We present results of an investigation of clustering evolution of field galaxies between a redshift of z ∼ 1 and the present epoch. The current analysis relies on a sample of ∼ 14000 galaxies in two fields of the COMBO 17 survey. The redshift distribution extends to z ∼ 1. The amplitude of the three-dimensional correlation function can be estimated by means of the projected correlation function...

In this paper, we focus on the problem of unsupervised clustering which allows automatic setting of optimal clusters number. We present a generalization of the competitive agglomeration clustering algorithm firstly introduced in [1]. This generalization is inspired by the regularization theory and suggests a new schema for using various cluster validity criteria continuously proposed in the lit...

A new method for finding fuzzy information granules from multivariate data through a gravitational inspired clustering algorithm is proposed in this paper. The proposed algorithm incorporates the theory of granular computing, which adapts the cluster size with respect to the context of the given data. Via an inspiration in Newton’s law of universal gravitation, both conditions of clustering sim...

Clustering is an important research topic that has practical applications in many 5elds. It has been demonstrated that fuzzy clustering, using algorithms such as the fuzzy C-means (FCM), has clear advantages over crisp and probabilistic clustering methods. Like most clustering algorithms, however, FCM and its derivatives need the number of clusters in the given data set as one of their initiali...

An analytical understanding of the strongly nonlinear regime of gravitational collapse has been difficult to achieve. The only insight has been the stable clustering hypothesis , which assumes that the number of neighbors for objects averaged over small length scales is constant in time. Our recently proposed analytic halo model for N-point correlation functions now provides a tool for calculat...

Bayesian hierarchical clustering (BHC) is an agglomerative clustering method, where a probabilistic model is defined and its marginal likelihoods are evaluated to decide which clusters to merge. While BHC provides a few advantages over traditional distance-based agglomerative clustering algorithms, successive evaluation of marginal likelihoods and careful hyperparameter tuning are cumbersome an...

Time series have become an important class of temporal data objects in our daily life while clustering analysis is an effective tool in the fields of data mining. However, the validity of clustering time series subsequences has been thrown into doubts recently by Keogh et al. In this work, we review this problem and propose the phase shift weighted spherical k-means algorithm (PS-WSKM in abbrev...

The management and analysis of big data has been identified as one of the most important emerging needs in recent years. This is because of the sheer volume and increasing complexity of data being created or collected. Current clustering algorithms can not handle big data, and therefore, scalable solutions are necessary. Since fuzzy clustering algorithms have shown to outperform hard clustering...

This paper presents the applications of hierarchical clustering to the generators in a power system. A useful application of fuzzy mathematics is that the correction of clustering results and determination of whether it can obtain correct transitive closure. Thus, the fuzzy transitive closure plays an important role in hierarchical clustering. Based on the fuzzy relation matrix, the hierarchica...

This paper addresses two most important issues in cluster analysis. The first issue pertains to the problem of deciding if two objects can be included in the same cluster. We propose a new similarity decision methodology which involves the idea of cluster validity index. The proposed methodology replaces a qualitative cluster recognition process with a quantitative comparison-based decision pro...