1. Data Driven SIMCA – more than One-Class Classifier
Semenov Institute of Chemical Physics, RAS
Moscow
Russian Chemometric Society
Oxana Rodionova, Alexey Pomerantsev
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2. Soft Independent Modeling of Class Analogy - SIMCA (S
Soft Independent Modeling of Class Analogy - SIMCA (S. Wold: Pattern Recognition by Means of Disjoint Principal Components Models, (1976)   t1 t2 t3
Disjoint PCA class -modeling
Cut-off levels using orthogonal distances
New object is compared with each class by calculation of the orthogonal distance
… … … many additions and modifications
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3. Data driven approach Projection Orthogonal distance vi
Score distance hi
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4. Distribution of distances: DoF estimation
= h/h0 x= = v/v0
x1,...., xI ~ χ2(N)/N
N = ?
Method of Moments
Interquartile Approach
x(1) ≤ x(2 )≤ .... ≤ x(I-1) ≤ x(I)
¼ IQR ¼
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5. Total Distance and Cut-off Level
Total distance (TD)
For given α,
the rate of wrong rejections of the target class samples, a type I error
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6. 2 distribution (reminder 1)
=h/h0 x= =v/v0
x ~ χ2(N)/N
N = DoF
E(x) = 1
D(x) = 2/N
A chi-squared variable with N degrees of freedom is defined as the sum of the squares of N independent standard normal random variables.
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7. 2 distribution (reminder 2)
1001
10020
N(0,)
E(i,j)
~ χ2(20)
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8. Simulated example 1 Gaussian noise only
10020
N(0,) E
PCA
DoFs
Rank(E)=K=20
DoF(SD)= A (principal component)
DoF(OD)=K-A
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9. Simulated example 2 Structure & no Noise
100200
ΛT=(150, 100, 50, 20, 1, 0.001) S
Rank(S)=6
S=UΛVT
PCA
DosF
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10. DoFs for matrix S, α=0.05 PC=1 PC=2 Theory Estimate Nh=1 Nv=5 Nv=2
10 out
6 out
PC=1
Theory
Estimate
Nh=2
Nv=4
Nv=1
9 out
4 out
PC=2
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11. Simulated example 3 Structure + Additive Noise
100200
ΛT=(150, 100, 50, 20, 1,0.001) S
100200
N(0,) E
PCA X= +
Estimates of DoFs for various 
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12. Extreme plot. Dependence on α
=0.1
=0.05
=0.01
Demonstrates the dependence of the observed number of the extremes versus theoretically expected values, calculated as n=I. The plot is obtained by varying =n/I.
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13. Extreme plot. Training & Test sets
Test set (20 objects)
Training set (80 objects)
PC=4
PC=3
PC=7
PC=2
PC=1
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14. Simulated example 4. Test set partly carries different structure
100200
Straining=UΛVt+E(0,) Λ
U(100×6)
Vnt(6×200)
Vt(6×200)
100200
Stest=UΛVnt+E1(0,)
Rank(S)=6
S=UΛVT
ΛT=(150, 100, 50, 20, 1,0.001)
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15. Simulated example 4 (PCs=3)
Training set
Test set
PC=3
Nh=4
Nv=1
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16. Simulated example 4 (PCs=4)
Training set
Test set
PC=4
Nh=5
Nv=1
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17. Real-world example “Olives in brine”
3 Classes
233 objects
1258 variables
Measurements: NIR spectra in DR mode cm-1
Class 1
Training set: 75 objects
Test set : 44 objects
O.Ye. Rodionova, P. Oliveri, A.L. Pomerantsev, "Rigorous and compliant approaches to one-class classification", Chemom. Intell. Lab. Syst. 159, (2016)
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18. Class 1.Training set 75×1258
PC=4
α=0.05
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19. Application of the Extreme plot (1)
‘Olive in brine’ Class 1. Test set:44 objects
PCs=4
PCs=5
PCs=7
PCs=2
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20. Application of the Extreme plot (2)
Assessment of instruments’ performance for monitoring of tablets’ quality and anti-counterfeiting
MicroNIR 1700
by VIAVI Solution
Working range is nm
Resolution is less than 12.5 nm
Aims: 1. Compare the results of 2 instruments
2. Compare the results of measurements in 2 days
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21. Anti-inflammatory medicine packed in PVC blisters
Objects: 50 tablets from 5 batches
Dataset (50 × 125)
DD-SIMCA model, PCs=3
Dataset “Instrument #1 day 1”
Dataset “Second day”
Dataset “Second instrument”
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22. New Datasets Second day PCs=3 PCs=4 PCs=2 PCs=1 Second instrument
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23. Interquartile Approach
Outlier detection
DoF: Classical and Robust estimates
= h/h0 x= = v/v0
x1,...., xI ~ χ2(N)/N
N = ?
Method of Moments
Interquartile Approach
x(1) ≤ x(2 )≤ .... ≤ x(I-1) ≤ x(I)
¼ IQR ¼
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24. Real-world example (Poster #23)
Confocal Raman Spectroscopy and MDA in Evaluation of Spermatozoa with Normal and Abnormal Morphology
Morphology classification
125 Normal
36 Abnormal
Study the sperm nuclear DNA quality. Compare the results of morphology and Raman spectroscopy analysis in revealing normal and abnormal cells.
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25. Sequential application of DD-SIMCA for outlier detection
Sequential application of DD-SIMCA for outlier detection. ‘Normal’ model. Initial step
Classical Nv=1; Nh=1
Classical Nv=1; Nh=2
PCs=4
PCs=3
Robust Nv=2; Nh=3
Robust Nv=3; Nh=4
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26. Sequential application of DD-SIMCA for outlier detection
Sequential application of DD-SIMCA for outlier detection. ‘Normal’ model. Final step
Classical Nv=2; Nh=3
Classical Nv=2; Nh=3
PCs=4
PCs=3
Robust Nv=3; Nh=4
Robust Nv=2; Nh=3
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27. 17 ‘Abnormal’-’Normal’ objects
Objects partitioning
Morphology classification
17 ‘Abnormal’-’Normal’ objects
125 Normal
102 Normal
23 Abnormal
Spectral classification
36 Abnormal
17 Normal
19 Abnormal
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28. Conclusions (1)
PCA. Determination of the number of principal components for…
Description of the X- data in details
Determination of hidden structures even for higher PCs
Separate structure from random noise
Revealing the main common features of the X-data, without analyzing between-objects’ differences
Outlier detection
Estimation of the DoF for SD and OD distances
Tool:
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29. Conclusions (2) Tool: PCA, application of various datasets for…
Comparison, to what extent the test set is similar to the training set
Comparison a new data with the training objects
Extreme plots for the training and test/new sets
Tool:
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30. Conclusions (3)
Both tools may be used not only for DD-SIMCA but for the preliminary analysis of any data set.
We acknowledge partly funding from the IAEA in the frame of
projects D5240 and G42007
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31. Software tools For Chemometrics Add-In users: SIMCA Template.xlsb
For Matlab users:
DD-SIMCA — a MATLAB GUI tool
Github:
Y.V. Zontov, O.Ye. Rodionova, S.V. Kucheryavskiy, A.L. Pomerantsev, "DD-SIMCA – A MATLAB GUI tool for data driven SIMCA approach",  Chemom. Intell. Lab. Syst. 167, (2017)