Relevant multichannel time series representation based on functional measures in RKHS

dc.contributorÁlvarez Meza, Andrés Marino
dc.contributorCastellanos Domínguez, César Germán
dc.contributorGrupo de Control y Procesamiento Digital de Señales
dc.creatorPulgarín Giraldo, Juan Diego
dc.date.accessioned2021-01-25T16:53:05Z
dc.date.accessioned2022-09-21T19:08:15Z
dc.date.available2021-01-25T16:53:05Z
dc.date.available2022-09-21T19:08:15Z
dc.date.created2021-01-25T16:53:05Z
dc.date.issued2020
dc.identifierhttps://repositorio.unal.edu.co/handle/unal/78904
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/3413559
dc.description.abstractKernels methods provide a powerful and unifying framework to solve nonlinear problems while retaining in many cases, the simplicity of linear solutions. However, in machine learning and kernels methods, data is assumed to be independent and identically-distributed (i.i.d), discarding time information. This work's focus is on the development of a functional representation framework based on reproducing kernel Hilbert spaces (RKHS). It will provide a suitable support for high-dimensional non-stationary spatio-temporal signals. This framework reveals data structures and thus improve multiple kernel learning. Besides, it allows us to analyze multiple RKHSs associated with different time series. Firstly we propose a functional measure by developing filters in RKHS. Secondly, we propose a method to encode multichannel time series dynamics with localized codebooks oriented to classification tasks. Lastly, we present a functional framework to compare multiple probability distributions based on Hilbert embeddings. The proposed framework is tested on both time series classification and human action analysis. This framework offers an innovative analytical and methodological approach to consider both the distribution and the structure of time series, either monochannel or multichannel.
dc.description.abstractLos métodos kernel proporcionan un espacio de trabajo único y potente para resolver problemas no lineales conservando en la mayoría de casos la simplicidad de las soluciones lineales. Sin embargo, en las áreas de aprendizaje de máquina y métodos kernel, los datos se asumen independientes e idénticamente distribuidos (i.i.d), perdiendo información en el tiempo. El énfasis de este trabajo es el desarrollo de un marco de representación funcional basado en espacios de Hilbert con núcleo reproductivo (RKHS) (por sus siglas en inglés: Reproducing Kernel Hilbert Spaces). Este proporcionará un soporte adecuado para señales espacio-temporales no estacionarias de alta dimensión. Este marco revela estructuras en los datos y por lo tanto, mejora el aprendizaje con múltiples núcleos (kernels). Adicionalmente, permite analizar múltiples RKHSs asociados con diferentes series de tiempo. En primer lugar proponemos una medida funcional desarrollando filtros en RKHS. En segundo lugar, proponemos un método para codificar dinámicas de series de tiempo multicanal con diccionarios localizados orientados a tareas de clasificación. Por último, presentamos un marco funcional para comparar distribuciones de probabilidad múltiples basadas en inmersiones de Hilbert. El marco propuesto se prueba tanto en la clasificación de series de tiempo como en el análisis de la movimiento humano. Este marco ofrece un enfoque analítico y metodológico innovador para considerar tanto la distribución como la estructura de las series de tiempo ya sean monocanal o multicanal.
dc.languageeng
dc.publisherManizales - Ingeniería y Arquitectura - Doctorado en Ingeniería - Automática
dc.publisherDepartamento de Ingeniería Eléctrica y Electrónica
dc.publisherUniversidad Nacional de Colombia - Sede Manizales
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dc.titleRelevant multichannel time series representation based on functional measures in RKHS
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