We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index α ∈ (1, 2). When the number n of vertices of the map tends to infinity, the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance pr...

Image matching is an important task. There are many available methods for occluded image matching, e.g. Hausdorff distance, Distance Transformi and wavelet decomposition based methods. We proposed Modified Chamfer Matching Algorithm (MCMA) [16], a new simple distance transform based image matching algorithm. Here we propose few more matching measures and compare them. Basic concepts relating to...

Received (received date) Revised (revised date) Communicated by (Name) The article analyzes similarity of closed polygonal curves in Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm that determines whether the Frechet distance between two closed polygonal curves with m and n vertices is less than a given ...

We continue our investigation of the space of geodesic laminations on a surface, endowed with the Hausdorff topology. We determine the topology of this space for the once punctured torus and the 4–times punctured sphere. For these two surfaces, we also compute the Hausdorff dimension of the space of geodesic laminations, when it is endowed with the natural metric which, for small distances, is ...

We refine the bound on the packing number, originally shown by Haussler, for shallow geometric set systems. Specifically, let V be a finite set system defined over an n-point set X; we view V as a set of indicator vectors over the n-dimensional unit cube. A δ-separated set of V is a subcollection W, s.t. the Hamming distance between each pair u,v ∈W is greater than δ, where δ > 0 is an integer ...

Relational generative topographic mappings (RGTM) provide a statistically motivated data inspection and visualization tool for pairwise dissimilarities by fitting a constraint Gaussian mixture model to the data. Since it is based on pairwise dissimilarities of data, it scales quadratically with the number of training samples, making the method infeasible for large data sets. In this contributio...

In this thesis we study the problems of distance approximation to monotonicity and distance approximation to convexity. Namely, we are interested in (randomized) sublinear algorithms that approximate the Hamming distance between a given function and the closest monotone/convex function. For the monotonicity property, we focus on functions over the d-dimensional hyper-cube, [n]d, with any finite...

In this note we study the Banach-Mazur distance between the n-dimensional cube and the crosspolytope. Previous work shows that the distance has order √ n, and here we will prove some explicit bounds improving on former results. Even in dimension 3 the exact distance is not known, and based on computational results it is conjectured to be 9 5 . Here we will also present computerbased potential o...

AMS subject classifications: primary 62G10 secondary 62H20 Keywords: dCor dCov Multivariate independence Distance covariance Distance correlation High dimension a b s t r a c t Distance correlation is extended to the problem of testing the independence of random vectors in high dimension. Distance correlation characterizes independence and determines a test of multivariate independence for rand...

Modern data analysis often faces high-dimensional data. Nevertheless, most neural network data analysis tools are not adapted to highdimensional spaces, because of the use of conventional concepts (as the Euclidean distance) that scale poorly with dimension. This paper shows some limitations of such concepts and suggests some research directions as the use of alternative distance definitions an...