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...

Organizing data into semantically more meaningful is one of the fundamental modes of understanding and learning. Cluster analysis is a formal study of methods for understanding and algorithm for learning. K-mean clustering algorithm is one of the most fundamental and simple clustering algorithms. When there is no prior knowledge about the distribution of data sets, K-mean is the first choice fo...

We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the k-level has subquadratic (O(n2 1 2s )) complexity. This answers one of the main open problems from the author’s previous paper (FOCS’00), which provided a weaker bound for a restricted class of curves (graphs of degree-s polynomials) only. When combin...

In this paper, we prove the Hyers-Ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$

A simple method is described, to prove some theorems for simple hyper K-algebras and to study positive implicative hyper K-ideals, weak (implicative ) hyper K-ideals in simple hyper K-algebras . Beside, some results on positive implicative and (weak) implicative simple hyper K-algebras are presented. Finally classification of simple hyper Kalgebras of order 4, which are satisfied in conditions ...

abstract: â in this study, the change in the crystalline structure of gas hydrate was predicted for ternary mixture of methane-ethane-water. for this purpose, the tangent plane distance (tpd) minimization method was used. first, the calculations were performed for the binary mixtures of methane-water and ethane-water as the gas and liquid phases. the results show that for a binary mixture of th...