Associated kernel discriminant analysis for multivariate mixed data

Associated kernels have been introduced to improve the classical (symmetric) continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. In this paper, an associated kernel for discriminant analysis with multivariate mixed variables is proposed. These variables are of three types: continuous, categorical and count. The method consists of using a product of adapted univariate associated kernels and an estimate of the misclassification rate. A new profile version cross-validation procedure of bandwidth matrices selection is introduced for multivariate mixed data, while a classical cross-validation is used for homogeneous data sets having the same reference measures. Simulations and validation results show the relevance of the proposed method. The method has been validated on real coronary heart disease data in comparison to the classical kernel discriminant analysis.