Fast and Space Efficient Convex Hull Vector Network For Breast Cancer Classification

Abstract

This work is all about an efficient new algorithm to find out Convex Hull for a large dataset which may or may not have duplicate values. This algorithm is basically an improvement over Graham Scan Convex Hull algorithm with the help of SSGM Sort. This algorithm is further referred as Efficient Convex Hull (ECH) algorithm throughout this article. The complexity of time taken by Efficient Convex Hull algorithm presented over here is O(n) at its best and O(n log n) in the worst scenario for a problem of size n elements. The amount of memory space taken by ECH is O(1) which breaches the lower bound rendered on it by sorting algorithms on Graham Scan convex hull. Here it would be better to understand that the type of problems convex hull deals with generally has large number of duplicate values. ECH utilizes this fact and give time complexity of small “o” that is o(n log n) which is much lesser than O(n log n). Further an application of ECH is Efficient Convex Hull Vector Network (ECHVN) is proposed by combining benefits of ECH and SVMs.