix spectrometer.
Arthur H. Carrieri, Jack Copper, David J. Owens, Erik S. Roese, Jerold R. Bottiger, Robert D. Everly, II, and Kevin C. Hung Appl. Opt. 49(3) 382-393 (2010)
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Mueller Matrix Detection of Isomers of Tartaric Acid by Neural Network Pattern
Recognitiona
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Analyte
(1,2)
(1,3)
(1,4)
(2,1)
(2,3)
(2,4)
(3,1)
(3,2)
(3,4)
(4,2)
(4,3)
1/λr (cm-1)
1/λo (cm-1)
Scaled Difference-
Element Distribution (Δ)
Corr Coeff
Output Vector
DL-tartaric acid
0
0
0
0
0
1
0
0
0
0
0
887.3
1038.4
0.211 × [1+0.112
× DIST(-1,1)]
-0.075
(1,0,1,1) CLASS 12
DL-tartaric acid
0
0
0
0
0
0
0
0
0
1
0
887.3
1038.4
-0.068 × [1+0.053
× DIST(-1,1)]
-0.019
(1,0,1,1) CLASS 12
L-tartaric acid
0
1
0
0
0
0
0
0
0
0
0
1082.3
1029.9
0.105 × [1+0.029
× DIST(-1,1)]
-0.001
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
1
0
0
0
0
0
0
0
1082.3
1029.9
1.587 × [1+1.081
× DIST(-1,1)]
-0.089
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
0
0
0
1
0
0
0
0
1082.3
1029.9
-1.101 × [1+0.270
× DIST(-1,1)]
-0.074
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
0
0
0
0
0
1
0
0
1082.3
1029.9
0.099 × [1+0.015
× DIST(-1,1)]
-0.031
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
0
0
0
0
0
0
0
1
1082.3
1029.9
0.003 × [1+0.005
× DIST(-1,1)]
-0.060
(1,1,0,0) CLASS 13
D-tartaric acid
0
1
0
0
0
0
0
0
0
0
0
1082.3
1029.9
0.552 × [1+0.222
× DIST(-1,1)]
-0.080
(1,1,1,0) CLASS 14
D-tartaric acid
0
0
0
0
0
0
0
0
0
0
1
1082.3
1029.9
0.011 × [1+0.032
× DIST(-1,1)]
-0.198
(1,1,1,0) CLASS 14
Δ are scaled and distributed feature differential
elements and DIST is a user-select distribution function bounded by ±1.
A binary 1(0) in columns 2–12 implies the active (deactivate)
differential element (i, j) measurement, and
1/λr and 1/λo are inverse laser beam wavelengths on and off the absorption band of the
analyte, respectively. The correlation coefficient is measured between sets
{Δ (αi, λo)}
and {Δ (αi,
λr)}, where α ranges from normal incidence
90.00° ± 20° in 0.01° increments and output
vector identifies the analyte as belonging to a unique class.
Table 2
Neural Network Transform Functions Built from a Database of 16 Biosimulants in the
Format of Table 1, a
Input/Output
Field
Neuron Transform
Functions
I
M12
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M13
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M14
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M21
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M23
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M24
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M31
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M32
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M34
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M42
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M43
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
ON-RES
T01 Linear,
-1.00,
1.00,
Avg 0.830,
1.095
T02 Log,
-1.00,
1.00,
Avg 0.830,
1.095
T03 Rt2,
-1.00,
1.00,
Avg 0.830,
1.095
I
OFF-RES
T01 linear,
-1.00,
1.00,
Avg 0.833,
1.050
T02 Rt2,
-1.00,
1.00,
Avg 0.833,
1.050
T03 In
x/(1- x),
-1.00,
1.00,
Avg 0.833,
1.050
I
SCALED DIFF
M
T01 Linear,
-1.00,
1.00,
Avg-2.279,
2.959
T02 Inv,
-1.00,
1.00,
Avg-2.123,
2.959
T03 Pwr2,
-1.00,
1.00,
Avg-2.123,
2.959
T04 Fzlft,
0.00,
1.00,
-5.515-5.515,
-2.123
T05 Fzrgt,
0.00,
1.00,
2.959 6.196,
6.196
I
CORR COEFF
T01 Linear,
-1.00,
1.00,
Avg-0.527,
-0.001
T02 InvPwr4,
-1.00,
1.00,
Avg-0.527,
-0.001
T03 Tanh,
-1.00,
1.00,
Avg-0.527,
-0.001
O
COMPONENT1
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
O
COMPONENT2
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
O
COMPONENT3
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
O
COMPONENT4
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
Input (I), hidden (H), and output
(O) neuron layers are grouped in a
15I:200H:4O architecture.
The network I/O variables are identified in column 2. In column 3 the transform
number (Tnn sequence), function, minimum (Tmin), maximum (Tmax), average method
of data mapping (Avg), field minimum (Tmin), and field maximum (Tmax) are
listed in order. The final three numerical arguments of the fuzzy logic
transforms (Fzlft and Fzrgt) are left, right, and center transition points.
The network training set consists of 16 biosimulants complementing 1113 records
(rows in the format of Table 1).
COM1–COM4 are the network output fields, R is the
linear correlation between actual and predicted outputs of the fully trained
network. The errors between predicted and actual outputs are represented in
three statistics: average absolute, maximum absolute, and rms error. Accuracy,
or fitness of true prediction, is measured to 20% tolerance of the true output.
The confidence interval yields deviation of network output from the target
value to a 95% confidence level.
