A new clustering algorithm based on hybrid global optimizationbased on a dynamical systems approach algorithm

Abstract

Many methods for local optimization are based on the notion of a direction of a local descent at a given point. A local improvement of a point in hand can be made using this direction. As a rule, modern methods for global optimization do not use directions of global descent for global improvement of the point in hand. From this point of view, global optimization algorithm based on a dynamical systems approach (GOP) is an unusual method. Its structure is similar to that used in local optimization: a new iteration can be obtained as an improvement of the previous one along a certain direction. In contrast with local methods, is a direction of a global descent and for more diversification combined with Tabu search. This algorithm is called hybrid GOP (HGOP). Cluster analysis is one of the attractive data mining techniques that are used in many fields. One popular class of data clustering algorithms is the center based clustering algorithm. K-means is used as a popular clustering method due to its simplicity and high speed in clustering large datasets. However, K-means has two shortcomings: dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort. In order to overcome local optima problem lots of studies have been done in clustering. In this paper, we proposed application of hybrid global optimization algorithm based on a dynamical systems approach. We compared HGOP with other algorithms in clustering, such as GAK, SA, TS, and ACO, by implementing them on several simulation and real datasets. Our finding shows that the proposed algorithm works better than others.