Projection Based Clustering of n-Dimensional Data in Tangential Space: A Belief Measure

Data when used for analysis purpose, shows high degree of similarity between points in space, leading to problem of overlapping data in clusters. Currently problem of overlapping of data points in clusters are addressed by kernel methods which maps data points in higher dimensional space or mapping of data from higher dimension to lower dimension. We addresses this problem with a novel concept of mapping the nearest neighbor points to the test point in space by referring projected data in tangential space. In our approach projection of points from the surface of the unit hyper sphere to the tangential space and then finding out the nearest neighbour using log-Euclidean or Geodesic distance measures.This is a dynamic projection based approach in which points of the surface of the hyper sphere are viewed from different tangential plane and nearest neighbor points are visible where the density of the similar data points is high. The proposed concept is also empirically proven using the belief measure which justify the existence of same nearest points of the projected plane and on the surface of the unit hyper sphere.