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هَو - K-means
 
I. INTRODUCTION
Clustering is an important technique with applications in many fields such as computer vision and genome analysis. The goal of clustering is to group a number of input data points into several sets, so that data points within one set share similar characteristics. The k-means algorithm , also
known as Lloyd’s algorithm, is a well known clustering method and widely used in various applications. The k-means algorithm assigns each data point to a closest cluster. For a data point, its distance to a cluster is defined as its distance to the centroid of the cluster, where the centroid of a cluster is defined as the mean position of all the data points contained in the cluster. kmeans algorithm uses an iterative approach. Initially, the positions of k clusters’ centroids are randomly chosen. In a standard k-means iteration, each data point is labeled to the nearest cluster. After all the data points labeled, the centroid of each cluster is then be updated according to its data points. The labeling step and updating step are iterated until the labels do not change any more. Improving the performance of the k-means algorithm has attracted a lot of research attentions. Among the large number of proposed methods, an important approaches is to use triangle inequalities to eliminate unnecessary distance calculations when searching for the nearest centroid. Algorithms based on this idea have been studied by various researchers. Considerable speedups were reported over the standard k-means algorithm.  


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