1. „The perfect is not good enough!” (Carl Benz) V ISUALIZATION OF HIGH DIMENSIONAL DATA BY USE OF GENETIC PROGRAMMING – APPLICATION TO ON - LINE INFRARED SPECTROSCOPY BASED PROCESS MONITORING T IBOR K ULCSÁR, J ÁNOS A BONYI U NIVERSITY OF P ANNONIA D EPARTMENT OF P ROCESS E NGINEERING

2. Preconditions  Online analyzers are widely used in oil industry to predict product properties like Density, Cloud point, etc.  Properties can’t be described using linear models  Visualization of high dimensional spectral database is needed for model development and proces monitoring  Cost function and a tool for equation discovery is needed to obtain compact and interpretable mapping of high dimensional data 2

3. Task I: Estimation 3

4. Similar spectra - Similar property Dmax Rsphere = 3Percentage of Dmax corresponding to the radius of the sphere EvEv imim 4

5. Finding similar spectra  Prediction model  Nearest Neighbors algorithm  The neighborhood is basis of the prediction  2D mapping  Define the range of validity for the local models  The mapped plain should follow the original spectral space  Quality measure  Measure the quality of mapping  Measure the neighborhood preserving 5 Property X = f ( Prop[S1, S2, S3, S4, S5, S6] ) S1 S2 S4 S6 S5 S3 N2 N4 N6 N5 N3 N1 X X

6. Chemical information – interpretable? 6 0.2.4.6.8 1 1.2 4000 4100 4200 4300 4400 4500 4600 4700 4800 Absorbency Aromatic Ethylenic Olefinic Aromatic Branched / cyclonic Linear Saturated Branched Wavenumber (cm -1 ) aromatic linear olefinic

7. Aggregates – need for explicit mapping 7 Aggrage 2 Aggrage 1 Two aggregate 2D mapping

8. Representation of Aggregates 8  One of the most popular method for representing structures is the binary tree. Terminal nodes: Variables: x 1, x 2 Parameters: p 1, p 2 Non terminal nodes Operators: +,-,*,/ Functions: exp(),cos()

9. Genetic Operators: Mutation 9 - x1x1 / * x2x2 x1x1 p1p1 - x1x1 / + x2x2 x1x1 p1p1

10. Genetic Operators: Crossover 10 - x1x1 / + x2x2 x1x1 p1p1 + x2x2 + x1x1 p1p1 + x2x2 - x1x1 + x1x1 p1p1 / + x2x2 x1x1 p1p1

11. Scheme of Genetic Programing 11 Creation of initial population Evaluation Selection Direct reproduction New generation End? End CrossoverMutation Parameter optimization Fitness value

12. Process of model development 12 Measurement Online spectrum Labor data MATLAB Preprocessing Data query MATLAB Genetic algorithm TOPNIR environment Online System

13. Results 13 Best pair from original set Best eq and an optimised pair Searche a better pair

14. Conclusion  The quality of mapping is measureable  Neighborhood preserving (forward and backward)  Discriminating operational regimes  Aggregate based mapping  Interpretable chemical information  Build aggregate – needs much experience (divination)  Genetic programing  Controlled method to make new equations  Needs proper cost function (measure the quality of mapping)  Visual representation of models  Aggregate -> 2D plot -> dashboard graph  Information about the model structure 14

15. Questions? … 15 The financial support of the TAMOP-4.2.2/B-10/1-2010-0025 project is acknowledged. In case of any question or remark please contact us kulcsart@fmt.uni-pannon.hu