Tables (3)
Table 1
Mueller Matrix Detection of Isomers of Tartaric Acid by Neural Network Pattern
Recognitiona
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Analyte
(1,2)
(1,3)
(1,4)
(2,1)
(2,3)
(2,4)
(3,1)
(3,2)
(3,4)
(4,2)
(4,3)
1/λr (cm-1)
1/λo (cm-1)
Scaled Difference-
Element Distribution (Δ)
Corr Coeff
Output Vector
DL-tartaric acid
0
0
0
0
0
1
0
0
0
0
0
887.3
1038.4
0.211 × [1+0.112
× DIST(-1,1)]
-0.075
(1,0,1,1) CLASS 12
DL-tartaric acid
0
0
0
0
0
0
0
0
0
1
0
887.3
1038.4
-0.068 × [1+0.053
× DIST(-1,1)]
-0.019
(1,0,1,1) CLASS 12
L-tartaric acid
0
1
0
0
0
0
0
0
0
0
0
1082.3
1029.9
0.105 × [1+0.029
× DIST(-1,1)]
-0.001
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
1
0
0
0
0
0
0
0
1082.3
1029.9
1.587 × [1+1.081
× DIST(-1,1)]
-0.089
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
0
0
0
1
0
0
0
0
1082.3
1029.9
-1.101 × [1+0.270
× DIST(-1,1)]
-0.074
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
0
0
0
0
0
1
0
0
1082.3
1029.9
0.099 × [1+0.015
× DIST(-1,1)]
-0.031
(1,1,0,0) CLASS 13
L-tartaric acid
0
0
0
0
0
0
0
0
0
0
1
1082.3
1029.9
0.003 × [1+0.005
× DIST(-1,1)]
-0.060
(1,1,0,0) CLASS 13
D-tartaric acid
0
1
0
0
0
0
0
0
0
0
0
1082.3
1029.9
0.552 × [1+0.222
× DIST(-1,1)]
-0.080
(1,1,1,0) CLASS 14
D-tartaric acid
0
0
0
0
0
0
0
0
0
0
1
1082.3
1029.9
0.011 × [1+0.032
× DIST(-1,1)]
-0.198
(1,1,1,0) CLASS 14
Δ are scaled and distributed feature differential
elements and DIST is a user-select distribution function bounded by ±1.
A binary 1(0) in columns 2–12 implies the active (deactivate)
differential element (i, j) measurement, and
1/λr and 1/λo are inverse laser beam wavelengths on and off the absorption band of the
analyte, respectively. The correlation coefficient is measured between sets
{Δ (αi, λo)}
and {Δ (αi,
λr)}, where α ranges from normal incidence
90.00° ± 20° in 0.01° increments and output
vector identifies the analyte as belonging to a unique class.
Table 2
Neural Network Transform Functions Built from a Database of 16 Biosimulants in the
Format of Table 1, a
Input/Output
Field
Neuron Transform
Functions
I
M12
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M13
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M14
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M21
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M23
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M24
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M31
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M32
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M34
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M42
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
M43
T01 Logical,
0.00,
1.00,
0.000,
1.000
I
ON-RES
T01 Linear,
-1.00,
1.00,
Avg 0.830,
1.095
T02 Log,
-1.00,
1.00,
Avg 0.830,
1.095
T03 Rt2,
-1.00,
1.00,
Avg 0.830,
1.095
I
OFF-RES
T01 linear,
-1.00,
1.00,
Avg 0.833,
1.050
T02 Rt2,
-1.00,
1.00,
Avg 0.833,
1.050
T03 In
x/(1- x),
-1.00,
1.00,
Avg 0.833,
1.050
I
SCALED DIFF
M
T01 Linear,
-1.00,
1.00,
Avg-2.279,
2.959
T02 Inv,
-1.00,
1.00,
Avg-2.123,
2.959
T03 Pwr2,
-1.00,
1.00,
Avg-2.123,
2.959
T04 Fzlft,
0.00,
1.00,
-5.515-5.515,
-2.123
T05 Fzrgt,
0.00,
1.00,
2.959 6.196,
6.196
I
CORR COEFF
T01 Linear,
-1.00,
1.00,
Avg-0.527,
-0.001
T02 InvPwr4,
-1.00,
1.00,
Avg-0.527,
-0.001
T03 Tanh,
-1.00,
1.00,
Avg-0.527,
-0.001
O
COMPONENT1
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
O
COMPONENT2
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
O
COMPONENT3
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
O
COMPONENT4
T01 Linear,
0.00,
1.00,
Avg 0.000,
1.000
Input (I), hidden (H), and output
(O) neuron layers are grouped in a
15I:200H:4O architecture.
The network I/O variables are identified in column 2. In column 3 the transform
number (Tnn sequence), function, minimum (Tmin), maximum (Tmax), average method
of data mapping (Avg), field minimum (Tmin), and field maximum (Tmax) are
listed in order. The final three numerical arguments of the fuzzy logic
transforms (Fzlft and Fzrgt) are left, right, and center transition points.
The network training set consists of 16 biosimulants complementing 1113 records
(rows in the format of Table 1).
COM1–COM4 are the network output fields, R is the
linear correlation between actual and predicted outputs of the fully trained
network. The errors between predicted and actual outputs are represented in
three statistics: average absolute, maximum absolute, and rms error. Accuracy,
or fitness of true prediction, is measured to 20% tolerance of the true output.
The confidence interval yields deviation of network output from the target
value to a 95% confidence level.
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