Resumen de Análisis conjunto de múltiples tablas de datos mixtos mediante PLS
Victor Manuel González Rojas
The fundamental content of this thesis corresponds to the development of the GNM-NIPALIS, GNM-PLS2 and GNM-RGCCA methods, used to quantify qualitative variables parting from the first k components given by the appropriate methods in the analysis of J matrices of mixed data. These methods denominated GNM-PLS (General Non Metric Partial Least Squares) are an extension of the NM-PLS methods that only take the first principal component in the quantification function. The transformation of the qualitative variables is done through optimization processes, usually maximizing functions of covariance or correlation, taking advantage of the flexibility of the PLS algorithms and keeping the properties of group belonging and order if it exists; The metric variables are keep their original state as well, excepting standardization. GNM-NIPALS has been created for the purpose of treating one (J = 1) mixed data matrix through the quantification via ACP type reconstruction of the qualitative variables parting from a k components aggregated function. GNM-PLS2 relates two (J = 2) mixed data sets Y~X through PLS regression, quantifying the qualitative variables of a space with the first H PLS components aggregated function of the other space, obtained through cross validation under PLS2 regression. When the endogenous matrix Y contains only one answer variable the method is denominated GNM-PLS1. Finally, in order to analyze more than two blocks (J = 2) of mixed data Y~X1+...+XJ through their latent variables (LV) the GNM-RGCCA was created, based on the RGCCA (Regularized Generalized Canonical Correlation Analysis) method, that modifies the PLS-PM algorithm implementing the new mode A and specifies the covariance or correlation maximization functions related to the process. The quantification of the qualitative variables on each Xj block is done through the inner Zj = ?j ej Yj function, which has J dimension due to the aggregation of the outer Yj estimations. Zj, as well as Yj estimate the ?j component associated to the j-th block.
