A three-step unsupervised neural model for visualizing high complex dimensional spectroscopic data sets

The interdisciplinary research presented in this study is based on a novel approach to clustering tasks and the visualization of the internal structure of high-dimensional data sets. Following normalization, a pre-processing step performs dimensionality reduction on a high-dimensional data set, using an unsupervised neural architecture known as cooperative maximum likelihood Hebbian learning (CMLHL), which is characterized by its capability to preserve a degree of global ordering in the data. Subsequently, the self organising-map (SOM) is applied, as a topology-preserving architecture used for two-dimensional visualization of the internal structure of such data sets. This research studies the joint performance of these two neural models and their capability to preserve some global ordering. Their effectiveness is demonstrated through a case of study on a real-life high complex dimensional spectroscopic data set characterized by its lack of reproducibility. The data under analysis are taken from an X-ray spectroscopic analysis of a rose window in a famous ancient Gothic Spanish cathedral. The main aim of this study is to classify each sample by its date and place of origin, so as to facilitate the restoration of these and other historical stained glass windows. Thus, having ascertained the sample’s chemical composition and degree of conservation, this technique contributes to identifying different areas and periods in which the stained glass panels were produced. The combined method proposed in this study is compared with a classical statistical model that uses principal component analysis (PCA) as a pre-processing step, and with some other unsupervised models such as maximum likelihood Hebbian learning (MLHL) and the application of the SOM without a pre-processing step. In the final case, a comparison of the convergence processes was performed to examine the efficacy of the CMLHL/SOM combined model.