The structural characteristics of clusters are investigated in the partitioning process. Two partition functions, which show opposite properties around the optimal cluster number, are found and a new cluster validity index is presented based on the combination of these functions. Some properties of the index function are discussed and numerical examples are presented. key words: clustering, val...

In this work we propose a modern statistical approach to the analysis and modeling of dynamics in online auctions. Online auction data usually arrive in the form of a set of bids recorded over the duration of an auction. We propose the use of a modern statistical approach called functional data analysis that preserves the entire temporal dimension in place of currently used methods that aggrega...

In the process of visualizing quantitative spatial data, it is necessary to classify attribute values into some class divisions. In a previous paper, the author proposed a classification method for minimizing the loss of information contained in original data. This method can be considered as a kind of smoothing method that neglects the characteristics of spatial distribution. In order to under...

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We investigate the clustering of dark energy within matter overdensities and voids. In particular, we derive an analytical expression for the dark energy density perturbations, which is valid both in the linear, quasi-linear and fully non-linear regime of structure formation. We also investigate the possibility of detecting such dark energy clustering through the ISW effect. In the case of unco...

in the analysis of spatial point patterns, complete spatial randomness (csr) hypothesis,which is a restriction of a homogenous poisson process to study region a, operates as a dividinghypothesis between “regular” and “aggregated” patterns. meanwhile, many alternatives to csr inaggregated patterns are extensions of homogenous poisson processes themselves. therefore, when thecsr hypothesis is rej...