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The colorant behaviour of cochineal and kermes insect dyes in 141 experimentally-dyed and 28 artificially-aged samples of silk and wool was investigated using ultra-high performance liquid chromatography coupled to photodiode array detector (UHPLC-PDA), liquid chromatography electrospray ionisation mass spectrometry (LC-ESI-MS) and image scanning electron microscopy - energy dispersive X-ray spectroscopy (SEM-EDX). Partial-least squares discriminant analysis (PLS-DA) was then used to model the acquired UHPLC-PDA data and assess the possibility of discriminating cochineal insect species, as well as their correspondent dyed and aged reference fibres. The resulting models helped to characterize a set of 117 red samples from 95 historical textiles, in which UHPLC-PDA analyses have reported the presence of cochineal and kermes insect dyes. Analytical investigation of the experimentally-dyed and artificially-aged fibres has demonstrated that the ratio of compounds in the insects dye composition can change, depending on the dyeing conditions applied and the type of fibres used. Similarities were observed when comparing the UHPLC-MS and SEM-EDX results from the dyed and aged references with the historical samples. This was verified with PLS-DA models of the chromatographic data, facilitating the classification of the cochineal species present in the historical samples. The majority of these samples were identified to contain American cochineal, which is in agreement with historical and dye identification literature that describe the impact of this dyestuff into European and Asian dyeing practices, after the Iberian Expansion in the 16th century. The analytical results emphasize the importance of using statistical data interpretation for the discrimination of cochineal dyes, besides qualitative and quantitative evaluation of chromatograms. Hence, the combination of UHPLC-PDA with a statistical classification method, such as PLS-DA, has been demonstrated to be an advisable approach in future investigations to assess closely related species of natural dyes in historical textile samples. This is particularly important when aiming to achieve more accurate interpretations about the history of works of art, or the application of natural dyes in old textile production.

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Analyses of multifactorial experimental designs are used as an explorative technique describing hypothesized multifactorial effects based on their variation. The procedure of analyzing multifactorial designs is well established for univariate data, and it is known as analysis of variance (ANOVA) tests, whereas only a few methods have been developed for multivariate data. In this work, we present the weighted-effect ASCA, named WE-ASCA, as an enhanced version of ANOVA-simultaneous component analysis (ASCA) to deal with multivariate data in unbalanced multifactorial designs. The core of our work is to use general linear models (GLMs) in decomposing the response matrix into a design matrix and a parameter matrix, while the main improvement in WE-ASCA is to implement the weighted-effect (WE) coding in the design matrix. This WE-coding introduces a unique solution to solve GLMs and satisfies a constrain in which the sum of all level effects of a categorical variable equal to zero. To assess the WE-ASCA performance, two applications were demonstrated using a biomedical Raman spectral data set consisting of mice colorectal tissue. The results revealed that WE-ASCA is ideally suitable for analyzing unbalanced designs. Furthermore, if WE-ASCA is applied as a preprocessing tool, the classification performance and its reproducibility can significantly improve.