Learning Block Structures in Gaussian Graphical Models for Spectrometric Data Analysis

Probabilistic graphical modeling serves as a robust framework for capturing the conditional dependencies among variables that follow a Gaussian distribution. Within such models, each node represents a variable, and the absence of an edge between nodes indicates conditional independence given all other variables. Previous studies have applied this methodology to spectrometric data analysis, aiming at discovering the relationships among substances within a compound by analyzing their spectra. Such a goal has been achieved by coupling smoothing techniques for functional data analysis with a Bayesian Gaussian graphical model on basis expansion coefficients, hence simultaneously smoothing the data and providing an estimate of their conditional independence structure. Empirical evidence from real-world applications has shown that the adjacency matrix describing the underlying graph often presents a block structure. This implies a natural clustering of variables into disjoint groups. In this work, a new prior for Gaussian graphical models is introduced to learn the underlying clustering structure of the nodes. The method builds upon stochastic block models while accounting for the natural ordering of the nodes. The model is employed to analyze fruit purees and discover groups of portions of their spectra.