Interpretation of FTIR spectra of polymers and Raman spectra of car paints by means of likelihood ratio approach supported by wavelet transform for reducing data dimensionality
- 447 Downloads
The problem of interpretation of common provenance of the samples within the infrared spectra database of polypropylene samples from car body parts and plastic containers as well as Raman spectra databases of blue solid and metallic automotive paints was under investigation. The research involved statistical tools such as likelihood ratio (LR) approach for expressing the evidential value of observed similarities and differences in the recorded spectra. Since the LR models can be easily proposed for databases described by a few variables, research focused on the problem of spectra dimensionality reduction characterised by more than a thousand variables. The objective of the studies was to combine the chemometric tools easily dealing with multidimensionality with an LR approach. The final variables used for LR models' construction were derived from the discrete wavelet transform (DWT) as a data dimensionality reduction technique supported by methods for variance analysis and corresponded with chemical information, i.e. typical absorption bands for polypropylene and peaks associated with pigments present in the car paints. Univariate and multivariate LR models were proposed, aiming at obtaining more information about the chemical structure of the samples. Their performance was controlled by estimating the levels of false positive and false negative answers and using the empirical cross entropy approach. The results for most of the LR models were satisfactory and enabled solving the stated comparison problems. The results prove that the variables generated from DWT preserve signal characteristic, being a sparse representation of the original signal by keeping its shape and relevant chemical information.
KeywordsRaman spectroscopy of blue car paints FTIR spectrometry of polymers Data dimensionality reduction Wavelet transform Comparison problem Likelihood ratio
The authors are grateful for Prof. Beata Walczak (University of Silesia, Institute of Chemistry, Chemometric Research Group, Katowice, Poland) for her assistance and helpful comments in the field of wavelet transform.
The authors wish to thank Dr. Beata Trzcinska and Rafal Kowalski for their assistance in the FTIR analyses.
This research was funded by the National Science Centre in Poland within the project Preludium 6 no. 2013/11/N/ST4/01547 and the Institute of Forensic Research in Krakow within the project no. VI/K-2013/14.
- 1.Aitken C, Lucy D (2004) Evaluation of trace evidence in the form of multivariate data. Appl Stat 53:109–122Google Scholar
- 9.Caddy B (2002) Forensic Examination of Glass and Paint. Taylor and FrancisGoogle Scholar
- 10.Chau F, Liang Y, Gao J, Shao X (2004) Chemometrics: From Basics to Wavelet Transform. WileyGoogle Scholar
- 13.Geladi P, Sethson B, Nystrom J, Lillhonga T, Lestander T, Burger J (2004) Chemometrics in spectroscopy: Part 2. Examples. Spectrochim Acta B 59:1347–1357Google Scholar
- 14.Hazewinkel M, Subbotin Y (eds) (2001) Encyclopedia of Mathematics. SpringerGoogle Scholar
- 18.R Core Team, R: (2012) A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
- 22.Walczak B (2000) Wavelets in Chemistry, (eds). ElsevierGoogle Scholar
- 25.Wee E, Grayden DB, Zhu Y, Petkovic-Duran K, Smith D (2008) A continuous wavelet transform algorithm for peak detection. Electrophoresis 29:4215–4225Google Scholar
- 29.Zadora G, Martyna A, Ramos D, Aitken C (2014) Statistical Analysis in Forensic Science Evidential Value of Multivariate Physicochemical Data. WileyGoogle Scholar