The Earth Mover’s Distance (EMD) is a distance measure between distributions with applications in image retrieval and matching. We consider the problem of computing a transformation of one distribution which minimizes its EMD to another. The applications discussed here include estimation of the size at which a color pattern occurs in an image, lighting-invariant object recognition, and point fe...

A new distance function dist (A,B) for fuzzy sets A and B is introduced. It is based on the descriptive complexity, i.e., the number of bits (on average) that are needed to describe an element in the symmetric difference of the two sets. The distance gives the amount of additional information needed to describe any one of the two sets given the other. We prove its mathematical properties and pe...

In case of fuzzy reasoning in sparse fuzzy rule bases, the question of selecting the suitable fuzzy similarity measure is essential. The rule antecedents of the sparse fuzzy rule bases are not fully covering the input universe therefore fuzzy reasoning methods applied for sparse fuzzy rule bases requires similarity measures able to distinguish the similarity of non-overlapping fuzzy sets, too. ...

We consider the problem of finding sets of points on xy = 1, where all of the interpoint distances are rational. The search for such points has links to both congruent and concordant numbers.

This paper is concerned with the simulation of the Partial Diierential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately t...

MOTIVATION Clustering algorithms are widely used in the analysis of microarray data. In clinical studies, they are often applied to find groups of co-regulated genes. Clustering, however, can also stratify patients by similarity of their gene expression profiles, thereby defining novel disease entities based on molecular characteristics. Several distance-based cluster algorithms have been sugge...

The decline in religious identification and corresponding increase in the unaffiliated has been one of the most important religious changes in the United Kingdom (UK). The emergence of the “religious nones” is the most obvious sign of continuing secularization and the declining social and cultural relevance of religion. Yet while the religiously-unaffiliated often form the plurality — if not so...