Publication: Optimización de la regresión de mínimos cuadrados parciales con funciones Kernel
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2021-05-07
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Universidad Complutense de Madrid
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Abstract
La regresión de mínimos cuadrados parciales (PLS) es un método lineal que busca predecir un conjunto de variables dependientes a partir de un conjunto de predictores, extrayendo factores ortogonales que maximizan la capacidad predictiva, también llamados componentes. Cuando las estructuras de datos exhiben variaciones no lineales, se recurre a la regresión de mínimos cuadrados parciales con kernel (KPLS), que transforma los conjuntos de datos originales a un espacio de características de dimensionalidad arbitraria donde sea posible la generación de un modelo lineal. Una dificultad recurrente al implementar la regresión KPLS es determinar el número de componentes y los parámetros de la función kernel que maximizan su desempeño..
Partial Least Squares (PLS) regression is a linear method that seeks to predict a set of dependent variables from a set of predictors by extracting orthogonal factors that maximize predictive ability, also called components. When data structures exhibit non-linear variations, Kernel Partial Least Squares (KPLS) regression is used, which transforms the original data sets into an arbitrarily dimensioned feature space where a linear model can be generated. A recurring difficulty in implementing KPLS regression is determining the number of components and the parameters of the kernel function that maximize its performance...
Partial Least Squares (PLS) regression is a linear method that seeks to predict a set of dependent variables from a set of predictors by extracting orthogonal factors that maximize predictive ability, also called components. When data structures exhibit non-linear variations, Kernel Partial Least Squares (KPLS) regression is used, which transforms the original data sets into an arbitrarily dimensioned feature space where a linear model can be generated. A recurring difficulty in implementing KPLS regression is determining the number of components and the parameters of the kernel function that maximize its performance...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 15-01-2021