Symbolic kernel discriminant analysis (Q1584190)

Kernel density estimation is a tool which allows the statistician to construct a density on any sample of data without any prior probabilistic hypothesis. These methods compute a weighted sum of kernels centered on each data point. Examples of kernel density estimations are to be found essentially for quantitative (discrete or continuous) and qualitative data. For mixed data of both previous types, the method of ``product kernels'' is suggested. Current technological progress in hardware, data bases and object oriented languages implies the manipulation, stock and representation of objects with more and more complex data. The notion of `symbolic objects' is introduced based on the work of \textit{E. Diday} [The symbolic approach in clustering. In: H.H. Bock (ed.), Classification and related methods of data analysis. (1988)], and the necessity to be adapted to this notion appears for most recent classification methods. The aim of this paper is the adaptation of the classical Bayesian discrimination rule to the symbolic objects problem. This is performed by prior probabilities' estimation and by kernel density estimation.