In the framework of variational approach to classification data analysis the formal statement of the problem is considered. The private cases of this problem are the unfuzzy and fuzzy cluster analysis problems, the problem of extremal parameter grouping, the problem of piece wise approximation. The different types of classification fuzziness are investigated: unfuzzy, fuzzy, classification with fuzzy boundaries, quality fuzzy classification, classification with overlapping classes etc. The form of the optimal classification for performance index is investigated. The optimization algorithms for finite and infinite sample are elaborated. The algorithms convergence is investigated. The application "Analitic" realized classification analysis methods is elaborated.