title: Selecting relevant Fourier transform infrared spectroscopy wavenumbers for clustering authentic and counterfeit drug samples.
abstract: This paper proposes a novel method for selecting subsets of wavenumbers provided by attenuated total reflectance by Fourier transform infrared (ATR-FTIR) spectroscopy able to improve the clustering of medicine samples into two groups; i.e., authentic or fraudulent. For that matter, we apply principal components analysis (PCA) to ATR-FTIR data, and derive two variable importance indices from the PCA parameters. Next, an iterative variable (i.e. wavenumbers) elimination procedure and sample clustering through k-means and Fuzzy C-means techniques are carried out; clustering performance is assessed by the Silhouette Index (SI). The performance of the proposed method is compared with a greedy variable selection method, the "leave one variable out at a time" approach, in terms of clustering quality, percent of retained variables, and computational time. When applied to Viagra ATR-FTIR data, our propositions increased the average SI from 0.5307 to 0.8603 using 0.61% of the original 661 wavenumbers; as for Cialis ATR-FTIR data, clustering quality increased from 0.7548 to 0.8681 when 1.21% of the original wavenumbers were retained in the procedure. The retained wavenumbers, located in the 1091-1046cm(-1) region, comprise the lactose typically hailed as key substance to discriminate between authentic and counterfeit samples.
authors.affiliation: Department of Industrial Engineering, Federal University of Rio Grande do Sul, Av. Osvaldo Aranha, 99-5° andar, Porto Alegre, RS, Brazil. Electronic address: michel.anzanello@gmail.com.
authors.forename: Michel J
authors.initials: MJ
authors.lastname: Anzanello
authors.affiliation: CRETIES - Centro de Referência em Avaliação de Tecnologias e Insumos Estratégicos em Saúde, Av. Osvaldo Aranha, 99-6o andar, Porto Alegre, RS 90035-190, Brazil. Electronic address: ffogliatto@producao.ufrgs.br.
authors.forename: Flavio S
authors.initials: FS
authors.lastname: Fogliatto
authors.affiliation: Rio Grande do Sul Technical and Scientifical Division, Brazilian Federal Police, Avenida Ipiranga 1365, 90160-093 Porto Alegre, RS, Brazil. Electronic address: rafaelortiz.rso@dpf.gov.br.
authors.forename: Rafael S
authors.initials: RS
authors.lastname: Ortiz
authors.affiliation: Department of Pharmacy, Universidade Federal do Rio Grande do Sul, Av. Ipiranga, 2752, 90610-000 Porto Alegre, RS, Brazil. Electronic address: renata@ufrgs.br.
authors.forename: Renata
authors.initials: R
authors.lastname: Limberger
authors.affiliation: Department of Pharmacy, Universidade Federal do Rio Grande do Sul, Av. Ipiranga, 2752, 90610-000 Porto Alegre, RS, Brazil. Electronic address: krismariotti@gmail.com.
authors.forename: Kristiane
authors.initials: K
authors.lastname: Mariotti
keywords: Clustering; Counterfeit medicines; Fourier transform infrared spectroscopy; Principal components analysis; Wavenumber selection