THE ULTRAMETRIC PROPERTIES OF BINARY DATASETS
Journal Title: Silesian Journal of Pure and Applied Mathematics - Year 2016, Vol 6, Issue 1
Abstract
Many multivariate algorithms commonly applied for binary datasets depend on a proper metric (i.e., dissimilarity function) imposed on binary vectors. In the following work the relationships between different metrics defined on the randomly generated binary datasets and the cophenetic correlation coefficient (CCC) will be presented.
Authors and Affiliations
Piotr Wilczek
THE TAYLOR TRANSFORMATION HYBRID METHOD APPLIED FOR SOLVING THE STEFAN PROBLEM
The paper presents the analytic-numerical hybrid method using, among others, the Taylor transformation, thanks to which the solution of the Stefan problem is replaced by the solution of a nonlinear system of equations.
BASIC SUMS AS PARAMETERS CHARACTERIZING
We discuss the method of distributions’ characterization of geometric objects on the plane. The method is based on the basic sums. These basic sums perform the same role in description of image as the n-point correlation...
THE METHOD OF FINDING POINTS OF INTERSECTION OF TWO CUBIC BEZIER CURVES USING THE SYLVESTER MATRIX
Sylvester matrix is used to create a 9th degree polynomial from coefficients of two cubic Bezier curves. The real roots of this polynomial allow to compute points of intersection of aforementioned curves. An additional c...
ESTIMATING RAPID FLOW TRANSIENTS USING EXTENDED KALMAN FILTER
Theoretical and numerical modeling of flow transients in pipelines is a challenging field of research. The governing flow equations constitute a system of nonlinear hyperbolic partial differential equations enforcing the...
NOTE ON SIMPLE LIE ALGEBRAS OF INFINITE MATRICES
We introduce Lie algebras of infinite N Ă— N matrices, with coefficients in a commutative rings, which have nonzero entries only in finite number of rows and study its properties. We show that algebra of matrices with tra...