Review and application of functional data analysis to chemical data—The example of the comparison, classification, and database search of forensic ink chromatograms

• Functional data analysis is introduced.
• Some methods of functional data representation, curve registration, and principle component analysis are presented.
• These methods are applied to the characterization, comparison, and classification of chemical spectra, in the context of forensic science.
• These methods enabled efficient classification algorithms to be developed.
• The classification algorithms are computationally complex compared to traditional multivariate analysis.

Functional data analysis is a relatively recent statistical method that can be applied to any dataset that can be thought of as a function. Functional data analysis considers functions as random elements. Modern chromatographic or spectroscopic techniques typically record analytical outputs as a function of time or wavelength. The purpose of this paper is to investigate the potential of functional data analysis for the characterization, comparison, and classification of chemical data. Forensic examination of ink is used as the main example in this paper as it covers different aspects of functional data analysis: (a) thin-layer chromatograms resulting from analysis of ink samples are characterized as functions of time and wavelength; (b) multiple samples analyzed at different times, or by different analysts, are registered into a common space; (c) a dimension reduction technique is applied to the sample functions to enable (d) their use for comparing between ink samples and for clustering large databases of inks. Our algorithms showed excellent performance and can readily be implemented to search and retrieve chemical profiles in large databases. From a theoretical standpoint, functional data analysis allows for a natural extension of multivariate analysis to datasets that can be thought of as functions. Algorithmically, functional data analysis proves to be a powerful technique that enables to detect functions minima and maxima, register multiple functions to a common space, and control the dimensionality and smoothness of a functional dataset. Nevertheless, we found that the implementation of functional data analysis is computationally complex when compared to classic multivariate analysis.