Hilbertian statistical models in music neuroscience

Abstract

This dissertation addresses the analysis of data emerging in the field of music neuroscience, specifically data collected from neurophysiological monitoring techniques that can be modeled as random objects in spaces of smooth functions. Spaces equipped with a Hilbert structure offer a versatile and elegant framework for the generalization of various statistical techniques, ensuring adaptability and robustness in analyzing complex data structures. Within the context of functional data analysis, these spaces serve as essential tools for understanding and interpreting dynamic data trends over continuous domains. Given the relevance of independent component analysis (ICA) in neuroscience research, our investigation is directed towards its functional counterpart, a technique whose potential still remains relatively overlooked. Functional ICA can be considered a refinement of functional principal component analysis, aimed at identifying low-dimensional structures "as independent as possible" by exploiting the underlying topological features of the data. We provide a comprehensive account of the theoretical foundations of functional ICA and extend the method to Sobolev spaces of smoother functions. Some theoretical properties regarding functional data classification are also presented. Additionally, we develop a repertoire of related functional data techniques tailored for pre-processing and analyzing data in the emerging field of embodied music neuroscience, which investigates the neurological basis of how the body influences musical experience. Two methods based on nonlinear wavelet and polynomial approximations are developed for pre-processing artifactual activity in EEG signals and pupillometry. These methods yield excellent outcomes for neuromotor research, particularly considering the suboptimal condition of the recorded data due to locomotor activity. We further introduce a set of neural descriptors derived from data collected through the aforementioned non-invasive methods, aiming to uncover brain behavior during embodied musical interactions. More specifically, we focus on methodologies for modeling neurotransmitter activity, a critical aspect shown to be essential in shaping motor functionality and other proprioceptive sensations. Our experimental research is portrayed by the concept of emotion transferred into a neurological domain, providing a unique framework to define and capture the neural essence of embodiment in music.

This dissertation addresses the analysis of data emerging in the field of music neuroscience, specifically data collected from neurophysiological monitoring techniques that can be modeled as random objects in spaces of smooth functions. Spaces equipped with a Hilbert structure offer a versatile and elegant framework for the generalization of various statistical techniques, ensuring adaptability and robustness in analyzing complex data structures. Within the context of functional data analysis, these spaces serve as essential tools for understanding and interpreting dynamic data trends over continuous domains. Given the relevance of independent component analysis (ICA) in neuroscience research, our investigation is directed towards its functional counterpart, a technique whose potential still remains relatively overlooked. Functional ICA can be considered a refinement of functional principal component analysis, aimed at identifying low-dimensional structures "as independent as possible" by exploiting the underlying topological features of the data. We provide a comprehensive account of the theoretical foundations of functional ICA and extend the method to Sobolev spaces of smoother functions. Some theoretical properties regarding functional data classification are also presented. Additionally, we develop a repertoire of related functional data techniques tailored for pre-processing and analyzing data in the emerging field of embodied music neuroscience, which investigates the neurological basis of how the body influences musical experience. Two methods based on nonlinear wavelet and polynomial approximations are developed for pre-processing artifactual activity in EEG signals and pupillometry. These methods yield excellent outcomes for neuromotor research, particularly considering the suboptimal condition of the recorded data due to locomotor activity. We further introduce a set of neural descriptors derived from data collected through the aforementioned non-invasive methods, aiming to uncover brain behavior during embodied musical interactions. More specifically, we focus on methodologies for modeling neurotransmitter activity, a critical aspect shown to be essential in shaping motor functionality and other proprioceptive sensations. Our experimental research is portrayed by the concept of emotion transferred into a neurological domain, providing a unique framework to define and capture the neural essence of embodiment in music.

En esta tesis se aborda el análisis de datos emergentes en el campo de la neurociencia de la música, más concretamente de datos grabados mediante técnicas de monitoreo neurofisiológico que pueden ser modelados como objetos aleatorios en espacios de funciones suaves. Los espacios equipados con estructura de Hilbert ofrecen un marco versátil y elegante para la generalización de un ámplio abanico de técnicas estadísticas, asegurando adaptabilidad y robustez en el análisis de estructuras de datos complejas. En el contexto del análisis de datos funcionales, estos espacios sirven como herramientas esenciales para comprender e interpretar tendencias dinámicas de datos sobre dominios continuos. Dada la relevancia del análisis en componentes independientes (ICA) para el análisis de datos neurocientíficos, nuestra investigación se dirige hacia su versión funcional, una técnica cuyo potencial aún permanece relativamente poco explorado. El ICA funcional puede considerarse una extensión del análisis en componentes principales funcional, orientado a identificar componentes "lo más independientes posible" mediante la explotación de las características topológicas subyacentes de los datos. Se proporciona un análisis exhaustivo de los fundamentos teóricos del ICA funcional y se extiende el método a espacios de Sobolev de funciones más suaves. También se presentan algunas propiedades teóricas sobre la clasificación de datos funcionales en relación al ICA functional. Asimismo, desarrollamos un repertorio de técnicas relacionadas de datos funcionales diseñadas para el preprocesamiento y análisis de datos en el campo emergente de la neurociencia musical encarnada, cuyo objetivo es investigar la base neurológica de cómo el cuerpo influye en las experiencias musicales. En particular, se desarrollan dos métodos basados en aproximaciones no lineales de wavelets y polinomios para el preprocesamiento de actividad artefactual en señales EEG y pupilometría. Estos métodos producen resultados excelentes para la investigación neuromotora, a pesar de la condición subómptima de los datos registrados durante la actividad locomotora. Además, presentamos un conjunto de descriptores neurales derivados de datos recopilados a través de los mencionados métodos no invasivos, con el objetivo de desvelar el comportamiento cerebral durante interacciones musicales encarnadas. Más específicamente, nos centramos en metodologías para modelar la actividad neurotransmisora, un aspecto crítico demostrado como esencial en la funcionalidad motora y otras sensaciones propioceptivas. Nuestra investigación experimental se presenta mediante el concepto de emoción transferido al dominio neurológico, proporcionando un marco único para definir y capturar la esencia neural de la encarnación en la música.