Survey of Nearest Neighbor Condensing Techniques <s> II. PROTOTYPE SELECTION <s> The problem of selecting of prototypes is to select a subset in the learning sample for which the set of minimum cardinality would provide the optimum of a given learning quality functional. In this article the problem of classification is considered in two classes, the method of classification by nearest neighbor, and three functional characteristics: the frequency of errors on the entire sample, a cross validation with one separated object, and a complete cross validation with k separated objects. It is shown that the problem of selection of prototypes in all three cases is NP-complete, which justifies the use of well-known heuristic methods for the prototype search. <s> BIB001 </s> Survey of Nearest Neighbor Condensing Techniques <s> II. PROTOTYPE SELECTION <s> Clustering is one of the most commonly techniques in Data Mining. Kmeans is one of the most popular clustering techniques due to its simplicity and efficiency. However, it is sensitive to initialization and easily trapped in local optima. K-harmonic means clustering solves the problem of initialization using a built-in boosting function, but it is suffering from running into local optima. Particle Swarm Optimization is a stochastic global optimization technique that is the proper solution to solve this problem. In this paper, PSOKHM not only helps KHM clustering escape from local optima but also overcomes the shortcoming of slow convergence speed of PSO. In this paper, a hybrid data clustering algorithm based on PSO and Genetic algorithm, GSOKHM, is proposed. We investigate local optima method in addition to the global optima in PSO, called LSOKHM. The experimental results on five real datasets indicate that LSOKHM is superior to the GSOKHM algorithm. <s> BIB002
Prototype selection is the process of finding representative patterns from the data, which can help in reducing these data. This problem is classified as an NP-hard problem by many researchers BIB002 BIB001 , because there is no polynomial algorithm allowing for the solution. The existing algorithms can just give acceptable solutions. Like many other combinatorial problems, the prototype selection (PS) would require an exhaustive search to obtain optimal solutions in the general case. This has led some researchers to consider the problem of PS as a combinatorial optimization problem and use general techniques which are known for their good results in similar situations. Heuristics, especially the nearest neighbor algorithm, and metaheuristics, especially genetic algorithms (GA) and tabu search (TS) have been proposed to solve this problem.