Analytical and Bioanalytical Chemistry

, Volume 407, Issue 12, pp 3357–3376 | Cite as

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

  • Agnieszka Martyna
  • Aleksandra Michalska
  • Grzegorz ZadoraEmail author
Research Paper


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.

Graphical Abstract

The schematic procedure of expressing the evidential value of multidimensional data (FTIR and Raman spectra) by means of the likelihood ratio approach supported by discrete wavelet transform for reducing data dimensionality


Raman 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Agnieszka Martyna
    • 1
  • Aleksandra Michalska
    • 2
  • Grzegorz Zadora
    • 2
    • 3
    Email author
  1. 1.Faculty of Chemistry, Department of Analytical ChemistryJagiellonian University in KrakowKrakowPoland
  2. 2.Institute of Forensic Research in KrakowKrakowPoland
  3. 3.Institute of Chemistry, Chemometric Research GroupUniversity of Silesia in KatowiceKatowicePoland

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