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...

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...

We study how to learn multiple dictionaries from a dataset, and approximate any data point by the sum of the codewords each chosen from the corresponding dictionary. Although theoretically low approximation errors can be achieved by the global solution, an effective solution has not been well studied in practice. To solve the problem, we propose a simple yet effective algorithm Group K-Means. S...

The k-means clustering algorithm is one of the most widely used, effective, and best understood clustering methods. However, successful use of k-means requires a carefully chosen distance measure that reflects the properties of the clustering task. Since designing this distance measure by hand is often difficult, we provide methods for training k-means using supervised data. Given training data...

Due to its simplicity and versatility, k-means remains popular since it was proposed three decades ago. Since then, continuous efforts have been taken to enhance its performance. Unfortunately, a good trade-off between quality and efficiency is hardly reached. In this paper, a novel k-means variant is presented. Different from most of k-means variants, the clustering procedure is explicitly dri...

K-means is a popular non-hierarchical method for clustering large datasets. The time requirements increase linearly with the size of the data set which make it particulary suited for extremely large datasets such as those found in digital libraries. The method was developed by MacQueen [4] in 1967. In our project we take a uniprocessor k-means algorithm and implement a parallel k-means algorith...

In many applications it is desirable to cluster high dimensional data along various subspaces, which we refer to as projective clustering. We propose a new objective function for projective clustering, taking into account the inherent trade-off between the dimension of a subspace and the induced clustering error. We then present an extension of the -means clustering algorithm for projective clu...

this paper compares clusters of aligned persian and english texts obtained from k-means method. text clustering has many applications in various fields of natural language processing. so far, much english documents clustering research has been accomplished. now this question arises, are the results of them extendable to other languages? since the goal of document clustering is grouping of docum...

When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. In this paper we present an improved algorithm for learning k while clustering. The G-means algorithm is based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution. G-means runs k-means with increasing k in a...