Spectra paint9/6/2023 ![]() ![]() Walczak B (2000) Wavelets in Chemistry, (eds). Silverman B (1986) Density estimation for statistics and data analysis. Ramos D, Gonzalez-Rodriguez J, Zadora G, Aitken C (2013) Information-theoretical assessment of the performance of likelihood ratio computation methods. Ramos D, Zadora G (2011) Information-theoretical feature selection using data obtained by scanning electron microscopy coupled with an energy dispersive X-ray spectrometer for the classification of glass traces. R Foundation for Statistical Computing, Vienna, Austria. R Core Team, R: (2012) A Language and Environment for Statistical Computing. Martyna A, Sjastad KE, Zadora G, Ramos D (2013) Analysis of lead isotopic ratios of glass objects with the aim of comparing them for forensic purposes. IEEE Trans Pattern Anal Mach Int 7:674–693 ![]() Mallat S (1989) A theory for multiresolution signal decomposition:the wavelet representation. Ma C, Shao X (2004) Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra. Hazewinkel M, Subbotin Y (eds) (2001) Encyclopedia of Mathematics. Geladi P, Sethson B, Nystrom J, Lillhonga T, Lestander T, Burger J (2004) Chemometrics in spectroscopy: Part 2. Geladi P (2003) Chemometrics in spectroscopy: Part 1. CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia Wileyĭaubechies I (1992) Ten Lectures on Wavelets. Taylor and FrancisĬhau F, Liang Y, Gao J, Shao X (2004) Chemometrics: From Basics to Wavelet Transform. Comput Speech Lang 20:230–275Ĭaddy B (2002) Forensic Examination of Glass and Paint. Math Prog 47:425–439īrümmer N, du Preez J (2006) Application independent evaluation of speaker detection. The Ann Math Stat 26:641–647īest M, Chakravarti N (1990) Active set algorithms for isotonic regression a unifying framework. The Anal 122: 645–652Īyer M, Brunk H, Ewing G, Reid W, Silverman E (1955) An empirical distribution function for sampling with incomplete information. Chemom Intell Lab Syst 37:215–239Īlsberg B, Woodward A, Winson M, Rowland J, Kell D (1997b) Wavelet denosing of infrared spectra. J Forensic Sci 52:412–419Īlsberg B, Woodward A, Kell D (1997a) An introduction to wavelet transforms for chemometricians: a time-frequency approach. Wiley, ChichesterĪitken C, Zadora G, Lucy D (2007) A two-level model for evidence evaluation. Appl Stat 53:109–122Īitken C, Taroni F (2004) Statistics and the evaluation of evidence for forensic scientists. 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.Īitken C, Lucy D (2004) Evaluation of trace evidence in the form of multivariate data. The results for most of the LR models were satisfactory and enabled solving the stated comparison problems. Their performance was controlled by estimating the levels of false positive and false negative answers and using the empirical cross entropy approach. Univariate and multivariate LR models were proposed, aiming at obtaining more information about the chemical structure of the samples. typical absorption bands for polypropylene and peaks associated with pigments present in the car paints. 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. The objective of the studies was to combine the chemometric tools easily dealing with multidimensionality with an LR approach. 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 research involved statistical tools such as likelihood ratio (LR) approach for expressing the evidential value of observed similarities and differences in the recorded spectra. ![]() 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. ![]()
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