On a Method of Multivariate Density Estimate Basedon Nearest Neighbours Graphs
Об одном методе оценки многомерной плотности на основеближайших соседей

G. Beliakov
2018 RUDN Journal of Mathematics Information Sciences and Physics  
A method of multivariate density estimation based on the reweighted nearest neighbours, mimicking the natural neighbours techniques, is presented. Estimation of multivariate density is important for machine learning, astronomy, biology, physics and econometrics. A 2-additive fuzzy measure is constructed based on proxies for pairwise interaction indices. The neighbours of a point lying in nearly the same direction are treated as redundant, and the contribution of the farthest neighbour is
more » ... rred to the nearer neighbour. The calculation of the local point density estimate is performed by the discrete Choquet integral, so that the contributions of the neighbours all around that point are accounted for. This way an approximation to the Sibson's natural neighbours is computed. The method relieves the computational burden of the Delaunay tessellation-based natural neighbours approach in higher dimensions, whose complexity is exponential in the dimension of the data. This method is suitable for density estimates of structured data (possibly lying on lower dimensional manifolds), as the nearest neighbours differ significantly from the natural neighbours in this case.
doi:10.22363/2312-9735-2018-26-1-58-73 fatcat:fshmhlhdnnarjbk67msm3pclze