GNM-NIPALS: general nonmetric-nonlinear estimation by iterative partial least squares

This paper develops GNM-NIPALS as an extension of the NM-PLS methods, which allows to quantify the qualitative variables of mixed data, by means of the reconstitution function using the first k principal com- ponents, maximizing the inertia in the plane k subspace associated with the PCA of the quan...

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Main Authors: Aluja, Tomás, González, Víctor Manuel
Format: Artículo
Language: Español
Published: 2015
Subjects:
ACP
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/14140
http://hdl.handle.net/10669/13047
Summary: This paper develops GNM-NIPALS as an extension of the NM-PLS methods, which allows to quantify the qualitative variables of mixed data, by means of the reconstitution function using the first k principal com- ponents, maximizing the inertia in the plane k subspace associated with the PCA of the quantified matrix. It generalizes the NM-NIPALS algo- rithm in the sense that the latter only uses the first principal component in the quantification of qualitative variables. From the maximization and positivity of the correlation ratio between each qualitative variable and the reconstituted function, we have that the accumulated inertia on the k- dimensional subspace associated to the quantification function of the same range is greater than or equal to the one generated on subspaces of equal dimension, but with quantification functions of different range. With the k principal components associated to the quantified matrix, a saturated in- ertia analysis is performed to evaluate if a dimension k∗< k still exists, from which the accumulated inertia on the axes of equal or superior order is already explained, in which case the definitive quantification function is of lesser range (k∗).