Geometry of manifolds according to convex constraints : neighborhood and co-dimenstion

الملخص EN

Summary of the study: We found that for the co – dimension k≥(cε^2)/log(1+ε^(-1) ) logn, we can estimate the diameter of the section E⊂R^n of the convex body K⊂R^n, which guarantee the best clustering of the data up to strong neighborhood E=B(x_0, α_0 2(L_K )^2 ((cε^2)/log(1+1/ε) ) logn ), to decrease the loosing information of geometrical structures of the scattering data in a manifolds.