Partial least squares regression PLS on interval data
Uncertainty in the data can be considered as a numerical interval in which a variable can assume its possible values, this has been known as interval data. In this paper the $PLS$ regression methodology is extended to the case where explanatory, response variables and coefficients regression are intervals. In this way a regression methodology solves three problems encountered with actual data type is proposed: first multicollinearity in explanatory and response variables, second real data does not belong to a Euclidean space and finally, problems when uncertainty in the data is represented by intervals. Today there are common tasks, such as planning and operation of electrical systems, production planning, transport logistics, inventory, management of securities portfolios; among others, involving uncertainty; this way models that take into account and the ability to make decisions for optimal results from a range of possibilities or scenarios are required. Furthermore, the analysis of real data is affected by different types of errors as measurement errors, miscalculations and imprecision related to the method adopted for estimating data. This paper is a methodological proposal of theoretical type and is based on development about mathematical optimization on multi-interval and multi-matrix spaces.
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Universidad Nacional de Colombia - Sede Medellín - Facultad de Ciencias
2016
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Gaviria Peña, Carlos Alberto Pérez Agámez, Raúl Alberto Puerta Yepes, María Eugenia |
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Gaviria Peña, Carlos Alberto Pérez Agámez, Raúl Alberto Puerta Yepes, María Eugenia Partial least squares regression PLS on interval data |
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Gaviria Peña, Carlos Alberto Pérez Agámez, Raúl Alberto Puerta Yepes, María Eugenia |
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Gaviria Peña, Carlos Alberto |
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Partial least squares regression PLS on interval data |
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Partial least squares regression PLS on interval data |
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Partial least squares regression PLS on interval data |
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Partial least squares regression PLS on interval data |
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Partial least squares regression PLS on interval data |
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partial least squares regression pls on interval data |
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Uncertainty in the data can be considered as a numerical interval in which a variable can assume its possible values, this has been known as interval data. In this paper the $PLS$ regression methodology is extended to the case where explanatory, response variables and coefficients regression are intervals. In this way a regression methodology solves three problems encountered with actual data type is proposed: first multicollinearity in explanatory and response variables, second real data does not belong to a Euclidean space and finally, problems when uncertainty in the data is represented by intervals. Today there are common tasks, such as planning and operation of electrical systems, production planning, transport logistics, inventory, management of securities portfolios; among others, involving uncertainty; this way models that take into account and the ability to make decisions for optimal results from a range of possibilities or scenarios are required. Furthermore, the analysis of real data is affected by different types of errors as measurement errors, miscalculations and imprecision related to the method adopted for estimating data. This paper is a methodological proposal of theoretical type and is based on development about mathematical optimization on multi-interval and multi-matrix spaces. |
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Universidad Nacional de Colombia - Sede Medellín - Facultad de Ciencias |
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2016 |
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AT gaviriapenacarlosalberto partialleastsquaresregressionplsonintervaldata AT perezagamezraulalberto partialleastsquaresregressionplsonintervaldata AT puertayepesmariaeugenia partialleastsquaresregressionplsonintervaldata AT gaviriapenacarlosalberto regresionporminimoscuadradosparcialesplscondatosdeintervalo AT perezagamezraulalberto regresionporminimoscuadradosparcialesplscondatosdeintervalo AT puertayepesmariaeugenia regresionporminimoscuadradosparcialesplscondatosdeintervalo |
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oai:www.revistas.unal.edu.co:article-546162018-06-09T20:34:09Z Partial least squares regression PLS on interval data Regresión por mínimos cuadrados parciales PLS con datos de intervalo Gaviria Peña, Carlos Alberto Pérez Agámez, Raúl Alberto Puerta Yepes, María Eugenia Principal components regression partial least squares regression PLS interval-valued optimization interval eigen values and eigen vectors Regresión por componentes principales mínimos cuadrados parciales PLS optimización intervalo-valuada intervalo valores y vectores propios Análisis multivariado optimización multi-objetivo Uncertainty in the data can be considered as a numerical interval in which a variable can assume its possible values, this has been known as interval data. In this paper the $PLS$ regression methodology is extended to the case where explanatory, response variables and coefficients regression are intervals. In this way a regression methodology solves three problems encountered with actual data type is proposed: first multicollinearity in explanatory and response variables, second real data does not belong to a Euclidean space and finally, problems when uncertainty in the data is represented by intervals. Today there are common tasks, such as planning and operation of electrical systems, production planning, transport logistics, inventory, management of securities portfolios; among others, involving uncertainty; this way models that take into account and the ability to make decisions for optimal results from a range of possibilities or scenarios are required. Furthermore, the analysis of real data is affected by different types of errors as measurement errors, miscalculations and imprecision related to the method adopted for estimating data. This paper is a methodological proposal of theoretical type and is based on development about mathematical optimization on multi-interval and multi-matrix spaces. La incertidumbre en los datos puede ser considerada mediante un intervalo numérico en el cual una variable puede asumir sus posibles valores, esto se conoce como datos de intervalo. En este artículo se extiende la metodología de regresión PLS al caso donde tanto las variables explicativas como las variables respuesta y los coeficientes de regresión son del tipo intervalo. De ésta manera se propone una metodología de regresión que resuelve tres problemas que se presentan con los datos de tipo real: en primer lugar problemas de multicolinealidad tanto en las variables explicativas como en las variables respuesta, en segundo lugar problemas cuando los datos no pertenecen a un espacio Euclídeo y por último problemas cuando la incertidumbre en los datos se representa por medio de intervalos. Hoy en día existen tareas del común, tales como planificación y operación de sistemas eléctricos, planificación de producción, logística del transporte, inventarios, gestión de carteras de valores, entre otras, que involucran incertidumbre. De ésta manera se requieren modelos que tengan en cuenta dicha incertidumbre y puedan dar la posibilidad de tomar decisiones para resultados óptimos desde una gama de posibilidades o escenarios posibles. Por otro lado, el análisis de datos reales a menudo se ve afectado por diferentes tipos de errores tales como: errores de medición, errores de cálculo e impresición relacionada con el método adoptado para la estimación de los datos. Este trabajo es una propuesta metodológica de tipo teórico y está fundamentada en los desarrollos teóricos sobre optimización matemática sobre los conjuntos de multi-intervalos y multi-matrices. Universidad Nacional de Colombia - Sede Medellín - Facultad de Ciencias 2016-01-01 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.unal.edu.co/index.php/rfc/article/view/54616 10.15446/rev.fac.cienc.v5n1.54616 Revista de la Facultad de Ciencias; Vol. 5 No. 1 (2016); 148-159 Revista de la Facultad de Ciencias; Vol. 5 Núm. 1 (2016); 148-159 2357-5549 0121-747X spa https://revistas.unal.edu.co/index.php/rfc/article/view/54616/57109 Derechos de autor 2016 Revista de la Facultad de Ciencias |