1. How to solve authentication problems
Semenov Institute of Chemical Physics, RAS
Moscow
Russian Chemometric Society
Oxana Rodionova, Alexey Pomerantsev
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2. What is authentication?
It is the process of determining whether an object is, in fact, what it is declared to be !
Quick/ relatively cheap / often non-destructive measurements
+ chemometrics
Direct chemical analysis
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3. Typical authentication problems
Counterfeit drug
Illegal additives in fuels
Food adulteration
Confirmation of geographical origin
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4. Discriminant analysis Fisher Iris data (1936)
setosa
versicolor
virginica
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5. Discrimination vs. Class Modeling
Target class
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6. Main differences Class modeling problems Discriminant problems
The goal
Determination whether an object is, in fact, what it is declared to be
Determination of a membership of an object to one of the predefined classes
Data sets
Objects that represent a target class
Several sets of objects that represent predefined classes
Statistical/Chemometric methods
UNECO, SIMCA, SVDD, etc…
LDA, QDA, PLS-DA, SVM, etc ...
Result of data modeling/ Decision rule development
Decision rule for a given  value
Boundaries/delineators between classes
Figures of merit
Sensitivity is given a priori. Specificity can be found theoretically when an alternative class is given.
Sensitivity and specificity are found empirically post factum
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7. Main steps of class modeling
Definition of a target class, objects which undoubtedly belong to the target class
Data are divided into training and validation sets.
Data processing. Establish a decision rule, acceptance area and/or values of thresholds
Validation. Carefully trained decision rules has to be suspiciously validated against new genuine objects.
Figures of merit. Type I error, sensitivity, type II error, specificity
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8. Figures of merit α β ‘Pure’ one-class classifier
Type I error α is the rate of wrong rejections of the target class samples
Sensitivity=(1-α)100%
Availability of alien class/classes α
Type II error β is the rate of wrong acceptances of aliens
Specificity=(1-β)100% β
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9. PLS DA Training Validation/Prediction CLASS 1 PLS CLASS 2 CLASS 3
x11
x12 …
x1k
xi1
Xi2
xik
xi+1,1
xi+1,2
x1+1,k
...
xn1
xn2
Xnk
xnk 1
CLASS 1
PLS
CLASS 2
CLASS 3
Fingerprints
Class membership
1.01
0.02
-0.05
0.98
1.02
-0.03
0.95
0.06
0.04
-0.02
1.05
0.08
1.1
x11
x12 …
x1k
x21
x22
x2k
x31
x32
x3k
x41
x42
x4k
x51
x52
x5k
x61
x62
...
x6k
PLS
CLASS 1
CLASS 2
CLASS 3
Validation/Prediction
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10. DD-SIMCA PCA Acceptance area Orthogonal distance vi Score distance hi
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11. Example
Raw spectra
Measurements in the diffuse reflection mode through a PVC blister
Working range: 7482–4056 cm-1 (889 wavenumbers).
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12. Data description ● ■ A3 ▲ 50 20 200 A4 30 180 A7 80
Calcium channel blocker, uncoated tablets ( API 10 mg)
Name
Marker
Number of training objects
Number of validation objects
Tablet mass, (mg) A3 ▲ 50 20
200 A4 ■ 30
180 A7 ● 80
O.Ye. Rodionova, K.S. Balyklova, A.V. Titova, A.L. Pomerantsev "Quantitative risk assessment in classification of drugs with identical API content", J. Pharm. Biomed. Anal. 2014, 98,
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13. Discriminat analysis PLS 1 PLS 2 Target class A4 Target class A7
Sensitivity/specificity PLS2-DA (3 PLS-components) A3 A4 A7
100%
97%
96%
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14. Class modeling approach Target class A4
Training
Validation/Prediction
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15. DD-SIMCA. Sensitivity and specificity
a=0.05 expected/observed (%) A3 A4 A7
95/96
100/100
95/95
95/99
a= expected/observed (%) A3 A4 A7
99/97
100/100
99/100
99/99
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16. Inactive substance Batch 1 FT-NIR DR spectra Batch 2
Training set 15 samples
Test Set 10 samples
FT-NIR
DR spectra
Batch 2
Training set 15 samples
Test Set 10 samples
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17. Difference in modeling
PLS-DA
PCA
Prediction
WLoading
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18. Conclusions 1
Class-modeling methods develop the acceptance area around the target class, and, thus, delimit the target objects from any other objects and classes. 2
Using one-class classifier, we should always account for a risk of misclassification of alien objects.
It is both important to validate the model using an independent set of the target objects, and to verify the model against a wide variety of the alien objects. 3
A well constructed discrimination method will perfectly classify a new sample only if this sample is a member of one of the predefined classes . If the new sample does not belong to any of such classes, the discriminant analysis is unable to properly define the membership of the sample.
Discriminant methods are inappropriate for solving authentication problems. 4
Every task at hand requires an application of a pertinent chemometric method best suited to answer the posed question.
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19. Thank you for your attention!
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