The paper is about speeding-up the k-means clustering method which processes the data in a faster pace, but produces the same clustering result as the k-means method. We present a prototype based method for this where prototypes are derived using the leaders clustering method. Along with prototypes called leaders some additional information is also preserved which enables in deriving the k mean...

Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to manipulate and analyze such information. In spite of its dependency on the initial settings and the large number of distance computations that it can require to converge, the K-means algorithm remains as one of the most popular clustering methods for massive data...

The k-means++ algorithm is the state of the art algorithm to solve k-Means clustering problems as the computed clusterings are O(log k) competitive in expectation. However, its seeding step requires k inherently sequential passes through the full data set making it hard to scale to massive data sets. The standard remedy is to use the k-means‖ algorithm which reduces the number of sequential rou...

The k-means method is a widely used technique for clustering points in Euclidean space. While it is extremely fast in practice, its worst-case running time is exponential in the number of data points. We prove that the k-means method can implicitly solve PSPACE-complete problems, providing a complexity-theoretic explanation for its worst-case running time. Our result parallels recent work on th...

Domain analysis tries to reuse software in an e ective way New methodologies are start ing to be able to automate the process in di erent degrees with the construction of a domain model for each problem The general process is divided into several phases One of the most di cult tasks is the generation of the relationships which have to be de ned between the components in the domain In this paper...

Hartigan’s method for k-means clustering is the following greedy heuristic: select a point, and optimally reassign it. This paper develops two other formulations of the heuristic, one leading to a number of consistency properties, the other showing that the data partition is always quite separated from the induced Voronoi partition. A characterization of the volume of this separation is provide...

T HE THEORY developed in the statistical literature for the method of k-means can be applied to the study of optimal k-level vector quantizers. In this paper, I describe some of this theory, including a consistency theorem (Section II) and a central lim it theorem (Section IV) for k-means cluster centers. These results help to explain the behavior of optimal vector quantizers constructed from l...

K-means is one of the most widely used algorithms for clustering in Data Mining applications, which attempts to minimize the sum of square of Euclidean distance of the points in the clusters from the respective means of the clusters. The simplicity and scalability of K-means makes it very appealing. However, K-means suffers from local minima problem, and comes with no guarantee to converge to t...

K-means is a popular clustering method used in data mining area. To work with large datasets, researchers propose PKMeans, which is a parallel k-means on MapReduce [3]. However, the existing k-means parallelization methods including PKMeans have many limitations. It can’t finish all its iterations in one MapReduce job, so it has to repeat cascading MapReduce jobs in a loop until convergence. On...