In this paper, we propose a novel hybrid genetic algorithm (GA) that finds a globally optimal partition of a given data into a specified number of clusters. GA's used earlier in clustering employ either an expensive crossover operator to generate valid child chromosomes from parent chromosomes or a costly fitness function or both. To circumvent these expensive operations, we hybridize GA with a...

In this paper we provide a fully distributed implementation of the k-means clustering algorithm, intended for wireless sensor networks where each agent is endowed with a possibly high-dimensional observation (e.g., position, humidity, temperature, etc.). The proposed algorithm, by means of one-hop communication, partitions the agents into measure-dependent groups that have small ingroup and lar...

k-means++ is a seeding technique for the k-means method with an expected approximation ratio of O(log k), where k denotes the number of clusters. Examples are known on which the expected approximation ratio of k-means++ is Ω(log k), showing that the upper bound is asymptotically tight. However, it remained open whether k-means++ yields an O(1)-approximation with probability 1/poly(k) or even wi...