Computation generalized estimates of objects and hierarchical clustering of features

We consider the set acceptable objects in T, broken into two disjoint subsets (classes). Representatives of the classes K ₁, K ₂ are given by the sample objects E ₀ = {S _b...,S _m}, Eo = K1 UK2 . Objects of the sample are described by n heterogeneous features X(n) = (x ₁,.,x _n) the set of acceptable values of E, which measurements are on the interval scale and n - E, are on the nominal. Given the rule is a sequence of partitions set X(n) into disjoint subsets X^k^.X-Tki), т>1, k ₁+.+k _x0. Required for each Xlh) algorithm to determine a, nonlinear display feature values X^k) of the object in the descriptionSj e E ₀ , j=1,...,m, a value (generalized estimation) on the real axis. For the identification generalized estimates (new features) in object descriptions on p-th step 0 1, v - the ordinal number of the element ordered ascending sequence of xj values of E ₀, determining interval limits as . Criterion r r r Y 2 II d =1 i=1 u ((-udS £ u1 (u1 -1)+uf ( -1) i=1_ £lK, I (-1) (1) ^ max 2 K1K2 c' 2 ],(c ₂ , c3 ]. The extremum of the criterion (1) is used as a weight w (0 < wp < 1) of feature xJ and for a decision by the rule of hierarchical clustering. n nonlinear mapping on the real axis of objects E ₀ on X _i (^ ) U{x _t} value (1) U Xd к) If Vxt EX(n)\ U Xd к) < d=1 less than or equal to the analogical value (with a less margin between classes) on X _i (^ ) U{x _t} that is formed new group for the synthesis of the generalized estimation. Calculation of generalized estimates using hierarchical clustering advisable for several reasons: - generalized estimates form a new feature space whose dimensions are smaller than the original; - solves the problem of the use of classification algorithms, the implementation of which was inefficient due to the large dimension of feature space, is possible at any single type measurement scales; - in the process of clustering occurs consistent selection of informative feature sets; - nonlinear mapping object description to real axis defined by a combination of features is a means of detection stable patterns of logic (new knowledge) in data warehouses.

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