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...

Cluster analysis is a useful technique in multivariate statistical analysis. Different types of hierarchical cluster analysis and K-means have been used for data analysis in previous studies. However, the K-means algorithm can be improved using some metaheuristics algorithms. In this study, we propose simulated annealing based algorithm for K-means in the clustering analysis which we refer it a...

An original approach to cluster multi-component data sets is proposed that includes an estimation of the number of clusters. Using Prim’s algorithm to construct a minimal spanning tree (MST) we show that, under the assumption that the vertices are approximately distributed according to a spatial homogeneous Poisson process, the number of clusters can be accurately estimated by thresholding the ...

October 21, 2009 Type Package Title Spherical k-Means Clustering Version 0.1-2 Author Kurt Hornik, Ingo Feinerer, Martin Kober Maintainer Kurt Hornik Description Algorithms to compute spherical k-means partitions. Features several methods, including a genetic and a simple fixed-point algorithm and an interface to the CLUTO vcluster program. License GPL-2 Imports slam...

Due to intensity overlaps between interested objects caused by noise and intensity inhomogeneity, image segmentation is still an open problem. In this paper, we propose a framework to segment images in the well-known image model in which intensities of the observed image are viewed as a product of the true image and the bias field. In the proposed framework, a CUDA accelerated non-local means d...

Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the kmeans algorithm. Solutions obtained from this technique are dependent on the initialization of cluster centers. In this article we propose a new algorithm to initialize the clusters. The proposed algorithm is based on finding a set of medians extracted from a dimension with maximu...

This paper describes a new approach to the segmentation of textured gray-scale images based on image pre-"ltering and fractal features. Traditionally, "lter bank decomposition methods consider the energy in each band as the textural feature, a parameter that is highly dependent on image intensity. In this paper, we use fractal-based features which depend more on textural characteristics and not...