Definición de semiproductos escalares útiles en análisis de datos

We develop the theory necessary for Data Analysis with inner semiproducts, extendingtha classical concepts of inner products usually employed. For this, we usethe basic algebraic definitions of non degenerated bilinear forms and develop all thealgebraic tools needed. We study the most important oper...

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Autor Principal: Trejos Zelaya, Javier
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/242
http://hdl.handle.net/10669/12887
Sumario: We develop the theory necessary for Data Analysis with inner semiproducts, extendingtha classical concepts of inner products usually employed. For this, we usethe basic algebraic definitions of non degenerated bilinear forms and develop all thealgebraic tools needed. We study the most important operators on the individualspace, such as the VM and the MV operators. We also study the case of the innersemiproduct of weights in the variable space, which corresponds to the introduction ofsupplementary individuals in the case of null weights. Finally, we arrive to the usualconcepts of Principal Component Analysis.Keywords: inner semiproducts, non degenerated bilinear forms, semimetrics, orthogonalprojection operator, principal component analysis.