1. Interval selection complexity
Reduced spectra (Xr) , size(Xr) = [m,k]
C, approx.
1st interval …
k-th interval
V1,1
V1,2
V1,k
V2,1
V2,2
V2,k ..
Vm,1
Vm,2
Vm,k k n C 5
100
1011 10
1021
1000
1016
1031
10000
1041
Polynomial complexity
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016
Solution to be found
In the case of interval notation problem complexity is defined by this polynomial equation. Therefore the task for 1 one thousand variables is much lower than for binary notation. I1 I2 … Ik +
width
concerning k intervals. Each interval Ij can contain any number of variables, width less than number variables in spectra n. Complexity for that case:
C =𝑛k+1

2. Idea The idea of JVSPO algorithm
Search the optimal solution as a combination of intervals, practically their centers
Simultaneously optimize interval width (one for all)
Simultaneously optimize preprocessing from the list of chosen candidates
Use no restrictions on interval arrangement:
Let intervals to be on the spectral boundaries
Let intervals to be overlapped
Perform optimization using any appropriate routine (GA, SA, PSO, MC, etc.)
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016

3. Genetic algorithm based optimization
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016
The skim of the genetic algorithm we use for optimization looks like this. The intervals and data preprocessing are applied inside of this fitness function.

4. Examples of parameters for optimization
Interval wavelength selection only I1 .. In IW
Interval selection and preprocessing optimization
SNV, MSC, AS I1 .. In IW
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016
SG.W
SG.P
SG.D I1 .. In IW
Interval selection, preprocessing optimization and modeling metaparameters
There are chromosome structures used in JVSPO. In general our parameter set consists of 3 parts: data preprocessing, intervals and modeling algorithm metaparameters. It can be tempting to optimize the maximum number of available parameters in one task. However this strategy doesn’t seem optimal because it may lead to the excessive complexity reducing the probability of finding a global optimum. Therefore we propose to keep the chromosome reasonably compact. It’s suggested to chose modeling strategies and try them instead of the total optimization.
SG.W
SG.P
SG.D I1 .. In IW
nLV
Generalized structure
Data pretreatment part
Variable selection part
Modeling part

5. Dataset 1
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016
The optimization has been tested on a previously published dataset including 1000 spectra of raw milk in visible and short-wave near infrared region used to predict fat and total protein content in the region 400–1100 nm in the presence of seasonal and geographical variability by means of PLS regression. Milk samples were collected and analyzed at a large dairy (Danone-Unimilk, Samara, Russia) over one year, from October 2013 to September 2014 from dairy farms in the district of Samara and surrounding regions.
Reference: Melenteva A., Galyanin V., Savenkova E., Bogomolov A., Building global models for fat and total protein content in raw milk based on historical spectroscopic data in the visible and short-wave near infrared range. Food Chemistry 203 (2016) 190–198

6. Calibration and validation stats for Dataset 1
Algorithm
nLV
Calibration CV
Prediction
RMSE R2
Fat content
raw data 5
0.163
0.882
0.172
0.867
0.165
0.881
iPLS
0.096
0.959
0.102
0.953
0.097
0.956
SG1D2.19+int.
0.093
0.961
0.091
SG1D2.19
0.154
0.893
0.167
0.875
0.160
Protein content 6
0.115
0.691
0.125
0.636
0.122
0.682
0.101
0.760
0.107
0.730
0.104
0.776
SG1D2.11+int.
0.797
0.758
0.805
SG1D2.11
0.121
0.657
0.135
0.571
0.677
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016
We have compared several regression methods for fat and protein content determination. JVSPO exhibited the best results using Savitzky-Golay derivative as a preprocessing. Derivatives parameters and interval width were included in to the optimization. Without variable selection the same preprocessing doesn’t give any noticeable improvement compaired to the raw data. Another interval method iPLS has also shown a good model performance, but it still worse than our JVSPO.
Reference: Melenteva A., Galyanin V., Savenkova E., Bogomolov A., Building global models for fat and total protein content in raw milk based on historical spectroscopic data in the visible and short-wave near infrared range. Food Chemistry 203 (2016) 190–198

7. Models for Dataset 1 fat protein Full spectra models JVSPO models
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JVSPO models

8. Dataset 2, IDRC 2014 shootout PCA a) c) b)
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016 b)
Another dataset was at software shootout at IDRC Using our JVSPO we won 2nd prize.

9. Validation stats for Dataset 2
Participant 1 (We, 2nd prize)
Participant 2
Participant 3 (Winner)
Participant 4
RMSEP
0.119
0.567
0.105
0.202
SEP
0.112
0.523
0.099
0.193 R2
0.935
0.002
0.984
0.921
Bias
-0.039
0.220
-0.035
-0.059
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016
The winner has used local regression approach. He build several models for different sample groups.
Reference: Benoit Igne, Andrey Bogomolov, Dongsheng Bu, Pierre Dardenne,
Vladislav Galyanin and Peter Tillmann, Summary of the 2014 IDRC software shoot-out,
NIR News 26 (2015) 8-14

10. Memento
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11. JVSPO is available online
JVSPO was performed in TPT-cloud, the web-based chemometrics software
Both models for milk available online for registered users
fat:
protein:
JVSPO and interval selection can be performed online in a few clicks
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12. Conclusion
JVSPO is very efficient algorithm for the optimization of the multivariate models.
Typically JVSPO works better than either intervals or optimal preprocessing determined individually.
JVSPO is especially advantageous when analyzing spectroscopy data with multicollinearity.
Selected intervals and preprocessing may provide useful information on data interpretation.
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13. Thanks for the attention! v.galyanin@gmail.com
WSC-10, Russia, samara, 29 Feb. – 4 Mar. 2016
That’s all. Thanks for attention.