We derive a new clustering algorithm based on information theory and statistical mechanics, which is the only algorithm that incorporates scale. It also introduces a new concept into clustering: cluster independence. The cluster centers correspond to the local minima of a thermodynamic free energy, which are identified as the fixed points of a one-parameter nonlinear map. The algorithm works by...

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by assessing the statistical significance of topological features of an empirical c...

If there is a Sidon subset of the integers Z which has a member of Z as a cluster point in the Bohr compactification of Z, then there is a Sidon subset of Z which is dense in the Bohr compactification. A weaker result holds for quasiindependent and dissociate subsets of Z. It is a long standing open problem whether Sidon subsets of Z can be dense in the Bohr compactification of Z ([LR]). Yitzha...

One of the generalizations of statistical convergence is I-convergence which was introduced by Kostyrko et al. [12]. In this paper, we define and study the concept of I-convergence, I∗-convergence, I-limit points and I-cluster points of double sequences in probabilistic normed space. We discuss the relationship between I2-convergence and I ∗ 2 -convergence, i.e., we show that I ∗ 2 -convergence...

Unsupervised clustering algorithms have been used in many applications to group the data based on relevant similarity metrics. K-Means clustering is one of the most widely used clustering techniques owing to its simplicity. Many improvements and extensions have been proposed for this algorithm in view to improve its performance. Out of the various dimensions that have been explored in this rega...

We compare the statistical analysis of indicator matrices and Burt tables by correspondence analysis (CA) and taxicab correspondence analysis (TCA). There are two new results in this paper. First, TCA of a Burt table corresponds to a particular kind of CA of the indicator matrix based on the centroid decomposition. Second, the response patterns in multiple TCA will be represented as (number of ...

A novel clustering algorithm CSHARP is presented for the purpose of finding clusters of arbitrary shapes and arbitrary densities in high dimensional feature spaces. It can be considered as a variation of the Shared Nearest Neighbor algorithm (SNN), in which each sample data point votes for the points in its k-nearest neighborhood. Sets of points sharing a common mutual nearest neighbor are cons...

hepatitis b infection is one of the health problems. a cross-sectional study was performed to determine the effective factors on hbsag in systan and blochestan province, iran. in this study sample of 1150 people aged 2-69 year were and interviewed using cluster sampling the following variables using x2 , fisher and cochran showed a significant relation with hbsag; xi, economical status (p < 0.0...

Currently, one of the main directions is developing of development based on the clustering of economic operations of Kazakhstan, providing for the organization and concentration of production capacity in one region or the most optimal system. In the modern economic literature clustering is regarded as one of the most effective tools to ensure competitive businesses, and improve their business i...