Dynamic Clustering of n-Dimensional Data on Tangential Space

Clustering of n-dimensional data into classes is consistent problem of research, Large number of efficient clustering techniques are in literature and still more are in development. K-means and Spherical K-means are standard clustering methods which are frequently used. Euclidean distance and cosine distance are mainly used by clustering methods. Data distribution is always non-linear and distributed in n-dimensional hyper sphere. Euclidean distance did not take care of topology of the hyper space. Clustering of data using spherical K-means clustering is done through mapping all data points in hyper sphere to the nearest cosine angular distance, but both do not take care of geodesic distance between the points on the surface of the hyper sphere. In this paper new mathematical dynamic clustering approach has been proposed which take care of topology of the data distribution between various clusters and geodesic distance between the points with in the cluster. Theoretical and mathematical results are discussed and empirically verified on the iris data set.