A non iterative method of separation of points by planes in n dimensions and its application

Given a set of N points, we have discovered an algorithm that can separate these points from one another by n-dimensional planes. Each point is chosen at random and put into a set S and planes which separate them are determined and put into S. The algorithm gives a method of choosing points and planes which separate them, till all the points are separated. A proof is provided with a worked example. The algorithm is non iterative and always halts successfully and the algorithm strictly follows Shannon's principle of making optimal use of information as it advances stage by stage. It also has a restart facility and can take care of new points from where it left off.At some later stage if the dimension of the data is increased from n to n+r, the algorithm can still continue from where it left off, after some simple adjustments, and tackle the new data points which are of a higher dimension. and separate them. The computational complexity is O(n.N log(N)) + O(n3 log(N)), where N is the given number of points and n3 is the cube of n - the dimension of space. The algorithm is made possible because a new concept called Orientation Vector is used. This vector is a Hamming vector and is associated with each point and has been so devised that it has all the information necessary to ascertain if two points are separate or not when among a collection of planes.Its application to data retrieval problems in very large medical data bases is also given.

K. Eswaran · 2015