Data clustering is the process of partitioning a set of data objects into meaning clusters or groups. Due to the vast usage of clustering algorithms in many fields, a lot of research is still going on to find the best and efficient clustering algorithm. K-means is simple and easy to implement, but it suffers from initialization of cluster center and hence trapped in local optimum. In this paper...

This paper proposes a new algorithm for K-medoids clustering which runs like the K-means algorithm and tests several methods for selecting.This paper proposes a new algorithm for K-medoids clustering which runs like the. A new Kmedoids clustering method that should be fast and efficient.

The primary role of the thyroid gland is to help regulation of the body’s metabolism. The correct diagnosis of thyroid dysfunctions is very important and early diagnosis is the key factor in its successful treatment. In this article, we used four different kinds of classifiers, namely Bayesian, k-NN, k-Means and 2-D SOM to classify the thyroid gland data set. The robustness of classifiers with ...

The k-means algorithm is widely used for clustering, compressing, and summarizing vector data. In this paper, we propose a new acceleration for exact k-means that gives the same answer, but is much faster in practice. Like Elkan’s accelerated algorithm [8], our algorithm avoids distance computations using distance bounds and the triangle inequality. Our algorithm uses one novel lower bound for ...

The sets Sj are the sets of points to which μj is the closest center. In each step of the algorithm the potential function is reduced. Let’s examine that. First, if the set of centers μj are fixed, the best assignment is clearly the one which assigns each data point to its closest center. Also, assume that μ is the center of a set of points S. Then, if we move μ to 1 |S| ∑ i∈S xi then we only r...

We consider the stability of k-means clustering problems. Clustering stability is a common heuristics used to determine the number of clusters in a wide variety of clustering applications. We continue the theoretical analysis of clustering stability by establishing a complete characterization of clustering stability in terms of the number of optimal solutions to the clustering optimization prob...

A new algorithm is proposed which accelerates the mini-batch k-means algorithm of Sculley (2010) by using the distance bounding approach of Elkan (2003). We argue that, when incorporating distance bounds into a mini-batch algorithm, already used data should preferentially be reused. To this end we propose using nested mini-batches, whereby data in a mini-batch at iteration t is automatically re...

A framework for multi-agent based clustering is described whereby individual agents represent individual clusters. A particular feature of the framework is that, after an initial cluster configuration has been generated, the agents are able to negotiate with a view to improving on this initial clustering. The framework can be used in the context of a number of clustering paradigms, two are inve...

Let us define some notation which will help us analyze the algorithm. L := A solution (k-subset) returned by Local Search. Copt := An optimal solution for the k-median problem. We will eventually show that Cost(L) ≤ 5 · Cost(Copt). For any p ∈ P,C ⊆ P, NN(p, C) := c̄ ∈ C that minimizes d(p, ·). So d(p,NN(p, C)) = d(p, C) by definition. Also, for any C ⊆ P, c̄ ∈ C, Cluster(C, c̄) := {q ∈ P | NN(q, ...