The gradient of a function defined on a manifold is perhaps one of the most important differential objects in data analysis. Most often in practice, the input function is available only at discrete points sampled from the underlying manifold, and the manifold is approximated by either a mesh or simply a point cloud. While many methods exist for computing gradients of a function defined over a m...

fuzzy measures are suitable in analyzing human subjective evaluation processes. several different strategies have been proposed for distance of fuzzy numbers. the distances introduced for fuzzy numbers can be categorized in two groups:1. the crisp distances which explain crisp values for the distance between two fuzzy numbers.2. the fuzzy distance which introduce a fuzzy distance for normal fuz...

In the paper a new measure of distance between events/observations in the pattern space is proposed and experimentally evaluated with the use of k-NN classifier in the context of binary classification problems. The application of the proposed approach visibly improves the results compared to the case of training without postulated enhancements in terms of speed and accuracy. Numerical results a...

We give the first 2-approximation algorithm for cluster vertex deletion problem. This is tight, since approximating problem within any constant factor smaller than 2 UGC-hard. Our combines previous approaches, based on local ratio technique and management of true twins, with a novel construction “good” cost function vertices at distance most from input graph.

In the paper an image interpolation method based on the mathematical morphology is proposed. The method deals with binary images and allows transforming one input binary object into another one. The proposed method is an improvement of the Hausdorff distance approach. Two ways of improvement are proposed. The first one allows controling more precisely the process of object growing during the in...

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we c...

The facility design problem is a common one in manufacturing and service industries and has been studied extensively in the literature. However, restrictions on the scope of the design problem have been imposed by the limitations of the optimization techniques employed. This paper uses an evolutionary approach with a subordinate network optimization algorithm to produce integrated designs that ...